## CBSEPORTAL.COM - : (Download) CBSE Class-10 2016-17 Sample Paper (Sindhi) |

- (Download) CBSE Class-10 2016-17 Sample Paper (Sindhi)
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- NCERT Mathematics Question Paper (Class - 12)

(Download) CBSE Class-10 2016-17 Sample Paper (Sindhi) Posted: 13 Feb 2017 04:07 AM PST ## (Download) CBSE Class-10 2016-17 Sample Paper And Marking Scheme (Sindhi)
## Section – B, Writing (Short composition)
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(Download) CBSE Class-10 2016-17 Sample Paper (Sherpa) Posted: 13 Feb 2017 04:02 AM PST ## (Download) CBSE Class-10 2016-17 Sample Paper (Sherpa)
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NCERT Mathematics Question Paper (Class - 12) Posted: 13 Feb 2017 03:07 AM PST
## NCERT Mathematics Question Paper (Class - 12)## :: Chapter 1 - Number System ::
(ii) Relation R in the set N of natural numbers defined as (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as (iv) Relation R in the set Z of all integers defined as (i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y) : x and y work at the same place} 3. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.4. Show that the relation R in R defined as R = {(a, b) : a ? b}, is reflexive and transitive but not symmetric. 5. Check whether the relation R in R defined by R = {(a, b) : a ? b3} is reflexive, symmetric or transitive. 6. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive. 7. Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation. 8. Show that the relation R in the set A = {1, 2, 3, 4, 5} given byR = {(a, b) : |a – b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.9. Show that each of the relation R in the set A = {x ? Z : 0 ? x ? 12}, given by(i) R = {(a, b) : |a – b| is a multiple of 4}(ii) R = {(a, b) : a = b} ## :: Chapter 2 - Inverse Trigonometric Functions ::## EXERCISE
Question 6. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive. Question 7. Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.
Question 9. Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by (i) R = {(a, b) : |a – b| is a multiple of 4} (ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.
(ii) Transitive but neither reflexive nor symmetric. (iii) Reflexive and symmetric but not transitive. (iv) Reflexive and transitive but not symmetric. (v) Symmetric and transitive but not reflexive. Question 11. Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with origin as centre. Question 12. Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related? Question 13. Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5? Question 14. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
(B) R is reflexive and transitive but not symmetric. (C) R is symmetric and transitive but not reflexive. (D) R is an equivalence relation.
(B) (3, 8) ∈ R (C) (6, 8) ∈ R (D) (8, 7) ∈ R ## EXERCISEQuestion 1. Show that the function f : R → R defined by f (x) = 1 x is one-one and onto, where R is the set of all non-zero real numbers. Is the result true, if the domain R is replaced by N with co-domain being same as R?
(i) f : N → N given by f (x) = x2
State whether the function f is bijective. Justify your answer.
(C) f is one-one but not onto (D) f is neither one-one nor onto.
(B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto. ## EXERCISE## |

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