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CBSE PORTAL : (Download) CBSE Class-12 Sample Paper And Marking Scheme 2017-18 : Sculpture

CBSE PORTAL : (Download) CBSE Class-12 Sample Paper And Marking Scheme 2017-18 : Sculpture

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(Download) CBSE Class-12 Sample Paper And Marking Scheme 2017-18 : Sculpture

Posted: 01 Jun 2018 10:50 PM PDT

(Download) CBSE Class-12 Sample Paper And Marking Scheme 2017-18 : Sculpture

SCULPTURE(THEORY) (History of India Art)
Sample Question Papers – 2018

Time allowed: 02 hours

Maximum Marks: 40
General Instructions:
(i) All the eight questions are compulsory which carry equal marks.
(ii) Answers to be written for question nos.1 and 2 in about200 word each. Question nos.6, 7 and 8 are objective type.

1.  Which one do you like or dislike most among all the contemporary (modern) Indian sculptures included in your course of study? Give your appropriate reasons in detail based on the aesthetic parameters.

2.  Write an essay on the origin and development of the Rajasthani or Pahari School of Miniature Painting.

3.  Do you receive any spiritual message from the famous Mughal miniature painting ‘Kabir and Raidas’ or famous Deccani miniature-painting?‘HazratNizamuddinAuliya and Amir Khusro?’Explain in short.

4.  Identify any relevant painting of the Bengal School included in your course of study comprising of the following features and explain them in that painting accordingly:

(a) The creation of mystic and mellow style by using gloomy colouring with diffused light background and absence of any dark line or tone, which provide the experience of the astral-world.
OR
(b) The delineation of attenuated human figures with extra elongated limbs and tapering fingers, which reflect the influence of the Rajasthani, Pahari and Mughal miniatures. Hence emphasis on the European realism is terminated.

5. Evaluate the artistic achievements of any of the following Contemporary (Modern) Indian artists, with special reference to his/her art-work included in your course:
(i) KamleshDuttPande (painter)
(ii) RamkinkerVaij (sculptor)
(iii) AnupamSud (graphic-artist)

6. Mention the names of any five painters of the Rajasthani and Pahari Schools of Miniature Painting included in your course of study.

7. Mention the titles of any five miniature paintings of the Mughal and Deccan Schools included in your course of study.

8. What is symbolized by each of the following used in the Indian National Flag?
(1) Indian Saffron Colour
(2) White Colour
(3) Indian Green Colour
(4) Ashoka-Wheel
(5) 24 Spokes in the Ashokan-Wheel

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NCERT Chemistry Question Paper (Class - 11)

Posted: 01 Jun 2018 10:40 PM PDT

NCERT Chemistry Question Paper (Class - 11)

 


(Chemistry) Chapter 1 Some Basic Concepts Of Chemistry


NCERT Exercises Questions

Question 1.1 Calculate the molecular mass of the following :
(i) H2O
(ii) CO2
(iii) CH4

Question 1.2 Calculate the mass per cent of different elements present in sodium sulphate (Na2SO4).

Question 1.3 Determine the empirical formula of an oxide of iron which has 69.9% iron and 30.1% dioxygen by mass.

Question 1.4 Calculate the amount of carbon dioxide that could be produced when
(i) 1 mole of carbon is burnt in air.
(ii) 1 mole of carbon is burnt in 16 g of dioxygen.
(iii) 2 moles of carbon are burnt in 16 g of dioxygen.

Question 1.5 Calculate the mass of sodium acetate (CH3COONa) required to make 500 mL of 0.375 molar aqueous solution. Molar mass of sodium acetate is 82.0245 g mol–1.

Question 1.6 Calculate the concentration of nitric acid in moles per litre in a sample which has a density, 1.41 g mL–1 and the mass per cent of nitric acid in it being 69%.

Question 1.7 How much copper can be obtained from 100 g of copper sulphate (CuSO4) ?

Question 1.8 Determine the molecular formula of an oxide of iron in which the mass per cent of iron and oxygen are 69.9 and 30.1 respectively.

Question 1.9 Calculate the atomic mass (average) of chlorine using the following data : % Natural Abundance Molar Mass 35Cl 75.77 34.9689 37Cl 24.23 36.9659

Question 1.10 In three moles of ethane (C2H6), calculate the following :
(i) Number of moles of carbon atoms.
(ii) Number of moles of hydrogen atoms.
(iii) Number of molecules of ethane.

Question 1.11 What is the concentration of sugar (C12H22O11) in mol L–1 if its 20 g are dissolved in enough water to make a final volume up to 2L?

Question 1.12 If the density of methanol is 0.793 kg L–1, what is its volume needed for making 2.5 L of its 0.25 M solution?

Question 1.13 Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below : 1Pa = 1N m–2 If mass of air at sea level is 1034 g cm–2, calculate the pressure in pascal.

Question 1.14 What is the SI unit of mass? How is it defined?

Question 1.15 Match the following prefixes with their multiples: Prefixes Multiples
(i) micro 106
(ii) deca 109
(iii) mega 10–6
(iv) giga 10–15
(v) femto 10

Question 1.16 What do you mean by significant figures ?

Question 1.17 A sample of drinking water was found to be severely contaminated with chloroform, CHCl3, supposed to be carcinogenic in nature. The level of contamination was 15 ppm (by mass).
(i) Express this in percent by mass.
(ii) Determine the molality of chloroform in the water sample.

Question 1.18 Express the following in the scientific notation:
(i) 0.0048
(ii) 234,000
(iii) 8008
(iv) 500.0
(v) 6.0012

Question 1.19 How many significant figures are present in the following?
(i) 0.0025
(ii) 208
(iii) 5005
(iv) 126,000
(v) 500.0
(vi) 2.0034

Question 1.20 Round up the following upto three significant figures:
(i) 34.216
(ii) 10.4107
(iii) 0.04597
(iv) 2808

Question 1.21 The following data are obtained when dinitrogen and dioxygen react together to form different compounds : Mass of dinitrogen Mass of dioxygen
(i) 14 g 16 g
(ii) 14 g 32 g
(iii) 28 g 32 g
(iv) 28 g 80 g

(a) Which law of chemical combination is obeyed by the above experimental data? Give its statement.
(b) Fill in the blanks in the following conversions:

(i) 1 km = ...................... mm = ...................... pm
(ii) 1 mg = ...................... kg = ...................... ng
(iii) 1 mL = ...................... L = ...................... dm3

Question 1.22 If the speed of light is 3.0 × 108 m s–1, calculate the distance covered by light in 2.00 ns.

Question 1.23 In a reaction A + B2 → AB2 Identify the limiting reagent, if any, in the following reaction mixtures.
(i) 300 atoms of A + 200 molecules of B
(ii) 2 mol A + 3 mol B
(iii) 100 atoms of A + 100 molecules of B
(iv) 5 mol A + 2.5 mol B
(v)2.5 mol A + 5 mol B

Question 1.24 Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation: N2 (g) + H2 (g) → 2NH3 (g)
(i) Calculate the mass of ammonia produced if 2.00 × 103 g dinitrogen reacts with 1.00 ×103 g of dihydrogen.
(ii) Will any of the two reactants remain unreacted?
(iii) If yes, which one and what would be its mass?

Question 1.25 How are 0.50 mol Na2CO3 and 0.50 M Na2CO3 different?

Question 1.26 If ten volumes of dihydrogen gas reacts with five volumes of dioxygen gas, how many volumes of water vapour would be produced?

Question 1.27 Convert the following into basic units:
(i) 28.7 pm
(ii) 15.15 pm
(iii) 25365 mg

Question 1.28 Which one of the following will have largest number of atoms?
(i) 1 g Au (s)
(ii) 1 g Na (s)
(iii) 1 g Li (s)
(iv) 1 g of Cl2(g)

Question 1.29 Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040.

Question 1.30 What will be the mass of one 12C atom in g ?

Question 1.31 How many significant figures should be present in the answer of the following calculations?
(i) 0.02856 29 0.5 ×
(ii) 5 × 5.364
(iii) 0.0125 + 0.7864 + 0.0215

Question 1.32 Use the data given in the following table to calculate the molar mass of naturally occuring argon isotopes: Isotope Isotopic molar mass Abundance 36Ar 35.96755 g mol–1 0.337% 38Ar 37.96272 g mol–1 0.063% 40Ar 39.9624 g mol–1 99.600%

Question 1.33 Calculate the number of atoms in each of the following
(i) 52 moles of Ar
(ii) 52 u of He
(iii) 52 g of He.

Question 1.34 A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide , 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calculate (i) empirical formula, (ii) molar mass of the gas, and (iii) molecular formula.

Question 1.35 Calcium carbonate reacts with aqueous HCl to give CaCl2 and CO2 according to the reaction, CaCO3 (s) + 2 HCl (aq) → CaCl2 (aq) + CO2(g) + H2O(l) What mass of CaCO3 is required to react completely with 25 mL of 0.75 M HCl?

Question 1.36 Chlorine is prepared in the laboratory by treating manganese dioxide (MnO2) with aqueous hydrochloric acid according to the reaction 4 HCl (aq) + MnO2(s) → 2H2O (l) + MnCl2(aq) + Cl2 (g) How many grams of HCl react with 5.0 g of manganese dioxide?

 


(Chemistry) Chapter 2 Structure Of Atom


NCERT Exercises Questions

Question 2.1 (i) Calculate the number of electrons which will together weigh one gram.
(ii) Calculate the mass and charge of one mole of electrons.

Question 2.2 (i) Calculate the total number of electrons present in one mole of methane.
(ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of 14C. (Assume that mass of a neutron = 1.675 × 10–27 kg).
(iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH3 at STP. Will the answer change if the temperature and pressure are changed ?

Question 2.3 How many neutrons and protons are there in the following nuclei ?
13 16 24 6 8 12 C, O, Mg,

Question 2.4 Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A)
(i) Z = 17 , A = 35.
(ii) Z = 92 , A = 233.
(iii) Z = 4 , A = 9.

Question 2.5 Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber ( ν ) of the yellow light.

Question 2.6 Find energy of each of the photons which
(i) correspond to light of frequency 3×1015 Hz.
(ii) have wavelength of 0.50 Å.

Question 2.7 Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0 × 10–10 s.

Question 2.8 What is the number of photons of light with a wavelength of 4000 pm that provide 1J of energy?

Question 2.9 A photon of wavelength 4 × 10–7 m strikes on metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron (1 eV= 1.6020 × 10–19 J).

Question 2.10 Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol–1.

Question 2.11 A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57μm. Calculate the rate of emission of quanta per second.

Question 2.12 Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate threshold frequency (ν0 ) and work function (W0 ) of the metal.

Question 2.13 What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2?

Question 2.14 How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom ( energy required to remove the electron from n =1 orbit).

Question 2.15 What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state?

Question 2.16 (i) The energy associated with the first orbit in the hydrogen atom is –2.18 × 10–18 J atom–1. What is the energy associated with the fifth orbit?
(ii) Calculate the radius of Bohr's fifth orbit for hydrogen atom.

Question 2.17 Calculate the wavenumber for the longest wavelength transition in the Balmer series of atomic hydrogen.

Question 2.18 What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.

Question 2.19 The electron energy in hydrogen atom is given by En = (–2.18 × 10–18 )/n2 J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Question 2.20 Calculate the wavelength of an electron moving with a velocity of 2.05 × 107 m s–1.

Question 2.21 The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.

Question 2.22 Which of the following are isoelectronic species i.e., those having the same number of electrons? Na+, K+, Mg2+, Ca2+, S2–, Ar.

Question 2.23 (i) Write the electronic configurations of the following ions:
(a) H–
(b) Na+
(c) O2–
(d) F–

(ii) What are the atomic numbers of elements whose outermost electrons are represented by
(a) 3s1
(b) 2p3
(c) 3p5 ?

(iii) Which atoms are indicated by the following configurations ?
(a) [He] 2s1
(b) [Ne] 3s2 3p3
(c) [Ar] 4s2 3d1.

Question 2.24 What is the lowest value of n that allows g orbitals to exist?

Question 2.25 An electron is in one of the 3d orbitals. Give the possible values of n, l and ml for this electron.

Question 2.26 An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element.

Question 2.27 Give the number of electrons in the species H H andO 2 2 2 + , +

Question 2.28 (i) An atomic orbital has n = 3. What are the possible values of l and ml ?
(ii) List the quantum numbers (ml and l ) of electrons for 3d orbital.
(iii) Which of the following orbitals are possible? 1p, 2s, 2p and 3f

Question 2.29 Using s, p, d notations, describe the orbital with the following quantum numbers.
(a) n=1, l=0;
(b) n = 3; l=1
(c) n 4; l =2;
(d) n=4; l=3.

Question 2.30 Explain, giving reasons, which of the following sets of quantum numbers are not possible.
(a) n = 0, l = 0, ml = 0, ms = + ½
(b) n = 1, l = 0, ml = 0, ms = – ½
(c) n = 1, l = 1, ml = 0, ms = + ½
(d) n = 2, l = 1, ml = 0, ms = – ½
(e) n = 3, l = 3, ml = –3, ms = + ½
(f) n = 3, l = 1, ml = 0, ms = + ½

Question 2.31 How many electrons in an atom may have the following quantum numbers?
(a) n = 4, ms = – ½
(b) n = 3, l = 0

Question 2.32 Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

Question 2.33 What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He+ spectrum ?

Question 2.34
Calculate the energy required for the process He+ (g) He2+ (g) + e– The ionization energy for the H atom in the ground state is 2.18 × 10–18 J atom–1

Question 2.35 If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across length of scale of length 20 cm long.

Question 2.36 2 ×108 atoms of carbon are arranged side by side. Calculate the radius of carbon atom if the length of this arrangement is 2.4 cm.

Question 2.37 The diameter of zinc atom is 2.6 Å.Calculate (a) radius of zinc atom in pm and (b) number of atoms present in a length of 1.6 cm if the zinc atoms are arranged side by side lengthwise.

Question 2.38 A certain particle carries 2.5 × 10–16C of static electric charge. Calculate the number of electrons present in it.

Question 2.39 In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is –1.282 × 10–18C, calculate the number of electrons present on it.

Question 2.40 In Rutherford's experiment, generally the thin foil of heavy atoms, like gold, platinum etc. have been used to be bombarded by the α-particles. If the thin foil of light atoms like aluminium etc. is used, what difference would be observed from the above results ?

Question 2.41 Symbols 79 35Br and 79Br can be written, whereas symbols 35 79 Br and 35Br are not acceptable. Answer briefly.

Question 2.42
An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign the atomic symbol.

Question 2.43 An ion with mass number 37 possesses one unit of negative charge. If the ion conatins 11.1% more neutrons than the electrons, find the symbol of the ion.

Question 2.44 An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign the symbol to this ion.

Question 2.45 Arrange the following type of radiations in increasing order of frequency:
(a) radiation from microwave oven (b) amber light from traffic signal (c) radiation from FM radio (d) cosmic rays from outer space and (e) X-rays.

Question 2.46 Nitrogen laser produces a radiation at a wavelength of 337.1 nm. If the number of photons emitted is 5.6 × 1024, calculate the power of this laser.

Question 2.47 Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate
(a) the frequency of emission (b) distance traveled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy.

Question 2.48 In astronomical observations, signals observed from the distant stars are generally


(Chemistry) Chapter 3 Classification of Elements and Periodicity in Properties


NCERT Exercises Questions

Question 3.1 What is the basic theme of organisation in the periodic table?

Question 3.2 Which important property did Mendeleev use to classify the elements in his periodic table and did he stick to that?

Question 3.3 What is the basic difference in approach between the Mendeleev's Periodic Law and the Modern Periodic Law?

Question 3.4 On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.

Question 3.5 In terms of period and group where would you locate the element with Z =114?

Question 3.6 Write the atomic number of the element present in the third period and seventeenth group of the periodic table.

Question 3.7
Which element do you think would have been named by
(i) Lawrence Berkeley Laboratory
(ii) Seaborg's group?

Question 3.8 Why do elements in the same group have similar physical and chemical properties?

Question 3.9
What does atomic radius and ionic radius really mean to you?

Question 3.10 How do atomic radius vary in a period and in a group? How do you explain the variation?

Question 3.11 What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions.
(i) F–
(ii) Ar
(iii) Mg2+
(iv) Rb+

Question 3.12 Consider the following species : N3–, O2–, F–, Na+, Mg2+ and Al3+
(a) What is common in them?
(b) Arrange them in the order of increasing ionic radii.

Question 3.13 Explain why cation are smaller and anions larger in radii than their parent atoms?

Question 3.14 What is the significance of the terms — 'isolated gaseous atom' and 'ground state' while defining the ionization enthalpy and electron gain enthalpy? Hint : Requirements for comparison purposes.

Question 3.15 Energy of an electron in the ground state of the hydrogen atom is –2.18×10–18J. Calculate the ionization enthalpy of atomic hydrogen in terms of J mol–1. Hint: Apply the idea of mole concept to derive the answer.

Question 3.16 Among the second period elements the actual ionization enthalpies are in the order Li < B < Be < C < O < N < F < Ne. Explain why
(i) Be has higher Δi H than B
(ii) O has lower Δi H than N and F?

Question 3.17
How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium?

Question 3.18
What are the various factors due to which the ionization enthalpy of the main group elements tends to decrease down a group?

Question 3.19
The first ionization enthalpy values (in kJ mol–1) of group 13 elements are : B Al Ga In Tl 801 577 579 558 589 How would you explain this deviation from the general trend ?

Question 3.20 Which of the following pairs of elements would have a more negative electron gain enthalpy?
(i) O or F
(ii) F or Cl

Question 3.21 Would you expect the second electron gain enthalpy of O as positive, more negative or less negative than the first? Justify your answer.

Question 3.22
What is the basic difference between the terms electron gain enthalpy and electronegativity?

Question 3.23 How would you react to the statement that the electronegativity of N on Pauling scale is Question 3.0 in all the nitrogen compounds?

Question 3.24
Describe the theory associated with the radius of an atom as it
(a) gains an electron
(b) loses an electron

Question 3.25
Would you expect the first ionization enthalpies for two isotopes of the same element to be the same or different? Justify your answer.

Question 3.26
What are the major differences between metals and non-metals?

Question 3.27 Use the periodic table to answer the following questions.
(a) Identify an element with five electrons in the outer subshell.
(b) Identify an element that would tend to lose two electrons.
(c) Identify an element that would tend to gain two electrons.
(d) Identify the group having metal, non-metal, liquid as well as gas at the room temperature.

Question 3.28 The increasing order of reactivity among group 1 elements is Li < Na < K < Rb CI > Br > I. Explain.

Question 3.29 Write the general outer electronic configuration of s-, p-, d- and f- block elements.

Question 3.30 Assign the position of the element having outer electronic configuration
(i) ns2np4 for n=3
(ii) (n-1)d2ns2 for n=4, and
(iii) (n-2) f 7 (n-1)d1ns2 for n=6, in the periodic table.

Question 3.31 The first (ΔiH1) and the second (ΔiH2) ionization enthalpies (in kJ mol–1) and the (ΔegH) electron gain enthalpy (in kJ mol–1) of a few elements are given below: Elements ΔH1 ΔH2 ΔegH I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be :
(a) the least reactive element.
(b) the most reactive metal.
(c) the most reactive non-metal.
(d) the least reactive non-metal.
(e) the metal which can form a stable binary halide of the formula MX2(X=halogen).
(f) the metal which can form a predominantly stable covalent halide of the formula MX (X=halogen)?

Question 3.32 Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements.
(a) Lithium and oxygen
(b) Magnesium and nitrogen
(c) Aluminium and iodine
(d) Silicon and oxygen
(e) Phosphorus and fluorine
(f) Element 71 and fluorine

Question 3.33 In the modern periodic table, the period indicates the value of :
(a) atomic number
(b) atomic mass
(c) principal quantum number
(d) azimuthal quantum number.

Question 3.34 Which of the following statements related to the modern periodic table is incorrect?
(a) The p-block has 6 columns, because a maximum of 6 electrons can occupy all the orbitals in a p-shell.
(b) The d-block has 8 columns, because a maximum of 8 electrons can occupy all the orbitals in a d-subshell.
(c) Each block contains a number of columns equal to the number of electrons that can occupy that subshell.
(d) The block indicates value of azimuthal quantum number (l) for the last subshell that received electrons in building up the electronic configuration.

Question 3.35 Anything that influences the valence electrons will affect the chemistry of the element. Which one of the following factors does not affect the valence shell?
(a) Valence principal quantum number (n)
(b) Nuclear charge (Z )
(c) Nuclear mass
(d) Number of core electrons.

Question 3.36 The size of isoelectronic species — F–, Ne and Na+ is affected by
(a) nuclear charge (Z )
(b) valence principal quantum number (n)
(c) electron-electron interaction in the outer orbitals
(d) none of the factors because their size is the same.

Question 3.37 Which one of the following statements is incorrect in relation to ionization enthalpy?
(a) Ionization enthalpy increases for each successive electron.
(b) The greatest increase in ionization enthalpy is experienced on removal of electron from core noble gas configuration.
(c) End of valence electrons is marked by a big jump in ionization enthalpy.
(d) Removal of electron from orbitals bearing lower n value is easier than from orbital having higher n value.

Question 3.38 Considering the elements B, Al, Mg, and K, the correct order of their metallic character is :
(a) B > Al > Mg > K
(b) Al > Mg > B > K
(c) Mg > Al > K > B
(d) K > Mg > Al > B

Question 3.39 Considering the elements B, C, N, F, and Si, the correct order of their non-metallic character is :
(a) B > C > Si > N > F
(b) Si > C > B > N > F
(c) F > N > C > B > Si
(d) F > N > C > Si > B

Question 3.40
Considering the elements F, Cl, O and N, the correct order of their chemical reactivity in terms of oxidizing property is :
(a) F > Cl > O > N
(b) F > O > Cl > N
(c) Cl > F > O > N
(d) O > F > N > Cl


(Chemistry) Chapter 4 Chemical Bonding and Molecular Structure


NCERT Exercises Questions

Question 4.1 Explain the formation of a chemical bond.

Question 4.2 Write Lewis dot symbols for atoms of the following elements :
Mg, Na, B, O, N, Br.

Question 4.3 Write Lewis symbols for the following atoms and ions:
S and S2–; Al and Al3+; H and H–

Question 4.4
Draw the Lewis structures for the following molecules and ions :
H2S, SiCl4, BeF2, 2 3 CO − , HCOOH

Question 4.5 Define octet rule. Write its significance and limitations.

Question 4.6
Write the favourable factors for the formation of ionic bond.

Question 4.7 Discuss the shape of the following molecules using the VSEPR model:
BeCl2, BCl3, SiCl4, AsF5, H2S, PH3

Question 4.8 Although geometries of NH3 and H2O molecules are distorted tetrahedral, bond angle in water is less than that of ammonia. Discuss.

Question 4.9
How do you express the bond strength in terms of bond order ?

Question 4.10 Define the bond length.

Question 4.11 Explain the important aspects of resonance with reference to the 2 3 CO − ion.

Question 4.12
H3PO3 can be represented by structures 1 and 2 shown below. Can these two structures be taken as the canonical forms of the resonance hybrid representing H3PO3 ? If not, give reasons for the same.

Question 4.13 Write the resonance structures for SO3, NO2 and 3 NO− .

Question 4.14 Use Lewis symbols to show electron transfer between the following atoms to form cations and anions : (a) K and (b) Ca and O (c) Al and N.

Question 4.15 Although both CO2 and H2O are triatomic molecules, the shape of H2O molecule is bent while that of CO2 is linear. Explain this on the basis of dipole moment. 4.16 Write the significance/applications of dipole moment.

Question 4.17 Define electronegativity. How does it differ from electron gain enthalpy ?

Question 4.18 Explain with the help of suitable example polar covalent bond.

Question 4.19 Arrange the bonds in order of increasing ionic character in the molecules: LiF, K2O, N2, SO2 and ClF3.

Question 4.20 The skeletal structure of CH3COOH as shown below is correct, but some of the bonds are shown incorrectly. Write the correct Lewis structure for acetic acid.

Question 4.21 Apart from tetrahedral geometry, another possible geometry for CH4 is square planar with the four H atoms at the corners of the square and the C atom at its centre. Explain why CH4 is not square planar ?
Question 4.22 Explain why BeH2 molecule has a zero dipole moment although the Be–H bonds are polar.

Question 4.23 Which out of NH3 and NF3 has higher dipole moment and why ?

Question 4.24 What is meant by hybridisation of atomic orbitals? Describe the shapes of sp, sp2, sp3 hybrid orbitals.

Question 4.25 Describe the change in hybridisation (if any) of the Al atom in the following reaction. 3 AlCl + Cl− → Al

Question 4.26 Is there any change in the hybridisation of B and N atoms as a result of the following reaction ? 3 3 3 BF + NH → F B

Question 4.27 Draw diagrams showing the formation of a double bond and a triple bond between carbon atoms in C2H4 and C2H2 molecules.

Question 4.28 What is the total number of sigma and pi bonds in the following molecules ?
(a) C2H2
(b) C2H4

Question 4.29 Considering x-axis as the internuclear axis which out of the following will not form a sigma bond and why?
(a) 1s and 1s
(b) 1s and 2px ;
(c) 2py and 2py
(d) 1s and 2s.

Question 4.30
Which hybrid orbitals are used by carbon atoms in the following molecules ?
(a)CH3–CH3;
(b) CH3–CH=CH2;
(c) CH3-CH2-OH;
(d) CH3-CHO
(e) CH3COOH

Question 4.31
What do you understand by bond pairs and lone pairs of electrons ? Illustrate by giving one exmaple of each type.

Question 4.32 Distinguish between a sigma and a pi bond.

Question 4.33 Explain the formation of H2 molecule on the basis of valence bond theory.

Question 4.34 Write the important conditions required for the linear combination of atomic orbitals to form molecular orbitals.

Question 4.35 Use molecular orbital theory to explain why the Be2 molecule does not exist.4.36 Compare the relative stability of the following species and indicate their magnetic properties; 2 2 2 O ,O+ ,O− (superoxide), 2 2 O − (peroxide)

Question 4.37 Write the significance of a plus and a minus sign shown in representing the orbitals.

Question 4.38 Describe the hybridisation in case of PCl5. Why are the axial bonds longer as compared to equatorial bonds ?

Question 4.39 Define hydrogen bond. Is it weaker or stronger than the van der Waals forces?

Question 4.40 What is meant by the term ond order ? Calculate the bond order of : N2, O2, O2 + and O2


(Chemistry) Chapter 5 States Of Matter


NCERT Solutions Questions

Question 5.1 What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C? 152 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.pmd 14.1.6 (Final), 17.1.6, 24.1.6

Question 5.2 A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What would be its pressure?

Question 5.3 Using the equation of state pV=nRT; show that at a given temperature density of a gas is proportional to gas pressure p.

Question 5.4 At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Question 5.5 Pressure of 1 g of an ideal gas A at 27 °C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

Question 5.6 The drain cleaner, Drainex contains small bits of aluminum which react with caustic soda to produce dihydrogen. What volume of dihydrogen at 20 °C and one bar will be released when 0.15g of aluminum reacts?

Question 5.7 What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of carbon dioxide contained in a 9 dm3 flask at 27 °C ?

Question 5.8 What will be the pressure of the gaseous mixture when 0.5 L of H2 at 0.8 bar and 2.0 L of dioxygen at 0.7 bar are introduced in a 1L vessel at 27°C?

Question 5.9 Density of a gas is found to be 5.46 g/dm3 at 27 °C at 2 bar pressure. What will be its density at STP?

Question 5.10
34.05 mL of phosphorus vapour weighs 0.0625 g at 546 °C and 0.1 bar pressure. What is the molar mass of phosphorus?

Question 5.11 A student forgot to add the reaction mixture to the round bottomed flask at 27 °C but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was 477 °C. What fraction of air would have been expelled out?

Question 5.12 Calculate the temperature of 4.0 mol of a gas occupying 5 dm3 at 3.32 bar. (R = 0.083 bar dm3 K–1 mol–1).

Question 5.13 Calculate the total number of electrons present in 1.4 g of dinitrogen gas.

Question 5.14
How much time would it take to distribute one Avogadro number of wheat grains, if 1010 grains are distributed each second ?

Question 5.15 Calculate the total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen confined in a vessel of 1 dm3 at 27°C. R = 0.083 bar dm3 K–1 mol–1.

Question 5.16
Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kg m–3 and R = 0.083 bar dm3 K–1 mol–1).

Question 5.17 Calculate the volume occupied by 8.8 g of CO2 at 31.1°C and 1 bar pressure. R = 0.083 bar L K–1 mol–1.

Question 5.18
2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C, at the same pressure. What is the molar mass of the gas?

Question 5.19 A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen. Calculate the partial pressure of dihydrogen.

Question 5.20
What would be the SI unit for the quantity pV 2T 2/n ?

Question 5.21
In terms of Charles' law explain why –273 °C is the lowest possible temperature.

Question 5.22
Critical temperature for carbon dioxide and methane are 31.1 °C and –81.9 °C respectively. Which of these has stronger intermolecular forces and why?

Question 5.23 Explain the physical significance of van der Waals parameters.


(Chemistry) Chapter 6 Thermodynamics


NCERT  Exercises Questions

Question 6. 1 Choose the correct answer. A thermodynamic state function is a quantity
(i) used to determine heat changes
(ii) whose value is independent of path
(iii) used to determine pressure volume work
(iv) whose value depends on temperature only.

Question 6. 2 For the process to occur under adiabatic conditions, the correct condition is:
(i) ΔT = 0
(ii) Δp = 0
(iii) q = 0
(iv) w = 0

Question 6. 3 The enthalpies of all elements in their standard states are:
(i) unity
(ii) zero
(iii) < 0
(iv) different for each element

Question 6. 4 ΔU0of combustion of methane is – X kJ mol–1. The value of ΔH0 is
(i) = ΔU0
(ii) > ΔU0
(iii) < ΔU0
(iv) = 0

Question 6. 5 The enthalpy of combustion of methane, graphite and dihydrogen at 298 K are, –890.3 kJ mol–1 –393.5 kJ mol–1, and –285.8 kJ mol–1 respectively. Enthalpy of formation of CH4(g) will be
(i) –74.8 kJ mol–1
(ii) –52.27 kJ mol–1
(iii) +74.8 kJ mol–1
(iv) +52.26 kJ mol–1.

Question 6. 6 A reaction, A + B → C + D + q is found to have a positive entropy change. The reaction will be
(i) possible at high temperature
(ii) possible only at low temperature
(iii) not possible at any temperature
(v) possible at any temperature

Question 6. 7 In a process, 701 J of heat is absorbed by a system and 394 J of work is done by the system. What is the change in internal energy for the process?

Question 6. 8 The reaction of cyanamide, NH2CN (s), with dioxygen was carried out in a bomb calorimeter, and ΔU was found to be –742.7 kJ mol–1 at 298 K. Calculate enthalpy change for the reaction at 298 K. NH2CN(g) + 3 2 O2(g) → N2(g) + CO2(g) + H2O(l)

Question 6. 9 Calculate the number of kJ of heat necessary to raise the temperature of 60.0 g of aluminium from 35°C to 55°C. Molar heat capacity of Al is 24 J mol–1 K–1.

Question 6. 10 Calculate the enthalpy change on freezing of 1.0 mol of water at10.0°C to ice at –10.0°C. ΔfusH =

Question 6. 03 kJ mol–1 at 0°C. Cp [H2O(l)] = 75.3 J mol–1 K–1 Cp [H2O(s)] = 3Question 6. 8 J mol–1 K–1

Question 6. 11 Enthalpy of combustion of carbon to CO2 is –393.5 kJ mol–1. Calculate the heat released upon formation of 35.2 g of CO2 from carbon and dioxygen gas.

Question 6. 12 Enthalpies of formation of CO(g), CO2(g), N2O(g) and N2O4(g) are –110, – 393, 81 and 9.7 kJ mol–1 respectively. Find the value of ΔrH for the reaction:
N2O4(g) + 3CO(g) → N2O(g) + 3CO2(g)

Question 6. 13 Given N2(g) + 3H2(g) → 2NH3(g) ; ΔrH0 = –92.4 kJ mol–1 What is the standard enthalpy of formation of NH3 gas?

Question 6. 14 Calculate the standard enthalpy of formation of CH3OH(l) from the following data: CH3OH (l) + 3 2 O2(g) → CO2(g) + 2H2O(l) ; ΔrH0 = –726 kJ mol–1 C(g) + O2(g) → CO2(g) ; ΔcH0 = –393 kJ mol–1 H2(g) + 1 2 O2(g) → H2O(l) ; Δf H0 = –286 kJ mol–1.

Question 6. 15 Calculate the enthalpy change for the process CCl4(g) → C(g) + 4 Cl(g) and calculate bond enthalpy of C – Cl in CCl4(g). ΔvapH0(CCl4) = 30.5 kJ mol–1. ΔfH0 (CCl4) = –135.5 kJ mol–1. ΔaH0 (C) = 715.0 kJ mol–1 , where ΔaH0 is enthalpy of atomisation ΔaH0 (Cl2) = 242 kJ mol–1 Question 6. 16 For an isolated system, ΔU = 0, what will be ΔS ?

Question 6. 17 For the reaction at 298 K, 2A + B → C ΔH = 400 kJ mol–1 and ΔS = 0.2 kJ K–1 mol–1 At what temperature will the reaction become spontaneous considering ΔH and ΔS to be constant over the temperature range.

Question 6. 18 For the reaction, 2 Cl(g) → Cl2(g), what are the signs of ΔH and ΔS ?


Question 6. 19 For the reaction 2 A(g) + B(g) → 2D(g) ΔU 0 = –10.5 kJ and ΔS0 = –44.1 JK–1. Calculate ΔG0 for the reaction, and predict whether the reaction may occur spontaneously.

Question 6. 20 The equilibrium constant for a reaction is 10. What will be the value of ΔG0 ? R = 8.314 JK–1 mol–1, T = 300 K.

Question 6. 21 Comment on the thermodynamic stability of NO(g), given 1 2 N2(g) + 1 2 O2(g) → NO(g) ; ΔrH0 = 90 kJ mol–1 NO(g) + 1 2 O2(g) → NO2(g) : ΔrH0= –74 kJ mol–1

Question 6. 22 Calculate the entropy change in surroundings when 1.00 mol of H2O(l) is formed under standard conditions. Δf H0 = –286 kJ mol–1.


(Chemistry) Chapter 7 Equilibrium


NCERT  Exercises Questions

Question 7.1 A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.
a) What is the initial effect of the change on vapour pressure?
b) How do rates of evaporation and condensation change initially?
c) What happens when equilibrium is restored finally and what will be the final vapour pressure?

Question 7.2 What is Kc for the following equilibrium when the equilibrium concentration of each substance is:
[SO2]= 0.60M, [O2] = 0.82M and [SO3] = 1.90M ? 2SO2(g) + O2(g) ƒ 2SO3(g)

Question 7.3 At a certain temperature and total pressure of 105Pa, iodine vapour contains 40% by volume of I atoms I2 (g) ƒ 2I(g) Calculate Kp for the equilibrium.

Question 7.4 Write the expression for the equilibrium constant, Kc for each of the following reactions:
(i) 2NOCl (g) ƒ 2NO (g) + Cl2 (g)
(ii) 2Cu(NO3)2 (s) ƒ 2CuO (s) + 4NO2 (g) + O2 (g)
(iii) CH3COOC2H5(aq) + H2O(l) ƒ CH3COOH (aq) + C2H5OH (aq)
(iv) Fe3+ (aq) + 3OH– (aq) ƒ Fe(OH)3 (s) (v) I2 (s) + 5F2 ƒ 2IF5

Question 7.5 Find out the value of Kc for each of the following equilibria from the value of Kp:
(i) 2NOCl (g) ƒ 2NO (g) + Cl2 (g); Kp= 1.8 × 10–2 at 500 K
(ii) CaCO3 (s) ƒ CaO(s) + CO2(g); Kp= 167 at 1073 K

Question 7.6 For the following equilibrium, Kc= 6.3 × 1014 at 1000 K NO (g) + O3 (g) ƒ NO2 (g) + O2 (g) Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is Kc, for the reverse reaction?

Question 7.7 Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression?

Question 7.8 Reaction between N2 and O2– takes place as follows: 2N2 (g) + O2 (g) ƒ 2N2O (g) If a mixture of 0.482 mol N2 and 0.933 mol of O2 is placed in a 10 L reaction vessel and allowed to form N2O at a temperature for which Kc= 2.0 × 10–37, determine the composition of equilibrium mixture. \

Question 7.9 Nitric oxide reacts with Br2 and gives nitrosyl bromide as per reaction given below: 2NO (g) + Br2 (g) ƒ 2NOBr (g) When 0.087 mol of NO and 0.0437 mol of Br2 are mixed in a closed container at constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate equilibrium amount of NO and Br2 .

Question 7.10 At 450K, Kp= 2.0 × 1010/bar for the given reaction at equilibrium. 2SO2(g) + O2(g) ƒ 2SO3 (g) What is Kc at this temperature ?

Question 7.11 A sample of HI(g) is placed in flask at a pressure of 0.2 atm. At equilibrium the partial pressure of HI(g) is 0.04 atm. What is Kp for the given equilibrium ? 2HI (g) ƒ H2 (g) + I2 (g)

Question 7.12 A mixture of 1.57 mol of N2, 1.92 mol of H2 and 8.13 mol of NH3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, Kc for the reaction N2 (g) + 3H2 (g) ƒ 2NH3 (g) is 1.7 × 102. Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?

Question 7.13 The equilibrium constant expression for a gas reaction is, [ ][ [ ] [ 4 3 2 4 2 NH O NO H O = c K Write the balanced chemical equation corresponding to this expression.

Question 7.14 One mole of H2O and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium 40% of water (by mass) reacts with CO according to the equation, H2O (g) + CO (g) ƒ H2 (g) + CO2 (g) Calculate the equilibrium constant for the reaction.

Question 7.15 At 700 K, equilibrium constant for the reaction: H2 (g) + I2 (g) ƒ 2HI (g) is 54.8. If 0.5 mol L–1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H2(g) and I2(g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700K?

Question 7.16 What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M ? 2ICl (g) ƒ I2 (g) + Cl2 (g); Kc = 0.14

Question 7.17 Kp = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C2H6 when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium? C2H6 (g) ƒ C2H4 (g) + H2 (g)

Question 7.18 Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as: CH3COOH (l) + C2H5OH (l) ƒ CH3COOC2H5 (l) + H2O (l)
(i) Write the concentration ratio (reaction quotient), Qc, for this reaction (note: water is not in excess and is not a solvent in this reaction)
(ii) At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
(iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after sometime. Has equilibrium been reached?

Question 7.19 A sample of pure PCl5 was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl5 was found to be 0.5 × 10–1 mol L–1. If value of Kc is 8.3 × 10–3, what are the concentrations of PCl3 and Cl2 at equilibrium? PCl5 (g) ƒ PCl3 (g) + Cl2(g)

Question 7.20 One of the reaction that takes place in producing steel from iron ore is the reduction of iron(II) oxide by carbon monoxide to give iron metal and CO2. FeO (s) + CO (g) ƒ Fe (s) + CO2 (g); Kp = 0.265 atm at 1050K What are the equilibrium partial pressures of CO and CO2 at 1050 K if the initial partial pressures are: pCO= 1.4 atm and CO2 p =0.80 atm?

Question 7.21 Equilibrium constant, Kc for the reaction N2 (g) + 3H2 (g) ƒ 2NH3 (g) at 500 K is 0.061 At a particular time, the analysis shows that composition of the reaction mixture is 3.0 mol L–1 N2, 2.0 mol L–1 H2 and 0.5 mol L–1 NH3. Isthe reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?


Question 7.22 Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium: 2BrCl (g) ƒ Br2 (g) + Cl2 (g) for which Kc= 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10–3 mol L–1, what is its molar concentration in the mixture at equilibrium?


Question 7.23 At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO2 in equilibrium with soild carbon has 90.55% CO by mass C (s) + CO2 (g) ƒ 2CO (g) Calculate Kc for this reaction at the above temperature.

Question 7.24 Calculate a) ΔG0 and b) the equilibrium constant for the formation of NO2 from NO and O2 at 298K NO (g) + ½ O2 (g) ƒ NO2 (g) where ΔfG0 (NO2) = 52.0 kJ/mol ΔfG0 (NO) = 87.0 kJ/mol ΔfG0 (O2) = 0 kJ/mol

Question 7.25 Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?
(a) PCl5 (g) ƒ PCl3 (g) + Cl2 (g)
(b) CaO (s) + CO2 (g) ƒ CaCO3 (s)
(c) 3Fe (s) + 4H2O (g) ƒ Fe3O4 (s) + 4H2 (g)

Question 7.26 Which of the following reactions will get affected by increasing the pressure? Also, mention whether change will cause the reaction to go into forward or backward direction.
(i) COCl2 (g) ƒ CO (g) + Cl2 (g)
(ii) CH4 (g) + 2S2 (g) ƒ CS2 (g) + 2H2S (g)
(iii) CO2 (g) + C (s) ƒ 2CO (g) (iv) 2H2 (g) + CO (g) ƒ CH3OH (g )
(v) CaCO3 (s) ƒ CaO (s) + CO2 (g)
(vi) 4 NH3 (g) + 5O2 (g) ƒ 4NO (g) + 6H2O(g)

Question 7.27 The equilibrium constant for the following reaction is 1.6 ×105 at 1024K H2(g) + Br2(g) ƒ 2HBr(g) Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024K.

Question28 Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction: CH4 (g) + H2O (g) ƒ CO (g) + 3H2 (g)
(a) Write as expression for Kp for the above reaction.
(b) How will the values of Kp and composition of equilibrium mixture be affected by
(i) increasing the pressure
(ii) increasing the temperature
(iii) using a catalyst ?

Question 7.29 Describe the effect of : a) addition of H2 b) addition of CH3OH c) removal of CO d) removal of CH3OH on the equilibrium of the reaction:
2H2(g) + CO (g) ƒ CH3OH (g)

Question 7.30 At 473 K, equilibrium constant Kc for decomposition of phosphorus pentachloride, PCl5 is 8.3 ×10-3. If decomposition is depicted as, PCl5 (g) ƒ PCl3 (g) + Cl2 (g) ΔrH0 = 124.0 kJ mol–1

a) write an expression for Kc for the reaction.
b) what is the value of Kc for the reverse reaction at the same temperature ?
c) what would be the effect on Kc if

(i) more PCl5 is added
(ii) pressure is increased
(iii) the temperature is increased ?

Question 7.31 Dihydrogen gas used in Haber's process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of CO and H2. In second stage, CO formed in first stage is reacted with more steam in water gas shift reaction, CO (g) + H2O (g) ƒ CO2 (g) + H2 (g) If a reaction vessel at 400 °C is charged with an equimolar mixture of CO and steam such that CO H2O p = p = 4.0 bar, what will be the partial pressure of H2 at equilibrium? Kp= 10.1 at 400°C

Question 7.32 Predict which of the following reaction will have appreciable concentration of reactants and products: a) Cl2 (g) ƒ 2Cl (g) Kc = 5 ×10–39 b) Cl2 (g) + 2NO (g) ƒ 2NOCl (g) Kc = 3.7 × 108 c) Cl2 (g) + 2NO2 (g) ƒ 2NO2Cl (g) Kc = 1.8

Question 7.33 The value of Kc for the reaction 3O2 (g) ƒ 2O3 (g) is 2.0 ×10–50 at 25°C. If the equilibrium concentration of O2 in air at 25°C is 1.6 ×10–2, what is the concentration of O3?

Question 7.34 The reaction, CO(g) + 3H2(g) ƒ CH4(g) + H2O(g) is at equilibrium at 1300 K in a 1L flask. It also contain 0.30 mol of CO, 0.10 mol of H2 and 0.02 mol of H2O and an unknown amount of CH4 in the flask. Determine the concentration of CH4 in the mixture. The equilibrium constant, Kc for the reaction at the given temperature is 3.90.

Question 7.35 What is meant by the conjugate acid-base pair? Find the conjugate acid/base for the following species: HNO2, CN–, HClO4, F –, OH–, CO3 2–, and S2–

Question 7.36 Which of the followings are Lewis acids? H2O, BF3, H+, and NH4 + 7.37 What will be the conjugate bases for the Brönsted acids: HF, H2SO4 and HCO3? 7.38 Write the conjugate acids for the following Brönsted bases: NH2 –, NH3 and HCOO–.

Question 7.39 The species: H2O, HCO3 –, HSO4 – and NH3 can act both as Brönsted acids and bases. For each case give the corresponding conjugate acid and base.

Question 7.40 Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:
(a) OH–
(b) F–
(c) H+
(d) BCl3 .

Question 7.41 The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10–3 M. what is its pH?

Question 7.42 The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.

Question 7.43 The ionization constant of HF, HCOOH and HCN at 298K are 6.8 × 10–4, 1.8 × 10–4 and 4.8 × 10–9 respectively. Calculate the ionization constants of the corresponding conjugate base.

Question 7.44 The ionization constant of phenol is 1.0 × 10–10. What is the concentration of phenolate ion in 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01M in sodium phenolate?

Question 7.45 The first ionization constant of H2S is 9.1 × 10–8. Calculate the concentration of HS– ion in its 0.1M solution. How will this concentration be affected if the solution is 0.1M in HCl also ? If the second dissociation constant of H2S is 1.2 × 10–13, calculate the concentration of S2– under both conditions.

Question 7.46 The ionization constant of acetic acid is 1.74 × 10–5. Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.

Question 7.47 It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its pKa .

Question 7.48 Assuming complete dissociation, calculate the pH of the following solutions:
(a) 0.003 M HCl
(b) 0.005 M NaOH
(c) 0.002 M HBr
(d) 0.002 M KOH

Question 7.49 Calculate the pH of the following solutions:

a) 2 g of TlOH dissolved in water to give 2 litre of solution.
b) 0.3 g of Ca(OH)2 dissolved in water to give 500 mL of solution.
c) 0.3 g of NaOH dissolved in water to give 200 mL of solution.
d) 1mL of 13.6 M HCl is diluted with water to give 1 litre of solution.

Question 7.50 The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pKa of bromoacetic acid.

Question 7.51 The pH of 0.005M codeine (C18H21NO3) solution is 9.95. Calculate its ionization constant and pKb.

Question 7.52 What is the pH of 0.001M aniline solution ? The ionization constant of aniline can be taken from Table7. Calculate the degree of ionization of aniline in the solution. Also calculate the ionization constant of the conjugate acid of aniline.

Question 7.53 Calculate the degree of ionization of 0.05M acetic acid if its pKa value is 4.74. How is the degree of dissociation affected when its solution also contains (a) 0.01M (b) 0.1M in HCl ?

Question 7.54 The ionization constant of dimethylamine is 5.4 × 10–4. Calculate its degree of ionization in its 0.02M solution. What percentage of dimethylamine is ionized if the solution is also 0.1M in NaOH?

Question 7.55 Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:
(a) Human muscle-fluid, 6.83
(b) Human stomach fluid, 1.2
(c) Human blood,7.38
(d) Human saliva, 6.4.

Question 7.56 The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each.

Question 7.57 If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions. What is its pH?

Question 7.58 The solubility of Sr(OH)2 at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution. \

Question 7.59 The ionization constant of propanoic acid is 1.32 × 10–5. Calculate the degree of ionization of the acid in its 0.05M solution and also its pH. What will be its degree of ionization if the solution is 0.01M in HCl also?

Question 7.60 The pH of 0.1M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.

Question 7.61 The ionization constant of nitrous acid is 4.5 × 10–4. Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.

Question 7.62 A 0.02M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.

Question 7.63 Predict if the solutions of the following salts are neutral, acidic or basic: NaCl, KBr, NaCN, NH4NO3, NaNO2 and KF

Question 7.64 The ionization constant of chloroacetic acid is 1.35 × 10–3. What will be the pH of 0.1M acid and its 0.1M sodium salt solution?

Question 7.65 Ionic product of water at 310 K is 2.7 × 10–14. What is the pH of neutral water at this temperature?

Question 7.66 Calculate the pH of the resultant mixtures:
a) 10 mL of 0.2M Ca(OH)2 + 25 mL of 0.1M HCl
b) 10 mL of 0.01M H2SO4 + 10 mL of 0.01M Ca(OH)2
c) 10 mL of 0.1M H2SO4 + 10 mL of 0.1M KOH

Question 7.67 Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants given in Table Determine also the molarities of individual ions.

Question 7.68 The solubility product constant of Ag2CrO4 and AgBr are 1.1 × 10–12 and 5.0 × 10–13 respectively. Calculate the ratio of the molarities of their saturated solutions.

Question 7.69 Equal volumes of 0.002 M solutions of sodium iodate and cupric chlorate are mixed together. Will it lead to precipitation of copper iodate? (For cupric iodate Ksp = 4 × 10–8 ).

Question 7.70 The ionization constant of benzoic acid is 6.46 × 10–5 and Ksp for silver benzoate is 2.5 × 10–13. How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?

Question 7.71 What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, Ksp = 6.3 × 10–18).

Question 7.72 What is the minimum volume of water required to dissolve 1g of calcium sulphate at 298 K? (For calcium sulphate, Ksp is 9.1 × 10–6).

Question 7.73 The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10–19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: FeSO4, MnCl2, ZnCl2 and CdCl2. in which of these solutions precipitation will take place?


(Chemistry) Chapter 8 Redox Reactions


NCERT Exercises Questions

Question 8. 1 Assign oxidation number to the underlined elements in each of the following species:
(a) NaH2PO4
(b) NaHSO4
(c) H4P2O7
(d) K2MnO4
(e) CaO2
(f) NaBH4
(g) H2S2O7
(h) KAl(SO4)2.12 H2O


Question 8. 2 What are the oxidation number of the underlined elements in each of the following and how do you rationalise your results ?
(a) KI3
(b) H2S4O6
(c) Fe3O4
(d) CH3CH2OH
(e) CH3COOH


Question 8. 3 Justify that the following reactions are redox reactions:
(a) CuO(s) + H2(g) → Cu(s) + H2O(g)
(b) Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g)
(c) 4BCl3(g) + 3LiAlH4(s) → 2B2H6(g) + 3LiCl(s) + 3 AlCl3 (s)
(d) 2K(s) + F2(g) → 2K+F– (s) (e) 4 NH3(g) + 5 O2(g) → 4NO(g) + 6H2O(g)


Question 8. 4 Fluorine reacts with ice and results in the change: H2O(s) + F2(g) → HF(g) + HOF(g) Justify that this reaction is a redox reaction.


Question 8. 5 Calculate the oxidation number of sulphur, chromium and nitrogen in H2SO5, Cr2O7 2– and NO3 –. Suggest structure of these compounds. Count for the fallacy.

Question 8. 6 Write formulas for the following compounds:
(a) Mercury(II) chloride
(b) Nickel(II) sulphate
(c) Tin(IV) oxide
(d) Thallium(I) sulphate
(e) Iron(III) sulphate
(f) Chromium(III) oxide

Question 8. 7 Suggest a list of the substances where carbon can exhibit oxidation states from –4 to +4 and nitrogen from –3 to +5.

Question 8. 8 While sulphur dioxide and hydrogen peroxide can act as oxidising as well as reducing agents in their reactions, ozone and nitric acid act only as oxidants. Why ?

Question 8. 9 Consider the reactions:
(a) 6 CO2(g) + 6H2O(l) → C6 H12 O6(aq) + 6O2(g)(b) O3(g) + H2O2(l) → H2O(l) + 2O2(g) Why it is more appropriate to write these reactions as : (a) 6CO2(g) + 12H2O(l) → C6 H12 O6(aq) + 6H2O(l) + 6O2(g) (b) O3(g) + H2O2 (l) → H2O(l) + O2(g) + O2(g) Also suggest a technique to investigate the path of the above (a) and (b) redox reactions.

Question 8. 10 The compound AgF2 is unstable compound. However, if formed, the compound acts as a very strong oxidising agent. Why ?

Question 8. 11 Whenever a reaction between an oxidising agent and a reducing agent is carried out, a compound of lower oxidation state is formed if the reducing agent is in excess and a compound of higher oxidation state is formed if the oxidising agent is in excess. Justify this statement giving three illustrations.

Question 8. 12 How do you count for the following observations ?
(a) Though alkaline potassium permanganate and acidic potassium permanganate both are used as oxidants, yet in the manufacture of benzoic acid from toluene we use alcoholic potassium permanganate as an oxidant. Why ? Write a balanced redox equation for the reaction.
(b) When concentrated sulphuric acid is added to an inorganic mixture containing chloride, we get colourless pungent smelling gas HCl, but if the mixture contains bromide then we get red vapour of bromine. Why ?

Question 8. 13 Identify the substance oxidised reduced, oxidising agent and reducing agent for each of the following reactions:
(a) 2AgBr (s) + C6H6O2(aq) → 2Ag(s) + 2HBr (aq) + C6H4O2(aq)
(b) HCHO(l) + 2[Ag (NH3)2]+(aq) + 3OH–(aq) → 2Ag(s) + HCOO–(aq) + 4NH3(aq) + 2H2O(l)
(c) HCHO (l) + 2 Cu2+(aq) + 5 OH–(aq) → Cu2O(s) + HCOO–(aq) + 3H2O(l)
(d) N2H4(l) + 2H2O2(l) → N2(g) + 4H2O(l) (e) Pb(s) + PbO2(s) + 2H2SO4(aq) → 2PbSO4(s) + 2H2O(l)

Question 8. 14 Consider the reactions : 2 S2O3 2– (aq) + I2(s) → S4 O6 2–(aq) + 2I–(aq) S2O3 2–(aq) + 2Br2(l) + 5 H2O(l) → 2SO4 2–(aq) + 4Br–(aq) + 10H+(aq) Why does the same reductant, thiosulphate react differently with iodine and bromine ?

Question 8. 15 Justify giving reactions that among halogens, fluorine is the best oxidant and among hydrohalic compounds, hydroiodic acid is the best reductant. What inference do you draw about the behaviour of Ag+ and Cu2+ from these reactions ?

Question 8. 18 Balance the following redox reactions by ion – electron method :
(a) MnO4 – (aq) + I– (aq) → MnO2 (s) + I2(s) (in basic medium)
(b) MnO4 – (aq) + SO2 (g) → Mn2+ (aq) + HSO4 – (aq) (in acidic solution)
(c) H2O2 (aq) + Fe2+ (aq) → Fe3+ (aq) + H2O (l) (in acidic solution)
(d) Cr2O7 2– + SO2(g) → Cr3+ (aq) + SO4 2– (aq) (in acidic solution)

Question 8. 19 Balance the following equations in basic medium by ion-electron method and oxidation number methods and identify the oxidising agent and the reducing agent.
(a) P4(s) + OH–(aq) → PH3(g) + HPO2 – (aq)
(b) N2H4(l) + ClO3 –(aq) → NO(g) + Cl–(g)
(c) Cl2O7 (g) + H2O2(aq) → ClO2 –(aq) + O2(g) + H+

Question 8. 20 What sorts of informations can you draw from the following reaction ? (CN)2(g) + 2OH–(aq) → CN–(aq) + CNO–(aq) + H2O(l)

Question 8. 21 The Mn3+ ion is unstable in solution and undergoes disproportionation to give Mn2+, MnO2, and H+ ion. Write a balanced ionic equation for the reaction.

Question 8. 22 Consider the elements :  Cs, Ne, I and F
(a) Identify the element that exhibits only negative oxidation state.
(b) Identify the element that exhibits only postive oxidation state.
(c) Identify the element that exhibits both positive and negative oxidation states.
(d) Identify the element which exhibits neither the negative nor does the positive oxidation state.

Question 8. 23 Chlorine is used to purify drinking water. Excess of chlorine is harmful. The excess of chlorine is removed by treating with sulphur dioxide. Present a balanced equation for this redox change taking place in water.

Question 8. 24 Refer to the periodic table given in your book and now answer the following questions:
(a) Select the possible non metals that can show disproportionation reaction.
(b) Select three metals that can show disproportionation reaction.

Question 8. 25 In Ostwald's process for the manufacture of nitric acid, the first step involves the oxidation of ammonia gas by oxygen gas to give nitric oxide gas and steam. What is the maximum weight of nitric oxide that can be obtained startingonly with 10.00 g. of ammonia and 20.00 g of oxygen ?

Question 8. 26 Using the standard electrode potentials given in the Table , predict if the reaction between the following is feasible:
(a) Fe3+(aq) and I–(aq)
(b) Ag+(aq) and Cu(s)
(c) Fe3+ (aq) and Cu(s)
(d) Ag(s) and Fe3+(aq)
(e) Br2(aq) and Fe2+(aq).

Question 8. 27 Predict the products of electrolysis in each of the following:
(i) An aqueous solution of AgNO3 with silver electrodes
(ii) An aqueous solution AgNO3 with platinum electrodes
(iii) A dilute solution of H2SO4 with platinum electrodes
(iv) An aqueous solution of CuCl2 with platinum electrodes.

Question 8. 28 Arrange the following metals in the order in which they displace each other from the solution of their salts. Al, Cu, Fe, Mg and Zn.

Question 8. 29 Given the standard electrode potentials, K+/K = –2.93V, Ag+/Ag = 0.80V, Hg2+/Hg = 0.79V Mg2+/Mg = –2.37V. Cr3+/Cr = –0.74V arrange these metals in their increasing order of reducing power.

Question 8. 30 Depict the galvanic cell in which the reaction Zn(s) + 2Ag+(aq) → Zn2+(aq) +2Ag(s) takes place, Further show:
(i) which of the electrode is negatively charged,
(ii) the carriers of the current in the cell, and
(iii) individual reaction at each electrode.


Chapter 9 Hydrogen


Question 9.1 Justify the position of hydrogen in the periodic table on the basis of its electronic configuration.

Question 9.2 Write the names of isotopes of hydrogen. What is the mass ratio of these isotopes?

Question 9.3 Why does hydrogen occur in a diatomic form rather than in a monoatomic form under normal conditions?

Question 9.4 How can the production of dihydrogen, obtained from 'coal gasification', be increased ?

Question 9.5 Describe the bulk preparation of dihydrogen by electrolytic method. What is the role of an electrolyte in this process ?

Question 9.6 Complete the following reactions:
(i) H2 (g ) + MmOo (s)Δ→
(ii) ( ) ( ) 2 catalyst CO g + H gΔ →
(iii) ( ) ( ) 3 8 2 catalyst C H g + 3H O g Δ →
(iv) Zn(s) + NaOH(aq) heat→

Question 9.7 Discuss the consequences of high enthalpy of H–H bond in terms of chemical reactivity of dihydrogen.

Question 9.8 What do you understand by (i) electron-deficient, (ii) electron-precise, and (iii) electron-rich compounds of hydrogen? Provide justification with suitable examples.

Question 9.9 What characteristics do you expect from an electron-deficient hydride with respect to its structure and chemical reactions?

Question 9.10 Do you expect the carbon hydrides of the type (CnH2n + 2) to act as 'Lewis' acid or base? Justify your answer.

Question 9.11 What do you understand by the term "non-stoichiometric hydrides"? Do you expect this type of the hydrides to be formed by alkali metals? Justify your answer.

Question 9.12 How do you expect the metallic hydrides to be useful for hydrogen storage? Explain.

Question 9.13 How does the atomic hydrogen or oxy-hydrogen torch function for cutting and welding purposes ? Explain.

Question 9.14 Among NH3, H2O and HF, which would you expect to have highest magnitude of hydrogen bonding and why?

Question 9.15 Saline hydrides are known to react with water violently producing fire. Can CO2, a well known fire extinguisher, be used in this case? Explain.

Question 9.16 Arrange the following
(i) CaH2, BeH2 and TiH2 in order of increasing electrical conductance.
(ii) LiH, NaH and CsH in order of increasing ionic character.
(iii) H–H, D–D and F–F in order of increasing bond dissociation enthalpy.
(iv) NaH, MgH2 and H2O in order of increasing reducing property.

Question 9.17 Compare the structures of H2O and H2O2.

Question 9.18 What do you understand by the term 'auto-protolysis' of water? What is its significance?

Question 9.19 Consider the reaction of water with F2 and suggest, in terms of oxidation and reduction, which species are oxidised/reduced.

Question 9.20 Complete the following chemical reactions.
(i) ( ) ( ) 2 2 PbS s + H O aq →
(ii) – ( ) ( ) 4 2 2 MnO aq + H O aq →
(iii) ( ) ( ) 2 CaO s + H O g →
(v) ( ) ( ) 3 2 AlCl g + H O l →
(vi) ( ) ( ) 3 2 2 Ca N s + H O l → Classify the above into

(a) hydrolysis,
(b) redox and
(c) hydration reactions.

Question 9.21 Describe the structure of the common form of ice.

Question 9.22 What causes the temporary and permanent hardness of water ?

Question 9.23 Discuss the principle and method of softening of hard water by synthetic ionexchange resins.

Question 9.24 Write chemical reactions to show the amphoteric nature of water.

Question 9.25 Write chemical reactions to justify that hydrogen peroxide can function as an oxidising as well as reducing agent.

Question 9.26 What is meant by 'demineralised' water and how can it be obtained ?

Question 9.27 Is demineralised or distilled water useful for drinking purposes? If not, how can it be made useful?

Question 9.28 Describe the usefulness of water in biosphere and biological systems.

Question 9.29 What properties of water make it useful as a solvent? What types of compound can it (i) dissolve, and (ii) hydrolyse ?

Question 9.30 Knowing the properties of H2O and D2O, do you think that D2O can be used for drinking purposes?

Question 9.31 What is the difference between the terms 'hydrolysis' and 'hydration' ?

Question 9.32 How can saline hydrides remove traces of water from organic compounds?

Question 9.33 What do you expect the nature of hydrides is, if formed by elements of atomic numbers 15, 19, 23 and 44 with dihydrogen? Compare their behaviour towards water.

Question 9.34 Do you expect different products in solution when aluminium(III) chloride and potassium chloride treated separately with (i) normal water (ii) acidified water, and (iii) alkaline water? Write equations wherever necessary.

Question 9.35 How does H2O2 behave as a bleaching agent?

Question 9.36 What do you understand by the terms:
(i) hydrogen economy
(ii) hydrogenation
(iii) 'syngas'
(iv) water-gas shift reaction
(v) fuel-cell ?


(Chemistry) Chapter 10 The S -Block Elements


NCERT  Exercises Questions

Question 10.1 What are the common physical and chemical features of alkali metals ?

Question 10.2 Discuss the general characteristics and gradation in properties of alkaline earth metals.

Question 10.3 Why are alkali metals not found in nature ?

Question 10.4 Find out the oxidation state of sodium in Na2O2. 5.5 Explain why is sodium less reactive than potassium.

Question 10.6 Compare the alkali metals and alkaline earth metals with respect to (i) ionisation enthalpy (ii) basicity of oxides and (iii) solubility of hydroxides.

Question 10.7 In what ways lithium shows similarities to magnesium in its chemical behaviour?

Question 10.8 Explain why can alkali and alkaline earth metals not be obtained by chemical reduction methods?

Question 10.9 Why are potassium and caesium, rather than lithium used in photoelectric cells?

Question 10.10 When an alkali metal dissolves in liquid ammonia the solution can acquire different colours. Explain the reasons for this type of colour change.

Question 10.11 Beryllium and magnesium do not give colour to flame whereas other alkaline earth metals do so. Why ?

Question 10.12 Discuss the various reactions that occur in the Solvay process.

Question 10.13 Potassium carbonate cannot be prepared by Solvay process. Why ?

Question 10.14 Why is Li2CO3 decomposed at a lower temperature whereas Na2CO3 at higher temperature?

Question 10.15 Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the alkaline earth metals.
(a) Nitrates
(b) Carbonates
(c) Sulphates.

Question 10.16 Starting with sodium chloride how would you proceed to prepare
(i) sodium metal
(ii) sodium hydroxide
(iii) sodium peroxide
(iv) sodium carbonate ?

Question 10.17 What happens when
(i) magnesium is burnt in air
(ii) quick lime is heated with silica
(iii) chlorine reacts with slaked lime
(iv) calcium nitrate is heated ?

Question 10.18 Describe two important uses of each of the following :
(i) caustic soda
(ii) sodium carbonate
(iii) quicklime.

Question 10.19 Draw the structure of
(i) BeCl2 (vapour)
(ii) BeCl2 (solid).

Question 10.20 The hydroxides and carbonates of sodium and potassium are easily soluble in water while the corresponding salts of magnesium and calcium are sparingly soluble in water. Explain.

Question 10.21 Describe the importance of the following :
(i) limestone
(ii) cement
(iii) plaster of paris.

Question 10.22 Why are lithium salts commonly hydrated and those of the other alkali ions usually anhydrous?

Question 10.23 Why is LiF almost insoluble in water whereas LiCl soluble not only in water but also in acetone ?

Question 10.24 Explain the significance of sodium, potassium, magnesium and calcium in biological fluids.

approx 1:10
What happens when
(i) sodium metal is dropped in water ?
(ii) sodium metal is heated in free supply of air ?
(iii) sodium peroxide dissolves in water ?

Question 10.26 Comment on each of the following observations:
(a) The mobilities of the alkali metal ions in aqueous solution are Li+ < Na+ < K+ < Rb+ < Cs+
(b) Lithium is the only alkali metal to form a nitride directly.
(c) E0 for M2+ (aq) + 2e– → M(s) (where M = Ca, Sr or Ba) is nearly constant.

Question 10.27 State as to why
(a) a solution of Na2CO3 is alkaline ?
(b) alkali metals are prepared by electrolysis of their fused chlorides ?
(c) sodium is found to be more useful than potassium ?

Question 10.28 Write balanced equations for reactions between
(a) Na2O2 and water
(b) KO2 and water
(c) Na2O and CO2.

Question 10.29 How would you explain the following observations?
(i) BeO is almost insoluble but BeSO4 in soluble in water,
(ii) BaO is soluble but BaSO4 is insoluble in water,
(iii) LiI is more soluble than KI in ethanol.

Question 10.30 Which of the alkali metal is having least melting point ?
(a) Na
(b) K
(c) Rb
(d) Cs

Question 10.31 Which one of the following alkali metals gives hydrated salts ?
(a) Li
(b) Na
(c) K
(d) Cs

Question 10.32 Which one of the alkaline earth metal carbonates is thermally the most stable ?
(a) MgCO3
(b) CaCO3
(c) SrCO3
(d) BaCO3


(Chemistry) Chapter 11 The P -Block Elements


NCERT Exercises Questions

Question 11.1 Discuss the pattern of variation in the oxidation states of (i) B to Tl and (ii) C to Pb.

Question 11.2 How can you explain higher stability of BCl3 as compared to TlCl3 ?

Question 11.3 Why does boron triflouride behave as a Lewis acid ?

Question 11.4 Consider the compounds, BCl3 and CCl4. How will they behave with water ? Justify.

Question 11.5 Is boric acid a protic acid ? Explain.

Question 11.6 Explain what happens when boric acid is heated .

Question 11.7 Describe the shapes of BF3 and BH4 –. Assign the hybridisation of boron in these species.

Question 11.8 Write reactions to justify amphoteric nature of aluminium.

Question 11.9 What are electron deficient compounds ? Are BCl3 and SiCl4 electron deficient species ? Explain.

Question 11.10 Write the resonance structures of CO3 2–and HCO3 – .

Question 11.11 What is the state of hybridisation of carbon in (a) CO3 2– (b) diamond (c) graphite?

Question 11.12 Explain the difference in properties of diamond and graphite on the basis of their structures.

Question 11.13 Rationalise the given statements and give chemical reactions : • Lead(II) chloride reacts with Cl2 to give PbCl4. • Lead(IV) chloride is highly unstable towards heat. • Lead is known not to form an iodide, PbI4.

Question 11.14 Suggest reasons why the B–F bond lengths in BF3 (130 pm) and BF4 – (143 pm) differ.

Question 11.15 If B–Cl bond has a dipole moment, explain why BCl3 molecule has zero dipole moment.

Question 11.16 Aluminium trifluoride is insoluble in anhydrous HF but dissolves on addition of NaF. Aluminium trifluoride precipitates out of the resulting solution when gaseous BF3 is bubbled through. Give reasons.

Question 11.17 Suggest a reason as to why CO is poisonous.

Question 11.18 How is excessive content of CO2 responsible for global warming ?

Question 11.19 Explain structures of diborane and boric acid.

Question 11.20 What happens when (a) Borax is heated strongly,
(b) Boric acid is added to water,
(c) Aluminium is treated with dilute NaOH,
(d) BF3 is reacted with ammonia ?

Question 11.21 Explain the following reactions
(a) Silicon is heated with methyl chloride at high temperature in the presence of copper;
(b) Silicon dioxide is treated with hydrogen fluoride;
(c) CO is heated with ZnO;
(d) Hydrated alumina is treated with aqueous NaOH solution.

Question 11.22 Give reasons :
(i) Conc. HNO3 can be transported in aluminium container.
(ii) A mixture of dilute NaOH and aluminium pieces is used to open drain.
(iii) Graphite is used as lubricant.
(iv) Diamond is used as an abrasive.
(v) Aluminium alloys are used to make aircraft body.
(vi) Aluminium utensils should not be kept in water overnight.
(vii) Aluminium wire is used to make transmission cables.

Question 11.23 Explain why is there a phenomenal decrease in ionization enthalpy from carbon to silicon ?

Question 11.24 How would you explain the lower atomic radius of Ga as compared to Al ?

Question 11.25 What are allotropes? Sketch the structure of two allotropes of carbon namely diamond and graphite. What is the impact of structure on physical properties of two allotropes?

Question 11.26 (a) Classify following oxides as neutral, acidic, basic or amphoteric: CO, B2O3, SiO2, CO2, Al2O3, PbO2, Tl2O3 (b) Write suitable chemical equations to show their nature.

Question 11.27 In some of the reactions thallium resembles aluminium, whereas in others it resembles with group I metals. Support this statement by giving some evidences.

Question 11.28 When metal X is treated with sodium hydroxide, a white precipitate (A) is obtained, which is soluble in excess of NaOH to give soluble complex (B). Compound (A) is soluble in dilute HCl to form compound (C). The compound (A) when heated strongly gives (D), which is used to extract metal. Identify (X), (A), (B), (C) and (D). Write suitable equations to support their identities.

Question 11.29 What do you understand by (a) inert pair effect (b) allotropy and (c) catenation?

Question 11.30 A certain salt X, gives the following results.
(i) Its aqueous solution is alkaline to litmus.
(ii) It swells up to a glassy material Y on strong heating.
(iii) When conc. H2SO4 is added to a hot solution of X,white crystal of an acid Z separates out. Write equations for all the above reactions and identify X, Y and Z.

Question 11.31 Write balanced equations for:
(i) BF3 + LiH →
(ii) B2H6 + H2O →
(iii) NaH + B2H6 →
(iv) H3BO3→Δ
(v) Al + NaOH →
(vi) B2H6 + NH3 →

Question 11.32. Give one method for industrial preparation and one for laboratory preparation of CO and CO2 each.

Question 11.33 An aqueous solution of borax is
(a) neutral
(b) amphoteric
(c) basic
(d) acidic

Question 11.34 Boric acid is polymeric due to
(a) its acidic nature
(b) the presence of hydrogen bonds
(c) its monobasic nature
(d) its geometry

Question 11.35 The type of hybridisation of boron in diborane is
(a) sp
(b) sp2
(c) sp3
(d) dsp2

Question 11.36 Thermodynamically the most stable form of carbon i
(a) diamond
(b) graphite
(c) fullerenes
(d) coal

Question 11.37 Elements of group 14
(a) exhibit oxidation state of +4 only
(b) exhibit oxidation state of +2 and +4
(c) form M2– and M4+ ion
(d) form M2+ and M4+ ions

Question 11.38 If the starting material for the manufacture of silicones is RSiCl3, write the structure of the product formed


(Chemistry) Chapter 12 Organic Chemistry – Some Basic Principles And Techniques


NCERT Exercises Questions

Question 12.1 What are hybridisation states of each carbon atom in the following compounds ? CH2=C=O, CH3CH=CH2, (CH3)2CO, CH2=CHCN, C6H6

Question 12.2 Indicate the σ and π bonds in the following molecules : C6H6, C6H12, CH2Cl2, CH2=C=CH2, CH3NO2, HCONHCH3

Question 12.3 Write bond line formulas for : Isopropyl alcohol, 2,3-Dimethyl butanal, Heptan-4- one.

Question 12.4 Give the IUPAC names of the following compounds :

Question 12.5 Which of the following represents the correct IUPAC name for the compounds concerned ?
(a) 2,2-Dimethylpentane or 2-Dimethylpentane
(b) 2,4,7- Trimethyloctane or 2,5,7-Trimethyloctane
(c) 2-Chloro-4-methylpentane or 4-Chloro-2-methylpentane
(d) But-3-yn-1-ol or But-4-ol-1-yne.

Question 12.6 Draw formulas for the first five members of each homologous series beginning with the following compounds
(a) H–COOH
(b) CH3COCH3
(c) H–CH=CH2

Question 12.7 Give condensed and bond line structural formulas and identify the functional group(s) present, if any, for :
(a) 2,2,4-Trimethylpentane
(b) 2-Hydroxy-1,2,3-propanetricarboxylic acid
(c) Hexanedial

Question 12.8 Identify the functional groups in the following compounds

Question 12.9 Which of the two: O2NCH2CH2O– or CH3CH2O– is expected to be more stable and why ?

Question 12.10 Explain why alkyl groups act as electron donors when attached to a π system.

Question 12.11 Draw the resonance structures for the following compounds. Show the electron shift using curved-arrow notation.
(a) C6H5OH
(b) C6H5NO2
(c) CH3CH=CHCHO
(d) C6H5–CHO
(e) 6 5 2 C H CH + −
(f) 3 2 CH CH CHCH + =

Question 12.12 What are electrophiles and nucleophiles ? Explain with examples.

Question 12.13 Identify the reagents shown in bold in the following equations as nucleophiles or electrophiles :
(a) 3 3 2 CH COOH + HO– → CH COO− + H O
(b) ( ) ( )( ) 3 3 3 2 CH COCH + → CH C CN OH – CN
(c) 6 5 6 5 3 C H + → C H COCH + 3 CH CO

Question 12.14 Classify the following reactions in one of the reaction type studied in this unit.
(a) 3 2 3 2 CH CH Br + HS− → CH CH SH
(b) ( ) ( ) 3 2 2 3 2 CH C = CH + HCl → CH ClC −
(c) 3 2 2 2 2 CH CH Br + HO− → CH = CH + H O
(d) ( ) ( ) 3 3 2 3 2 2 CH C − CH OH + HBr → CH CBrCH CH

Question 12.15 What is the relationship between the members of following pairs of structures ? Are they structural or geometrical isomers or resonance contributors ?

Question 12.16 For the following bond cleavages, use curved-arrows to show the electron flow and classify each as homolysis or heterolysis. Identify reactive intermediate produced as free radical, carbocation and carbanion.

Question 12.17 Explain the terms Inductive and Electromeric effects. Which electron displacement effect explains the following correct orders of acidity of the carboxylic acids?
(a) Cl3CCOOH > Cl2CHCOOH > ClCH2COOH
(b) CH3CH2COOH > (CH3)2CHCOOH > (CH3)3C.COOH

Question 12.18 Give a brief description of the principles of the following techniques taking an example in each case.
(a) Crystallisation
(b) Distillation
(c) Chromatography

Question 12.19 Describe the method, which can be used to separate two compounds with different solubilities in a solvent S.

Question 12.20 What is the difference between distillation, distillation under reduced pressure and steam distillation ?

Question 12.21 Discuss the chemistry of Lassaigne's test 12.22 Differentiate between the principle of estimation of nitrogen in an organic compound by (i) Dumas method and (ii) Kjeldahl's method.

Question 12.23 Discuss the principle of estimation of halogens, sulphur and phosphorus present in an organic compound.

Question 12.24 Explain the principle of paper chromatography.

Question 12.25 Why is nitric acid added to sodium extract before adding silver nitrate for testing halogens?

Question 12.26 Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen, sulphur and halogens.

Question 12.27 Name a suitable technique of separation of the components from a mixture of calcium sulphate and camphor.

Question 12.28 Explain, why an organic liquid vaporises at a temperature below its boiling point in its steam distillation ?

Question 12.29 Will CCl4 give white precipitate of AgCl on heating it with silver nitrate? Give reason for your answer.

Question 12.30 Why is a solution of potassium hydroxide used to absorb carbon dioxide evolved during the estimation of carbon present in an organic compound?

Question 12.31 Why is it necessary to use acetic acid and not sulphuric acid for acidification of sodium extract for testing sulphur by lead acetate test?

Question 12.32 An organic compound contains 69% carbon and 4.8% hydrogen, the remainder being oxygen. Calculate the masses of carbon dioxide and water produced when 0.20 g of this substance is subjected to complete combustion.

Question 12.33 A sample of 0.50 g of an organic compound was treated according to Kjeldahl's method. The ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M solution of NaOH for neutralisation. Find the percentage composition of nitrogen in the compound.

Question 12.34 0.3780 g of an organic chloro compound gave 0.5740 g of silver chloride in Carius estimation. Calculate the percentage of chlorine present in the compound.

Question 12.35 In the estimation of sulphur by Carius method, 0.468 g of an organic sulphur compound afforded 0.668 g of barium sulphate. Find out the percentage of sulphur in the given compound.

Question 12.36 In the organic compound CH2 = CH – CH2 – CH2 – C ≡ CH, the pair of hydridised orbitals involved in the formation of: C2 – C3 bond is:
(a) sp – sp2
(b) sp – sp3
(c) sp2 – sp3
(d) sp3 – sp3

Question 12.37 In the Lassaigne's test for nitrogen in an organic compound, the Prussian blue colour is obtained due to the formation of:
(a) Na4[Fe(CN)6]
(b) Fe4[Fe(CN)6]3
(c) Fe2[Fe(CN)6]
(d) Fe3[Fe(CN)6]4

Question 12.38 Which of the following carbocation is most stable ?
(a) (CH3)3C. +C H2
(b) (CH3)3 +C
(c) CH3CH2 +C H2
(d) CH3 +C H CH2CH3

Question 12.39 The best and latest technique for isolation, purification and separation of organic compounds is:
(a) Crystallisation
(b) Distillation
(c) Sublimation
(d) Chromatography

Question 12.40 The reaction: CH3CH2I + KOH(aq) → CH3CH2OH + KI is classified as :
(a) electrophilic substitution
(b) nucleophilic substitution
(c) elimination
(d) addition


(Chemistry) Chapter 13 Hydrocarbons


NCERT Exercises Questions

Question 13.1 How do you account for the formation of ethane during chlorination of methane ?

Question 13.2 Write IUPAC names of the following compounds :
(a) CH3CH=C(CH3)2
(b) CH2=CH-C≡C-CH3

Question 13.3 For the following compounds, write structural formulas and IUPAC names for all possible isomers having the number of double or triple bond as indicated :
(a) C4H8 (one double bond)
(b) C5H8 (one triple bond)

Question 13.4 Write IUPAC names of the products obtained by the ozonolysis of the following compounds :
(i) Pent-2-ene
(ii) 3,4-Dimethyl-hept-3-ene
(iii) 2-Ethylbut-1-ene
(iv) 1-Phenylbut-1-ene

Question 13.5 An alkene 'A' on ozonolysis gives a mixture of ethanal and pentan-3- one. Write structure and IUPAC name of 'A'.

Question 13.6 An alkene 'A' contains three C – C, eight C – H σ bonds and one C – C π bond. 'A' on ozonolysis gives two moles of an aldehyde of molar mass 44 u. Write IUPAC name of 'A'.

Question 13.7 Propanal and pentan-3-one are the ozonolysis products of an alkene? What is the structural formula of the alkene?

Question 13.8 Write chemical equations for combustion reaction of the following hydrocarbons:
(i) Butane
(ii) Pentene
(iii) Hexyne
(iv) Toluene

Question 13.9 Draw the cis and trans structures of hex-2-ene. Which isomer will have higher b.p. and why?

Question 13.10 Why is benzene extra ordinarily stable though it contains three double bonds?

Question 13.11 What are the necessary conditions for any system to be aromatic?13.12 Explain why the following systems are not aromatic?

Question 13.13 How will you convert benzene into
(i) p-nitrobromobenzene
(ii) m- nitrochlorobenzene
(iii) p - nitrotoluene
(iv) acetophenone?

Question 13.14 In the alkane H3C – CH2 – C(CH3)2 – CH2 – CH(CH3)2, identify 1°,2°,3° carbon atoms and give the number of H atoms bonded to each one of these.

Question 13.15 What effect does branching of an alkane chain has on its boiling point?

Question 13.16 Addition of HBr to propene yields 2-bromopropane, while in the presence of benzoyl peroxide, the same reaction yields 1-bromopropane. Explain and give mechanism.

Question 13.17 Write down the products of ozonolysis of 1,2-dimethylbenzene (o-xylene). How does the result support Kekulé structure for benzene?

Question 13.18 Arrange benzene, n-hexane and ethyne in decreasing order of acidic behaviour. Also give reason for this behaviour.

Question 13.19 Why does benzene undergo electrophilic substitution reactions easily and nucleophilic substitutions with difficulty?

Question 13.20 How would you convert the following compounds into benzene?
(i) Ethyne
(ii) Ethene
(iii) Hexane

Question 13.21 Write structures of all the alkenes which on hydrogenation give 2-methylbutane.

Question 13.22 Arrange the following set of compounds in order of their decreasing relative reactivity with an electrophile, E+
(a) Chlorobenzene, 2,4-dinitrochlorobenzene, p-nitrochlorobenzene
(b) Toluene, p-H3C – C6H4 – NO2, p-O2N – C6H4 – NO2. 13.23 Out of benzene, m–dinitrobenzene and toluene which will undergo nitration most easily and why?

Question 13.24 Suggest the name of a Lewis acid other than anhydrous aluminium chloride which can be used during ethylation of benzene.

Question 13.25 Why is Wurtz reaction not preferred for the preparation of alkanes containing odd number of carbon atoms? Illustrate your answer by taking one example.


 (Chemistry) Chapter 14 Environmental Chemistry


NCERT Exercises Questions

Question 14. 1 Define environmental chemistry.

Question 14. 2 Explain tropospheric pollution in 100 words. 1

Question 14. 3 Carbon monoxide gas is more dangerous than carbon dioxide gas. Why?

Question 14. 4 List gases which are responsible for greenhouse effect.

Question 14. 5 Statues and monuments in India are affected by acid rain. How?

Question 14. 6 What is smog? How is classical smog different from photochemical smogs?

Question 14. 7 Write down the reactions involved during the formation of photochemical smog.

Question 14. 8 What are the harmful effects of photochemical smog and how can they be controlled?

Question 14. 9 What are the reactions involved for ozone layer depletion in the stratosphere?

Question 14. 10 What do you mean by ozone hole? What are its consequences?

Question 14. 11 What are the major causes of water pollution? Explain.

Question 14. 12 Have you ever observed any water pollution in your area? What measures would you suggest to control it?

Question 14. 13 What do you mean by Biochemical Oxygen Demand (BOD)?

Question 14. 14 Do you observe any soil pollution in your neighbourhood? What efforts will you make for controlling the soil pollution?

Question 14. 15 What are pesticides and herbicides? Explain giving examples.

Question 14. 16 What do you mean by green chemistry? How will it help decrease environmental pollution?

Question 14. 17 What would have happened if the greenhouse gases were totally missing in the earth's atmosphere? Discuss. 1

Question 14.18 A large number of fish are suddenly found floating dead on a lake. There is no evidence of toxic dumping but you find an abundance of phytoplankton. Suggest a reason for the fish kill.

Question 14. 19 How can domestic waste be used as manure?

Question 14. 20 For your agricultural field or garden you have developed a compost producing pit. Discuss the process in the light of bad odour, flies and recycling of wastes for a good produce.


 

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NCERT Mathematics Question Paper (Class - 11)

Posted: 01 Jun 2018 10:38 PM PDT

NCERT Mathematics Question Paper (Class - 11)


(Mathematics) : Chapter 1 Sets


EXERCISE 1.1

Question 1. Which of the following are sets ? Justify your asnwer.

(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter. (ix) A collection of most dangerous animals of the world.

Question 2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or in the blank spaces:

(i) 5. . .A
(ii) 8 . . . A
(iii) 0. . .A
(iv) 4. . . A
(v) 2. . .A
(vi) 10. . .A

Question 3. Write the following sets in roster form:

(i) A = {x : x is an integer and –3 < x < 7}
(ii) B = {x : x is a natural number less than 6}
(iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x : x is a prime number which is divisor of 60}
( v) E = The set of all letters in the word
(vi) F = The set of all letters in the word

Question 4. Write the following sets in the set-builder form :

(i) (3, 6, 9, 12}
(ii) {2,4,8,16,32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6, . . .} (v) {1,4,9, . . .,100}

Question 5. List all the elements of the following sets :

(i) A = {x : x is an odd natural number}
(ii) B = {x : x is an integer, 1 2 – < x 9 2 }
(iii) C = {x : x is an integer, x2 ≤ 4}
(iv) D = {x : x is a letter in the word "LOYAL"}
(v) E = {x : x is a month of a year not having 31 days}
(vi) F = {x : x is a consonant in the English alphabet which precedes k }.

Question 6. Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}
(ii) {2, 3} (b) {x : x is an odd natural number less than 10}
(iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.

EXERCISE 1.2

Question 1. 1Which of the following are examples of the null set]

(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) { x : x is a natural numbers, x < 5 and x > 7 }
(iv) { y : y is a point common to any two parallel lines}

Question 2. Which of the following sets are finite or infinite

(i) The set of months of a year
(ii) {1, 2, 3, . . .}
(iii) {1, 2, 3, . . .99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99

Question 3. State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0,0)

Question 4. In the following, state whether A = B or not:

(i) A = { a, b, c, d } B = { d, c, b, a }
(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}
(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }

Question 4. Are the following pair of sets equal ? Give reasons.

(i) A = {2, 3}, B = {x : x is solution of x2 + 5x + 6 = 0}
(ii) A = { x : x is a letter in the word FOLLOW} B = { y : y is a letter in the word WOLF}

Question 5. From the sets given below, select equal sets : A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2} E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

EXERCISE 1.3

Question 1. Make correct statements by filling in the symbols ⊂ or in the blank spaces :

(i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }
(ii) { a, b, c } . . . { b, c, d }
(iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school}
(iv) {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit}
(v) {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}
(vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}
(vii) {x : x is an even natural number} . . . {x : x is an integer}

Question 2. Examine whether the following statements are true or false:

(i) { a, b } { b, c, a }
(ii) { a, e } ⊂ { x : x is a vowel in the English alphabe t}
(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 }
(iv) { a }⊂ { a, b, c }
(v) { a }∈ { a, b, c }
(vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number which divides 36}

Question 3. Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

(i) {3, 4} ⊂ A
(ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A (iv) 1 ∈ A
(v) 1 ⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) φ ∈ A
(x) φ ⊂ A
(xi) {φ} ⊂ A

Question 4. Write down all the subsets of the following sets

(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) φ

Question 5. How many elements has P(A), if A = φ? 6. Write the following as intervals :

(i) {x : x ∈ R, – 4 < x ≤ 6}
(ii) {x : x ∈ R, – 12 < x < –10}
(iii) {x : x ∈ R, 0 ≤ x < 7}
(iv) {x : x ∈ R, 3 ≤ x ≤ 4}

Question 6. Write the following intervals in set-builder form :

(i) (– 3, 0)
(ii) [6 , 12]
(iii) (6, 12]
(iv) [–23, 5)

Question 7. What universal set(s) would you propose for each of the following :

(i) The set of right triangles.
(ii) The set of isosceles triangles.

Question 8. Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6}
(ii) φ
(iii) {0,1,2,3,4,5,6,7,8,9,10}
(iv) {1,2,3,4,5,6,7,8}

EXERCISE 1.4

Question 1. Find the union of each of the following pairs of sets :

(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = [ a, e, i, o, u} B = {a, b, c}
(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}
(iv) A = {x : x is a natural number and 1 < x ≤ 6 } B = {x : x is a natural number and 6 < x < 10 }
(v) A = {1, 2, 3}, B = φ

Question 2. Let A = { a, b }, B = {a, b, c}. Is A ⊂ B ? What is A ∪ B ?

Question 3. If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

Question 4. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) B ∪ D
(v) A ∪ B ∪ C
(vi) A ∪ B ∪ D
(vii) B ∪ C ∪ D

Question 5. Find the intersection of each pair of sets of question 1 above.

Question 6. If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find

(i) A ∩ B
(ii) B ∩ C
(iii) A ∩ C ∩ D
(iv) A ∩ C
(v) B ∩ D (vi) A ∩ (B ∪ C)
(vii) A ∩ D
(viii) A ∩ (B ∪ D)
(ix) ( A ∩ B ) ∩ ( B ∪ C ) (x) ( A ∪ D) ∩ ( B ∪ C)

Question 7. If A = {x : x is a natural number }, B = {x : x is an even natural number} C = {x : x is an odd natural number}andD = {x : x is a prime number }, find

(i) A ∩ B
(ii) A ∩ C
(iii) A ∩ D
(iv) B ∩ C
(v) B ∩ D
(vi) C ∩ D

Question 8. Which of the following pairs of sets are disjoint

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }
(ii) { a, e, i, o, u } and { c, d, e, f }
(iii) {x : x is an even integer } and {x : x is an odd integer} ]

Question 9. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find

(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C

Question 10. If X= { a, b, c, d } and Y = { f, b, d, g}, find

(i) X – Y
(ii) Y – X
(iii) X ∩ Y

Question 11. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

Question 12. State whether each of the following statement is true or false. Justify your answer.

(i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets.
(ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets.
(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.
(iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.
 

EXERCISE 1.5

Question 1. Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find

(i) A′
(ii) B′
(iii) (A ∪ C)′
(iv) (A ∪ B)′
(v) (A′)′
(vi) (B – C)′

Question 2. If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :

(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g} (iv) D = { f, g, h, a}

Question 3. Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {x : x is an even natural number}
(ii) { x : x is an odd natural number }
(iii) {x : x is a positive multiple of 3}
(iv) { x : x is a prime number }
(v) {x : x is a natural number divisible by 3 and 5}
(vi) { x : x is a perfect square }
(vii) { x : x is a perfect cube}
(viii) { x : x + 5 = 8 }
(ix) { x : 2x + 5 = 9} (x) { x : x ≥ 7 }
(xi) { x : x ∈ N and 2x + 1 > 10 }

Question 4. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that

(i) (A ∪ B)′ = A′ ∩ B′
(ii) (A ∩ B)′ = A′ ∪ B′

Question 5. Draw appropriate Venn diagram for each of the following :

(i) (A ∪ B)′
(ii) A′ ∩ B′
(iii) (A ∩ B)′,
(iv) A′ ∪ B′

Question 6. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?

Question 7. Fill in the blanks to make each of the following a true statement :

(i) A ∪ A′ = . . .
(ii) φ′ ∩ A = . . .
(iii) A ∩ A′ = . . .
(iv) U′ ∩ A = . . .

EXERCISE 1.6

Question 1. If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).

Question 2. If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements ; how many elements does X ∩ Y have?

Question 3. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Question 4. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

Question 5. If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Question 6. In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Question 7. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Question 8. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?


(Mathematics) : Chapter 2 Relations And Functions


EXERCISE  2.1

Qusetion 1. If 1 2 5 1 3 3 33 , find the values of x and y.

Question 2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

Question 3. If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

Question 4. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}.
(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.

Question 5. If A = {–1, 1}, find A × A × A. 6. If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

Question 6. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.

Question 7. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Question 8. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

Question 10. The Cartesian product A × A has 9 elements among which are found (–1, 0) and\ (0,1). Find the set A and the remaining elements of A × A

EXERCISE  2.2

Qusetion 1. Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range. 

Question 2. Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y ∈N}. Depict this relationship using roster form. Write down the domain and the range.

Question 3. A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

Question 4. The Fi 2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?

Question 5. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a , b ∈A, b is exactly divisible by a}.

(i) Write R in roster form
(ii) Find the domain of R
(iii) Find the range of R.

Question 6. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}.

Question 7. Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

Question 8. Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

Question 9. Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.

EXERCISE 2.3

Qusetion 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii) {(1,3), (1,5), (2,5)}.

Question 2. Find the domain and range of the following real functions: (i) f(x) = – x (ii) f(x) = 9 − x 2.

Question 3. A function f is defined by f(x) = 2x –5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3).

Question 4. The function 't' which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by tC) = 9C 5 + 3 2.Find

(i) t(0)
(ii) t(28)
(iii) t(–10)
(iv) The value of C, when t(C) = 212.

Question 5. Find the range of each of the following functions.

(i) f (x) = 2 – 3x, x ∈ R, x > 0.
(ii) f (x) = x2 + 2, x is a real number.
(iii) f (x) = x, x is a real number 


(Mathematics) : Chapter 3 Trigonometric Functions


EXERCISE 3. 1

Question 1. Find the radian measures corresponding to the following degree measures:

(i) 25°
(ii) – 47°30
(iii)240°
(iv) 520°

Question 2. Find the degree measures corresponding to the following radian measurs (Use π 22 7 = ).

(i) 11 16
(ii) – 4
(iii) 5π 3
(iv) 7π 6

Question 3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Question 4.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π 22 7 = ).

Question 5. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Question 6. If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Question 7. Find the angle in radian through which a pendulum swings if its length is 75 cm and th e tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

EXERCISE 3. 2

Find the values of other five trigonometric functions in Exercises 1 to 5.

Question 1. cos x = – 1 2 , x lies in third quadrant.

Question 2. sin x = 3 5, x lies in second quadrant.

Question 3. cot x = 4 3 , x lies in third quadrant.

Question 4. sec x = 13 5 , x lies in fourth quadrant.

Question 5. tan x = – 5 12 , x lies in second quadrant. Find the values of the trigonometric functions in Exercises 6 to 10.

Question 6. sin 765°

Question 7. cosec (– 1410°) 8. tan 19π 3 9. sin (– 11π 3 ) 10. cot (– 15π 4 )

EXERCISE  3. 3

Prove that:

Question 1. sin2 π 6 + cos2 3 π – tan2 – 1 4 2 π =

Question 2. 2sin2 6 π + cosec2 7 cos2 3 6 3 2 π π =

Question 3. cot2 cosec 5 3tan2 6 6 6 6 π π π + + =

Question 4. 2sin2 3 2cos2 2sec2 10 4 4 3 π π π + + =

Question 5. Find the value of:
(i) sin 75°
(ii) tan 15°

Find the principal and general solutions of the following equations:

Question 6. tan x = 3

Question 7. sec x = 2

Question 8. cot x = − 3

Question 9. cosec x = – 2

Find the general solution for each of the following equations:

Question 10. cos 4 x = cos 2 x

Question 11. cos 3x + cos x – cos 2x = 0

Question 12. sin 2x + cosx = 0 8. sec2 2x = 1– tan 2x


(Mathematics) : Chapter 4 Principle of Mathematical Induction 


EXERCISE 4.1

Prove the following by using the principle of mathematical induction for all n ∈ N:

Question 1. 1 + 3 + 32 + ... + 3n – 1 = (3 1) 2 n − .

Question 2. 13 + 23 + 33 + … +n3 = 2 ( 1) 2 n n + .

Question 3. 1 1 1 1 2 (1 2) (1 2 3) (1 2 3 ) ( 1) ... n ...n n + + + + = + + + + + + + .

Question 4. 1.2.3 + 2.3.4 +…+ n(n+1) (n+2) = ( 1)( 2)( 3) 4 n n + n + n + .

Question 5. 1.3 + 2.32 + 3.33 +…+ n.3n = (2 1)3 1 3 4 n − n+ + .

Question 6. 1.2 + 2.3 + 3.4 +…+ n.(n+1) = ( 1)( 2) 3 n n + n +.

Question 7. 1.3 + 3.5 + 57 +…+ (2n–1) (2n+1) = (4 2 6 1) 3 n n + n − .

Question 8. 1.2 + 2.22 + 3.22 + ...+n.2n = (n–1) 2n + 1 + 2.

Question 9. 1 1 1 ... 1 1 1 2 4 8 2n 2n + + + + = − .

Question 10. 1 1 1 ... 1 2.5 5.8 8.11 (3 1)(3 2) (6 4) n n n n + + + + = − + + .

Question 11. 1 1 1 ... 1 ( 3) 1.2.3 2.3.4 3.4.5 ( 1)( 2) 4( 1)( 2)

Question 12. a + ar + ar2 +…+ arn-1 = ( 1) 1 a rn r − − .

Question 13. 2 2 1 3 1 5 1 7 ... 1 (2 1) ( 1) 1 4 9 n n

Question 14. 12 + 32 + 52 + …+ (2n–1)2 = (2 1)(2 1) 3 n n − n + .

Question 15. 1 1 1 ... 1 1.4 4.7 7.10 (3 2)(3 1) (3 1) n n n n + + + + = − + + .

Question 16. 1 1 1 ... 1 3.5 5.7 7.9 (2 1)(2 3) 3(2 3) n n n n + + + + = + + + .

Question 17. 1 + 2 + 3 +…+ n < 1 8 (2n + 1)2.

Question 18. n (n + 1) (n + 5) is a multiple of 3.

Question 19. 102n – 1 + 1 is divisible by 11.

Question 20. x2n – y2n is divisible by x + y.

Question 21. 32n+2 – 8n – 9 is divisible by 8.

Question 22. 41n – 14n is a multiple of 27.

Question 23."> (2n + 7) < (n + 3)2.


(Mathematics) : Chapter 5 Complex Numbers and Quadratic Equations


EXERCISE 5.1

Question 1. z = – 1 – i

Question 2. z = – + i Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Question 3. 1 – i 4. – 1 + i 5. – 1 – i 6. – 3 7. + i 8. i

EXERCISE 5.2

Solve each of the following equations:

Question 1. x2 + 3 = 0

Question 2. 2x2 + x + 1 = 0

Question 3. x2 + 3x + 9 = 0

Question 4. – x2 + x – 2 = 0

Question 5. x2 + 3x + 5 = 0

Question 6. x2 – x + 2 = 0

Question 7. 2x2 + x + 2 = 0

Question 8. 3x2 − 2x + 3 3 = 0

Question 9. 2 1 0 2 x + x + =

Question 10. 2 1 0 2 x + x


(Mathematics) : Chapter 6 Linear Inequalities


EXERCISE 6.1

Question 1. Solve 24x < 100, when
(i) x is a natural number.
(ii) x is an integer.

Question 2.Solve – 12x > 30, when
(i) x is a natural number.
(ii) x is an integer.

Question 3. Solve 5x – 3 < 7, when
(i) x is an integer.
(ii) x is a real number.

Question 4. Solve 3x + 8 >2, when
(i) x is an integer.
(ii) x is a real number. Solve the inequalities in Exercises 5 to 16 for real x.

Question 5. 4x + 3 < 6x + 7

Question 6. 3x – 7 > 5x – 1

Question 7. 3(x – 1) ≤ 2 (x – 3)

Question 8.3 (2 – x) ≥ 2 (1 – x)

Question 9. 11 2 3 x + x + x <

Question 10. 1 3 2 x x > +

Question 11. 3( 2) 5(2 ) 5 3 x − − x ≤

Question 12. 1 3 4 1 ( 6) 2 5 3 x + ⎞≥ x −

Question 13. 2 (2x + 3) – 10 < 6 (x – 2)

Question 14. 37 – (3x + 5) > 9x – 8 (x – 3)

Question 15. (5 2) (7 3) 4 3 5 x x− x − < −

Question 16. (2 1) (3 2) (2 ) 3 4 5 x − x − − x ≥ −

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line

Question 17. 3x – 2 < 2x + 1

Question 18.
5x – 3 > 3x – 5

Question 19. 3 (1 – x) < 2 (x + 4)

Question 20. (5 2) (7 3) 2 3 5 x x − x − < −

Question 21. Ravi obtained 70 and 75 marks in first two unit test. Find the number if minimum marks he should get in the third test to have an average of at least 60 marks.

Question 22. To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.

Question 23. Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Question 24. Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

Question 25. The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

Question 26. A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second? [Hint: If x is the length of the shortest board, then x , (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x + (x + 3) + 2x ≤ 91 and 2x ≥ (x + 3) + 5]


(Mathematics) : Chapter 7 Permutations And Combinations


EXERCISE 7.1

Question 1.How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?

Question 2.How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Question 3.How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Question 4.How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Question 5.A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Question 6.Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

EXERCISE 7.2

Question 1.Evaluate
(i) 8 !
(ii) 4 ! – 3 !

Question 2.Is 3 ! + 4 ! = 7 ! ?

Question 3.Compute 8! 6!× 2!

Question 4.If 1 1 6! 7! 8! + = x , find x

Question 5.Evaluate ( ) ! ! n n − r , when
(i) n = 6, r = 2
(ii) n = 9, r = 5.

EXERCISE 7.3

Question 1.How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Question 2.How many 4-digit numbers are there with no digit repeated?

Question 3.How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Question 4.Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Question 5.From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?

Question 6.Find n if n – 1P3 : nP4 = 1 : 9.

Question 7.Find r if
(i) 5 6 Pr 2 Pr−1 =
(ii) 5 6 Pr Pr−1 = .

Question 8.How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Question 9.How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel?

Question 10.In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

Question 11.In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S, (ii) vowels are all together, (iii) there are always 4 letters between P and S?

EXERCISE 7.4

Question 1.If nC8 = nC2, find nC 2.

Question 2.Determine n if (i) 2nC2 : nC2 = 12 : 1 (ii) 2nC3 : nC3 = 11 : 1

Question 3.How many chords can be drawn through 21 points on a circle?

Question 4.In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Question 5.Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Question 6.Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Question 7.In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Question 8.A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Question 9.In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


(Mathematics) :  Chapter 8 Binomial Theorem


EXERCISE 8.1


Expand each of the expressions in Exercises 1 to 5. Using binomial theorem, evaluate each of the following:

 

Question 6. (96)3

Question 7. (102)5

Question 8. (101)4

Question 9. (99)5

Question 10. Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

Question 11. Find (a + b)4 – (a – b)4. Hence, evaluate ( 3 + 2)4– ( 3 – 2)4 .

Question 12. Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate ( 2 + 1)6 + ( 2 – 1)6.

Question 13. Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.

EXERCISE 8.2


Find the coefficient of

Question 1. x5 in (x + 3)8 2. a5b7 in (a – 2b)1

Question 2. Write the general term in the expansion of

Question 3. (x2 – y)6

Question 4. (x2 – yx)12, x ≠ 0.

Question 5. Find the 4th term in the expansion of (x – 2y)12.

Question 6. Find the 13th term in the expansion of 18 9 1 3 x x , x ≠ 0. Find the middle terms in the expansions of

Question 7. 3 7 6 3 − x

Question 8. 10 9 3 x + y

Question 9. In the expansion of (1 + a)m+n, prove that coefficients of am and an are equal.

Question 10. The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1 : 3 : 5. Find n and r.

Question 11. Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n – 1.

Question 12. Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6.


(Mathematics) : Chapter 9 Sequences and Series


EXERCISE 9.1


Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

Question 1.an = n (n + 2)

Question 2.an = 1 n n +

Question 3.an = 2n

Question 4.an = 2 3 6 n −

Question 5.an = (–1)n–1 5n+1

Question 6.an 2 5 4 n n + = . Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

Question 7.an = 4n – 3; a17, a24

Question 8.an = 2 7 ; 2n n a

Question 9.an = (–1)n – 1n3; a9 Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

Question 10.20 ( –2); n 3 a n n a n =

EXERCISE 9.2


Question 1.Find the sum of odd integers from 1 to 2001.

Question 2.Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Question 3.In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –11 2.

Question 4.How many terms of the A.P. – 6, 11 2 − , – 5, … are needed to give the sum –25?

Question 5.In an A.P., if pth term is 1 q and qth term is 1 p , prove that the sum of first pq terms is 1 2 (pq +1), where p ≠ q.

Question 6.If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 11 7 Find the last term. Find the sum to n terms of the A.P., whose kth term is 5k +1

Question 8.If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.

Question 9.The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

Question 10.If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms. 1

Question 11.Sum of the first p, q and r terms of an A.P are. a, b and c, respectively. Prove that a (q r) b (r p) c ( p q) 0 p q r − + − + − = 1

Question 12.The ratio of the sums of m and n terms of an A.P. is m2 : n 2.Show that the ratio of mth and nth term is (2m – 1) : (2n – 1). 1

Question 13.If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m. 1

Question 14.Insert five numbers between 8 and 26 such that the resulting sequence is an A.P. 1

Question 15.If 1 1 n n n n a b a − b − + + is the A.M. between a and b, then find the value of n.

Question 16.Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7th and (m – 1)th numbers is 5 9. Find the value of m.

Question 17.A man starts repaying a loan as first instalment of Rs. 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30th instalment?

Question 18.The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120° , find the number of the sides of the polygon.

EXERCISE 9.3


Question 1.Find the 20th and nth terms of the G.P. 5 5 5 2 4 8 , , , ...

Question 2.Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Question 3.The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.

Question 4.The 4th term of a G.P. is square of its second term, and the first term is – 3. Determine its 7th term.

Question 5.Which term of the following sequences: (a) 2,2 2,4,... is 128 ? (b) 3,3,3 3,...is729 ? (c) 1 1 1 is 1 3 9 27 19683 , , ,... ?

Question 6.For what values of x, the numbers 2 2 7 7 – ,x,– are in G.P.? Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10:

Question 7.0.15, 0.015, 0.0015, ... 20 terms.

Question 8.7 , 21 , 3 7 , ... n terms.

Question 9.1, – a, a2, – a3, ... n terms (if a ≠ – 1).

Question 10.x3, x5, x7, ... n terms (if x ≠ ± 1).

Question 11.Evaluate 11 1 (2 3k ) k = Σ + . 1

Question 12.The sum of first three terms of a G.P. is 39 10 and their product is 1. Find the common ratio and the terms.

Question 13.How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?

Question 14.The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 12 8. Determine the first term, the common ratio and the sum to n terms of the G.P.

Question 15.Given a G.P. with a = 729 and 7th term 64, determine S 7.

Question 16.Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.

Question 17.If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Question 18.Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

Question 19.Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1 2 20.

Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … ARn – 1 form a G.P, and find the common ratio.

Question 1.Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

Question 2.If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq – r br – pcP – q =1.

Question 3.If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.

Question 4.Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is 1 rn .

Question 5.If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2

Question 6.Insert two number between 3 and 81 so that the resulting sequence is G.P. 2

Question 7.Find the value of n so that a b a b n n n n + + + + 1 1 may be the geometric mean between a and b.

Question 8.The sum of two numbers is 6 times their geometric means, show that numbers are in the ratio (3+ 2 2 ): (3−2 2).

Question 9.If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A A G A G ( )( ) ± + −. 30.

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?

Question 1.What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Question 2.If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation

EXERCISE 9.4


Find the sum to n terms of each of the series in Exercises 1 to 7.

Question 1. 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 +...

Question 2. 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + ...

Question 3. 3 × 12 + 5 × 22 + 7 × 32 + ...

Question 4. 1 1 1 1 2 2 3 3 4 + + + × × × ...

Question 5. 52 + 62 + 72 + ... + 202

Question 6 .3 × 8 + 6 × 11 + 9 × 14 + ...

Question 7. 12 + (12 + 22) + (12 + 22 + 32) + ...

Find the sum to n terms of the series in Exercises 8 to 10 whose nth terms is given by

Question 8.n (n+1) (n+4).

Question 9.n2 + 2n

Question nbsp;10.(2n – 1)2

Miscellaneous Exercise On Chapter 9


Question 1.Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

Question 2.If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

Question 3.Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3(S2 – S1)

Question 4.Find the sum of all numbers between 200 and 400 which are divisible by 7.

Question 5.Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Question 6.Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Question 7.If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and 1 ( ) 120 n x f x = Σ = , find the value of n.

Question 8.The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms

Question 9.The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Question 10.The sum of three numbers in G.P. is 5 6.If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression.

Find the numbers.

Question 1.A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Question 2.The sum of the first four terms of an A.P. is 56.The sum of the last four terms is 12. If its first term is 11, then find the number of terms.

Question 3.If a bx a bx b cx b cx c dx c dx x + − = + − = + − ( ≠ 0) , then show that a, b, c and d are in G.P.

Question 4. Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn.

Question 5.The pth, qth and rth terms of an A.P. are a, b, c, respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0

Question 6.If a 1 1 ,b 1 1 ,c 1 1 b c c a a b are in A.P., prove that a, b, c are in A.P.

Question 7.If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.

Question 8.If a and b are the roots of x2 – 3x + p = 0 and c, d are roots of x2 – 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q – p) = 17:15.

Question 9.The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a :b = (m + m2 – n2 ): (m – m2 – n2 ) 20. If a, b, c are in A.P.; b, c, d are in G.P. and 1 , 1 ,1 c d e are in A.P. prove that a, c, e are in G.P.

Question 10.Find the sum of the following series up to n terms: (i) 5 + 55 +555 + … (ii) .6 +. 66 +. 666+…

Question 11.Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + ... + n terms.

Question 12.Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…

Question 13.If S1, S2, S3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9 22 S = S3 (1 + 8S1).

Question 14 .Find the sum of the following series up to n terms: 13 13 22 13 23 33 1 1 3 1 3 5... + + + + + + + + +

Question 15.Show that 2 2 2 2 2 2 1 2 2 3 ( 1) 3 5 1 2 2 3 ( 1) 3 1 ... n n n ... n n n × + × + + × + + = × + × + + × + + .

Question 16.A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

Question 17.Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Question 18.A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.


(Mathematics) : Chapter 10 Straight Lines


EXERCISE 10.1


Question 1. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

Question 2. The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

Question 3. Find the distance between P (x1, y1) and Q (x2, y2) when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.

Question 4. Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

Question 5. Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

Question 6. Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

Question 7. Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Question 8. Find the value of x for which the points (x, – 1), (2,1) and (4, 5) are collinear.

Question 9. Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

Question 10. Find the angle between the x-axis and the line joining the points (3,–1) and (4,–2).

Question 11. The slope of a line is double of the slope of another line. If tangent of the angle between them is 3 1 , find the slopes of the lines.

Question 12. A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).

Question 13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that + = 1 k b h a .

Question 14. Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?

EXERCISE 10.2

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions:

Question 1. Write the equations for the x-and y-axes.

Question 2. Passing through the point (– 4, 3) with slope 2 1 .

Question 3. Passing through (0, 0) with slope m.

Question 4. Passing through (2, 2 3)and inclined with the x-axis at an angle of 75o.

Question 5. Intersecting the x-axis at a distance of 3 units to the left of origin with slope –2.

Question 6. Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30o with positive direction of the x-axis.

Question 7. Passing through the points (–1, 1) and (2, – 4).

Question 8. Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 300.

Question 9. The vertices of Δ PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Question 10. Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).

Question 11. A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1: n. Find the equation of the line.

Question 12. Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Question 13. Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Question 14. Find equation of the line through the point (0, 2) making an angle 2π 3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Question 15. The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

Question 16. The length L (in centimetrs) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L= 125.134 when C = 110, express L in terms of C.

Question 17. The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

Question 18. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is + = 2 b y a x .

Question 19. Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

Question 20. By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear

EXERCISE 10.3

Question 1. Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts.
(i) x + 7y = 0, (ii) 6x + 3y – 5 = 0, (iii) y = 0.

Question 2. Reduce the following equations into intercept form and find their intercepts on the axes.
(i) 3x + 2y – 12 = 0, (ii) 4x – 3y = 6, (iii) 3y + 2 = 0.

Question 3. Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. (i) x – 3y + 8 = 0, (ii) y – 2 = 0, (iii) x – y = 4.

Question 4. Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).

Question 5. Find the points on the x-axis, whose distances from the line 1 3 4 x y + = are 4 units.

Question 6. Find the distance between parallel lines
(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l (x + y) + p = 0 and l (x + y) – r = 0.

Question 7. Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3).

Question 8. Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.

Question 9. Find angles between the lines 3x + y = 1and x + 3y = 1.

Question 10. The line through the points (h, 3) and (4, 1) intersects the line 7x − 9y −19 = 0. at right angle. Find the value of h .

Question 11. Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.

Question 12. Two lines passing through the point (2, 3) intersects each other at an angle of 60o. If slope of one line is 2, find equation of the other line.

Question 13. Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).

Question 14. Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.

Question 15. The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the values of m and c.

Question 16. If p and q are the lengths of perpendiculars from the origin to the lines x cosθ − ysin θ = k cos2θ and x sec θ + y cosec θ = k, respectively, prove that p2 + 4q2 = k2.

Question 17. In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.

Question 18. If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that .

Miscellaneous Exercise on Chapter 10

Question 1. Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin.

Question 2. Find the values of θ and p, if the equation x cos θ + y sinθ = p is the normal form of the line 3 x + y + 2 = 0.

Question 3. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.

Question 4. What are the points on the y-axis whose distance from the line 1 3 4 x + y = is 4 units.

Question 5. Find perpendicular distance from the origin of the line joining the points (cosθ, sin θ) and (cos φ, sin φ).

Question 6. Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x – 7y + 5 = 0 and 3x + y = 0.

Question 7. Find the equation of a line drawn perpendicular to the line 1 4 6 x + y = through the point, where it meets the y-axis.

Question 8. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.

Question 9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Question 10. If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0

Question 11. Find the equation of the lines through the point (3, 2) which make an angle of 45o with the line x – 2y = 3.

Question 12. Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

Question 13. Show that the equation of the line passing through the origin and making an angle θ with the line tan θ 1 tanθ y mx c is y m x m + = + = ±− .

Question 14. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

Question 15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.

Question 16. Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Question 17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Question 18. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.

Question 19. If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

Question 20. If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y +7 = 0 is always 10. Show that P must move on a line.

Question 21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

Question 22. A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

Question 23. Prove that the product of the lengths of the perpendiculars drawn from the points ( a2 − b2 ,0)and (− a2 − b2 ,0)to the line x cosθ y sin θ 1is b2 a b + = .

Question 24. A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.


(Mathematics) : Chapter 11 Conic Sections


EXERCISE 11.1

In each of the following Exercises 1 to 5, find the equation of the circle with

Question 1.centre (0,2) and radius2.

Question 2.centre (–2,3) and radius 4

Question 3.centre ( 4 , 1 2 1 ) and radius 12 1

Question 4.centre (1,1) and radius 2

Question 5.centre (–a, –b) and radius a2 − b 2.In each of the following Exercises 6 to 9, find the centre and radius of the circles.

Question 6.(x + 5)2 + (y – 3)2 = 36

Question 7.x2 + y2 – 4x – 8y – 45 = 0

Question 8.x2 + y2 – 8x + 10y – 12 = 0

Question 9.2x2 + 2y2 – x = 0

Question 10.Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16.

Question 11.Find the equation of the circle passing through the points (2,3) and (–1,1) and whose centre is on the line x – 3y – 11 = 0.

Question 12.Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

Question 13.Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Question 14.Find the equation of a circle with centre (2,2) and passes through the point (4,5).

Question1 5.Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?

EXERCISE 11.2

In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Question 1.y2 = 12x

Question 2.x2 = 6y

Question 3.y2 = – 8x

Question 4.x2 = – 16y

Question 5.y2 = 10x

Question 6.x2 = – 9y In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions:

Question 7.Focus (6,0); directrix x = – 6

Question 8.Focus (0,–3); directrix y = 3

Question 9.Vertex (0,0); focus (3,0)

Question 10.Vertex (0,0); focus (–2,0 )

Question 1.Vertex (0,0) passing through (2,3) and axis is along x-axis.

Question 2.Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.

EXERCISE 11.3

In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

Question 1. 2 2 1 36 16 x + y =

Question 2. 2 2 1 4 25 x + y =

Question 3. 2 2 1 16 9 x + y =

Question 4. 2 2 1 25 100 x + y =

Question 5. 2 2 1 49 36 x + y =

Question 6. 100 400 x2 y2 + = 1

Question 7. 36x2 + 4y2 = 144

Question 8. 16x2 + y2 = 16

Question 9. 4x2 + 9y2 = 36 In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions:

Question 10. Vertices (± 5, 0), foci (± 4, 0)

Question 11. Vertices (0, ± 13), foci (0, ± 5)

Question 12.Vertices (± 6, 0), foci (± 4, 0)

Question 13.Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)

Question 14.Ends of major axis (0, ± 5 ), ends of minor axis (± 1, 0)

Question 15.Length of major axis 26, foci (± 5, 0)

Question 16.Length of minor axis 16, foci (0, ± 6).

Question 17. Foci (± 3, 0), a = 4

Question 18.b = 3, c = 4, centre at the origin; foci on a x axis.

Question 19.Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).

Question 20. Major axis on the x-axis and passes through the points (4,3) and (6,2).

EXERCISE 11.4

In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

Question 1. 2 2 1 16 9 x – y =

Question 2. 2 2 1 9 27 y – x =

Question 3. 9y2 – 4x2 = 36

Question 4. 16x2 – 9y2 = 576

Question 5. 5y2 – 9x2 = 36

Question 6 .49y2 – 16x2 = 78 4 .In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions.

Question 7.Vertices (± 2, 0), foci (± 3, 0)

Question 8. Vertices (0, ± 5), foci (0, ± 8)

Question 9. Vertices (0, ± 3), foci (0, ± 5)

Question 10. Foci (± 5, 0), the transverse axis is of length 8.

Question 11.Foci (0, ±13), the conjugate axis is of length 2 4.

Question 2.Foci (± 3 5 , 0), the latus rectum is of length 8.

Question 3.Foci (± 4, 0), the latus rectum is of length 12.

Question 4.vertices (± 7,0), e = 3 4.

Question 5.Foci (0, ± 10 ), passing through (2,3)

Miscellaneous Exercise on Chapter 11

Question 1.If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Question 2.An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Question 3.The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Question 4.An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Question 5.A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Question 6.Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Question 7.A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Question 8.An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.


(Mathematics) : Chapter 12 Introduction To Three Dimensional Geometry


EXERCISE 12.1

Question 1. A point is on the x-axis. What are its y-coordinate and z-coordinates?

Question 2.A point is in the XZ-plane. What can you say about its y-coordinate?

Question 3.Name the octants in which the following points lie:
(1,. 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (2, – 4, –7).

Question 4.Fill in the blanks:
(i) The x-axis and y-axis taken together determine a plane known as_______.
(ii) The coordinates of points in the XY-plane are of the form _______.
(iii) Coordinate planes divide the space into ______ octants.

EXERCISE 12.2

Question 1. Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1) (ii) (–3, 7, 2) and (2, 4, –1)
(iii) (–1, 3, – 4) and (1, –3, 4) (iv) (2, –1, 3) and (–2, 1, 3).

Question 2.Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.

Question 3.Verify the following:
(i) (0, 7, –10), (1, 6, – 6) and (4, 9, – 6) are the vertices of an isosceles triangle.
(ii) (0, 7, 10), (–1, 6, 6) and (– 4, 9, 6) are the vertices of a right angled triangle.
(iii) (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram

Question 4.Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).

Question 5.Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10.

EXERCISE 12.3

Question 1. Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Question 2.Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

Question 3.Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

Question 4.Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and C 0 1 2 3 are collinear.

Question 5.Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

Miscellaneous Exercise on Chapter 12

Question 1. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

Question 2.Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

Question 3.If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

Question 4.Find the coordinates of a point on y-axis which are at a distance of 5 2 from the point P (3, –2, 5).

Question 5.A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [Hint Suppose R divides PQ in the ratio k :1.The coordinates of the point R are given by , 10 4 1 , 3 1 8 2 k k k k k ]. .


(Mathematics) : Chapter 13 Limits And Derivatives


EXERCISE 13.1

Evaluate the following limits in Exercises 1 to 22.

Question 1. 3 lim 3 x x → +

Question 2. π lim 22 x 7 x →

Question 3. 2 1 limπ r r →

Question 4. 4 lim 4 3 x 2 x → x + −

Question 5. 10 5 1 lim 1 x 1 x x → − x + + −

Question 6. ( )5 0 1 1 lim x x → x + −

Question 7. 2 2 2 lim 3 10 x 4 x x → x − − −

Question 8. 4 3 2 lim 81 x 2 5 3 x → x x − − −

Question 9. 0 lim x 1 ax b → cx + +

Question 10. 1 3 1 1 6 lim 1 1 z z z → − −

Question 11. 2 1 2 lim , 0 x ax bx c a b c → cx bx a + + + + ≠ + +

Question 12. 2 1 1 lim 2 x 2 x →− x + +

Question 13. 0 lim sin x ax → bx

Question 14. 0 lim sin , , 0 x sin ax a b → bx ≠

Question 15. ( ) π ( ) sin π lim x π π x → x − −

Question 16. 0 lim cos x π x → − x

Question 17. 0 limcos 2 1 x cos 1 x → x − −

Question 18. 0 lim cos x sin ax x x → b x +

Question 19. 0 lim sec x x x →

Question 20. 0 lim sin , , 0 x sin ax bx a b a b → ax bx + + ≠ + ,

Question 21. 0 lim (cosec cot ) x x x → −

Question 22. π 2 lim tan 2π 2 x x → x −

Question 23. Find ( ) 0 lim x f x → and ( ) 1 lim x f x → , where ( ) ( ) 2 3, 0 3 1, 0 x x f x x x + ≤ = +>

Question 24. Find ( ) 1 lim x f x → , where ( ) 2 2 1, 1 1, 1 x x f x x x − ≤ = − − >

Question 25. Evaluate ( ) 0 lim x f x → , where ( ) | |, 0 0, 0 x x f x x x ≠ = =

Question 26. Find ( ) 0 lim x f x → , where ( ) , 0 | | 0, 0 x x f x x x ≠ = =

Question 27. Find ( ) 5 lim x f x → , where f (x) = | x | −5

Question 28. Suppose ( ) , 1 4, 1 , 1 a bx x fx x b ax x + <= = − > and if 1 lim x→ f (x) = f (1) what are possible values of a and b?

Question 29. Let a1, a2, . . ., an be fixed real numbers and define a function f (x) = (x − a1 ) (x − a2 )...(x − an ) . What is 1 lim x→a (x) ? For some a ≠ a1, a2, ..., an, compute lim x→a f (x).

Question 30. If ( ) 1, 0 0, 0 1, 0 x x f x x x x + < = = − > . For what value (s) of a does lim x→a f (x) exists?

Question 31. If the function f(x) satisfies ( ) 1 2 2 lim π x 1 f x → x − = − , evaluate ( ) 1 lim x f x → .

Question 32. If ( ) 2 3 , 0 , 0 1 , 1 mx n x f x nx m x nx m x + < = + ≤ ≤ + > . For what integers m and n does both ( ) 0 lim x f x → and ( ) 1 lim x f x → exist?

EXERCISE 13.2

Question 1. Find the derivative of x2 – 2 at x = 10.

Question 2. Find the derivative of 99x at x = l00.

Question 3. Find the derivative of x at x = 1.

Question 4. Find the derivative of the following functions from first principle.
(i) x3 − 27
(ii) (x −1)(x − 2)
(iii) 2 1 x
(iv) 1 1 x x + −

Question 5. For the function ( ) 100 99 2 .1 100 99 2 f x = x + x + + x + x + . Prove that f ′(1) =100 f ′(0) .

Question 6. Find the derivative of xn + axn−1 + a2 xn−2 + . . .+ an−1x + an for some fixed real number a.

Question 7. For some constants a and b, find the derivative of
(i) (x − a) (x − b)
(ii) ( )ax2 b 2 +
(iii) x a x b − −

Question 8. Find the derivative of xn an x a − − for some constant a.

Question 9. Find the derivative of
(i) 2 3 4 x −
(ii) (5x3 + 3x −1) (x −1)
(iii) x−3 (5 + 3x)
(iv) x5 (3 − 6x−9 )
(v) x−4 (3 − 4x−5 )
(vi) 2 2 1 3 1 x x x − + −

Question 10. Find the derivative of cos x from first principle.

Question 11. Find the derivative of the following functions:
(i) sin x cos x
(ii) sec x
(iii) 5sec x + 4cos x
(iv) cosec x
(v) 3cot x + 5cosec x
(vi) 5sin x − 6cos x + 7
(vii) 2tan x − 7sec x


(Mathematics) : Chapter 14 Mathematical Reasoning 


EXERCISE 14.1

Question 1.Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.

Question 2.Give three examples of sentences which are not statements. Give reasons for the answers.

EXERCISE 14.2

Question 1.Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu
(ii) 2 is not a complex number
(iii) All triangles are not equilateral triangle
(iv) The number 2 is greater than 7.
(v) Every natural number is an integer.

Question 2.Are the following pairs of statements negations of each other:
(i) The number x is not a rational number. The number x is not an irrational number.
(ii) The number x is a rational number. The number x is an irrational number.

Question 3.Find the component statements of the following compound statements and check whether they are true or false.
(i) Number 3 is prime or it is odd.
(ii) All integers are positive or negative.
(iii) 100 is divisible by 3, 11 and 5.

EXERCISE 14.3


Question 1.For each of the following compound statements first identify the connecting words and then break it into component statements.
(i) All rational numbers are real and all real numbers are not complex.
(ii) Square of an integer is positive or negative.
(iii) The sand heats up quickly in the Sun and does not cool down fast at night.
(iv) x = 2 and x = 3 are the roots of the equation 3x2 – x – 10 = 0.

Question 2.Identify the quantifier in the following statements and write the negation of the statements.
(i) There exists a number which is equal to its square.
(ii) For every real number x, x is less than x +1.
(iii) There exists a capital for every state in India.

Question 3.Check whether the following pair of statements are negation of each other. Give reasons for your answer.
(i) x + y = y + x is true for every real numbers x and y.
(ii) There exists real numbers x and y for which x + y = y + x. 4. State whether the "Or" used in the following statements is "exclusive "or" inclusive. Give reasons for your answer.
(i) Sun rises or Moon sets.
(ii) To apply for a driving licence, you should have a ration card or a passport.
(iii) All integers are positive or negative. 

EXERCISE 14.4


Question 1.Rewrite the following statement with "if-then" in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

Question 2.Write the contrapositive and converse of the following statements.
(i) If x is a prime number, then x is odd. (ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that x is divisible by 4.

Question 3.Write each of the following statements in the form "if-then"
(i) You get a job implies that your credentials are good.
(ii) The Bannana trees will bloom if it stays warm for a month.
(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.
(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.

Question 4.Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes.
(i) If you do not have winter clothes, then you do not live in Delhi.
(ii) If you have winter clothes, then you live in Delhi.
(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. 

EXERCISE 14.5

Question 1.Show that the statement p: "If x is a real number such that x3 + 4x = 0, then x is 0" is true by
(i) direct method,
(ii) method of contradiction,
(iii) method of contrapositive

Question 2.Show that the statement "For any real numbers a and b, a2 = b2 implies that a = b" is not true by giving a counter-example.

Question 3.Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2 is even, then x is also even.

Question 4.By giving a counter example, show that the following statements are not true.
(i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
(ii) q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.

Question 5.Which of the following statements are true and which are false? In each case give a valid reason for saying so.
(i) p: Each radius of a circle is a chord of the circle.
(ii) q: The centre of a circle bisects each chord of the circle.
(iii) r: Circle is a particular case of an ellipse.
(iv) s: If x and y are integers such that x > y, then –x < – y. (v) t : 11 is a rational number.

Miscellaneous Exercise on Chapter 14

Question 1.Write the negation of the following statements:
(i) p: For every positive real number x, the number x – 1 is also positive.
(ii) q: All cats scratch.
(iii) r: For every real number x, either x > 1 or x <1.
(iv) s: There exists a number x such that 0 < x <1.

Question 2.State the converse and contrapositive of each of the following statements:
(i) p: A positive integer is prime only if it has no divisors other than 1 and itself .
(ii) q: I go to a beach whenever it is a sunny day.
(iii) r: If it is hot outside, then you feel thirsty.

Question 3.Write each of the statements in the form "if p, then q"
(i) p: It is necessary to have a password to log on to the server.
(ii) q: There is traffic jam whenever it rains.
(iii) r: You can access the website only if you pay a subsciption fee.

Question 4.Rewrite each of the following statements in the form "p if and only if q"
(i) p: If you watch television, then your mind is free and if your mind is free, then you watch television.
(ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
(iii) r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Question 5.Given below are two statements p :
25 is a multiple of 5.q : 25 is a multiple of 8. Write the compound statements connecting these two statements with "And" and "Or". In both cases check the validity of the compound statement.

Question 6. Check the validity of the statements given below by the method given against it.
(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).
(ii) q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).

Question 7. Write the following statement in five different ways, conveying the same meaning. p: If a triangle is equiangular, then it is an obtuse angled triangle. 


 (Mathematics) : Chapter 15 Statistics


EXERCISE 15.1

Find the mean deviation about the mean for the data in Exercises 1 and 2.

Question 1. 4, 7, 8, 9, 10, 12, 13, 17

Question 2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Find the mean deviation about the median for the data in Exercises 3 and 4.

Question 3. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Question 4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Find the mean deviation about the mean for the data in Exercises 5 and 6.

Question 5. xi 5 10 15 20 25 f i 7 4 6 3 5

Question 6. xi 10 30 50 70 90 f i 4 24 28 16 8

Find the mean deviation about the median for the data in Exercises 7 and 8.

Question 7. xi 5 7 9 10 12 15 f i 8 6 2 2 2 6

Question 8. xi 15 21 27 30 35 f i 3 5 6 7 8

Find the mean deviation about the mean for the data in Exercises 9 and 10.

Question 9. Income 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
per day Number 4 8 9 10 7 5 4 3
of persons

Question 10. Height 95-105 105-115 115-125 125-135 135-145 145-155
in cms
Number of 9 13 26 30 12 10
boys

Question 11. Find the mean deviation about median for the following data :
Marks 0-10 10-20 20-30 30-40 40-50 50-60
Number of 6 8 14 16 4 2
Girls

Question 12. Calculate the mean deviation about median age for the age distribution of 100 persons given below:
Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55
Number 5 6 12 14 26 12 16 9

EXERCISE 15.2

Find the mean and variance for each of the data in Exercies 1 to 5.

Question 1. 6, 7, 10, 12, 13, 4, 8, 12

Question 2. First n natural numbers

Question 3. First 10 multiples of 3

Question 4. xi 6 10 14 18 24 28 30 fi 2 4 7 12 8 4 3

Question 5. xi 92 93 97 98 102 104 109 f i 3 2 3 2 6 3 3

Question 6. Find the mean and standard deviation using short-cut method.
xi 60 61 62 63 64 65 66 67 68
f i 2 1 12 29 25 12 10 4 5

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.

Question 7. Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequencies 2 3 5 10 3 5 2

Question 8. Classes 0-10 10-20 20-30 30-40 40-50
Frequencies 5 8 15 16 6

Question 9. Find the mean, variance and standard deviation using short-cut method
Height 70-75 75-80 80-85 85-90 90-95 95-100 100-105105-110 110-115
in cms No. of 3 4 7 7 15 9 6 6 3
children

Question 10. The diameters of circles (in mm) drawn in a design are given below:
Diameters 33-36 37-40 41-44 45-48 49-52 No. of circles 15 17 21 22 25 Calculate the standard deviation and mean diameter of the circles.[ Hint First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]


EXERCISE 15.3

Question 1. From the data given below state which group is more variable, A or B?
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7

Question 2. From the prices of shares X and Y below, find out which is more stable in value:
X 35 54 52 53 56 58 52 50 51 49
Y 108 107 105 105 106 107 104 103 104 101

Question 3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: Firm A Firm B No. of wage earners 586 648 Mean of monthly wages Rs 5253 Rs 5253 Variance of the distribution 100 121 of wages
(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm, A or B, shows greater variability in individual wages?

Question 4. The following is the record of goals scored by team A in a football session:
No. of goals scored 0 1 2 3 4
No. of matches 1 9 7 5 3
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Question 5. The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: 50 1 i 212 i x = Σ = , 50 2 1 i 902 8 i x . = Σ = , 50 1 i 261 i y = Σ = , 50 2 1 i 1457 6 i y . = Σ = Which is more varying, the length or weight?


 (Mathematics) : Chapter 16 Probability


  EXERCISE 16.1


1 to 7, describe the sample space for the indicated experiment.

Question 1.A coin is tossed three times.

Question 2.A die is thrown two times.

Question 3.A coin is tossed four times.

Question 4.A coin is tossed and a die is thrown.

Question 5.A coin is tossed and then a die is rolled only in case a head is shown on the coin

Question 6.2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Question 7. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

Question 8. An experiment consists of recording boy–girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?

Question 9.A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Question 10. An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

Question 11.Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non – defective(N). Write the sample space of this experiment.

Question 12.A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

Question 13.The numbers 1, 2, 3 and 4 are written separatly on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

Question 14.An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Question 15.A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Question&nbsnbsp;16.A die is thrown repeatedly untill a six comes up. What is the sample space for this experiment?

EXERCISE 16.2

Question 1.A die is rolled. Let E be the event "die shows 4" and F be the event "die shows even number". Are E and F mutually exclusive?

Question 2.A die is thrown. Describe the following events
(i) A: a number less than 7
(ii) B: a number greater than 7
(iii) C: a multiple of 3
(iv) D: a number less than 4
(v) E: an even number greater than 4
(vi) F: a number not less than 3 Also find A ∪ B, A ∩ B, E ∪ F, D ∩ E, A – C, D – E, F′, E ∩ F′,

Question 3.An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: A: the sum is greater than 8, B: 2 occurs on either die C: the sum is at least 7 and a multiple to 3 Which pairs of these events are mutually exclusive?

Question 4.Three coins are tossed once. Let A denote the event 'three heads show", B denote the event "two heads and one tail show", C denote the event" three tails show and D denote the event 'a head shows on the first coin". Which events are
(i) mutually exclusive?
(ii) simple?
(iii) Compound?

Question 5.Three coins are tossed. Describe
(i) Two events which are mutually exclusive .
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.

Question 6.Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice ≤

Question 5.Describe the events
(i) A′
(ii) not B
(iii) A or B
(iv) A and B
(v) A but not C
(vi) B or C
(vii) B and C
(viii) A ∩ B′ ∩ C′

Question 7. Refer to question 6 above, state true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B′
(iv) A and C are mutually exclusive (v) A and B′ are mutually exclusive. (vi) A′, B′, C are mutually exclusive and exhaustive.

EXERCISE 16.3

Question 1.Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = { } ω1,ω2 ,ω3,ω4 ,ω5 ,ω6 ,ω7

Question 2.A coin is tossed twice, what is the probability that atleast one tail occurs?

Question 3.A die is thrown, find the probability of following events:
(i) A prime number will appear,
(ii) A number greater than or equal to 3 will appear,
(iii) A number less than or equal to one will appear,
(iv) A number more than 6 will appear,
(v) A number less than 6 will appear.

Question 4.A card is selected from a pack of 52 cards .
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is
(i) an ace
(ii) black card.

Question 5.A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is
(i) 3
(ii) 12

Question 6.There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

Question 7. A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Question 8.Three coins are tossed once. Find the probability of getting
(i) 3 heads
(ii) 2 heads
(iii) atleast 2 heads
(iv) atmost 2 heads
(v) no head
(vi) 3 tails
(vii) exactly two tails
(viii) no tail
(ix) atmost two tails

Question 9.If 11 2 is the probability of an event, what is the probability of the event 'not A'.

Question 10.A letter is chosen at random from the word 'ASSASSINATION'. Find the probability that letter is
(i) a vowel
(ii) a consonan

Question 11.In a lottery, a person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of Winning the prize in the game. [Hint order of the numbers is not important.]

Question 12.Given P(A) = 5 3 and P(B) = 51. Find P(A or B), if A and B are mutually exclusive events.

Question 13.If E and F are events such that P(E) = 4 1 , P(F) = 2 1 and P(E and F) = 8 1 , find
(i) P(E or F),
(ii) P(not E and not F).

Question 14.Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.

Question 15. A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0

Question 6.Determine
(i) P(not A)
(ii) P(not B) and
(iii) P(A or B)

Question 16. In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Question 17. In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0. 7. The probability of passing atleast one of them is 0.99. What is the probability of passing both?

Question 18. The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 01. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?

Question 20.In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student has opted NSS but not NCC.


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