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Home Explore Exam Corner- RELATION FUNCTION

Exam Corner- RELATION FUNCTION

Published by Willington Island, 2021-07-07 05:00:26

Description: LT-23 (G1) - JEE MAIN - RELATION FUNCTION-03-07

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Name ................................................ ONLINE JEE MAIN OBJECTIVE EXAM Batch.................... Roll No. ............... Relation functions Batch: LT.2023 (GROUP-1) 03- 07- 2021 23A/TP/M In part I (20 Questions). Each question has four options (A),(B), (C) & (D). Only one of these four option is correct. Each correct answer will be awarded four mark. One mark will be deducted for each incorrect answer. 1. IfA= {1, 2, 3, 4} which of the following is a function fromAto itself: 1) y = 2x 2) 2 (x - 1) 3) 2x - 5 4) {(x, y) / x + y = 5} 2. Let Aand B be two sets such that n A  B  6 . If three elements of A  B are (3, 2), (7, 5), (8, 5), then 1) A  3, 7,8 2) A  2,5, 7 3) A  2,5 4) A  7,8 3. Let A1, 2,3 B  1,3, 5 . If relation R fromAto B is given by 1, 3,2,5,3,3 then R–1 is: 1) 3,33,15,3 2) 1,3,2,5,3,3 3) 1,3,5,2 4) 3,1,5,2,3,3 4. The domain ofthe function f x  x  3 is: x3 1) 3 2) R 3 3 R 3 4) 3 5. How many relations are there between a set of 5 elements and a set of 8 elements: 1) 40 2) 402 3) 240 4) 85 6. IfAis a finite set and n (A) = m. Then n P A  A  1) 2m2 2) 2m 3) 22m 4) 2 7. Let A= {1,2,3,4}, B = {a,b,c,d,e} and R = {(1,a), (2,c), (3,a), (2,a)}. Then Range (R), 1) {a,b,c,d,e} 2) {1,2,3,4} 3) {1,2,3} 4) {a,c} 8. If two setsA and B are having 44 elements in common, then number of elements common to A  B and B A is 1) 44 2) 1900 3) 1936 4) 1976 9. If f  x  1   x2  1  1, x  0, then f(x) =  x  x2 1) x2 – 1 2) x2 – 2 3) x2 – 3 4) x2 – 4 l q l q10. Let A  a, b,c B  1,2 . Consider a relation R defined from set Ato Set B. Then R is equal to the subset of: 1) A 2) B 3) A x B 4) B x A x2  x 1 11. The domain of the function f (x)  x2  x  1 is 1) R 1 2) R 0, 1 3) R 4) R 1,1 12. The relation R defined on set A {x :| x | 3, xz} by R = {(x,y): y = |x|} is 1) {(–2,2), (–1,1), (–1,–1), (0,0), (1,1), (2,2)} 2) {(–2, –2), (–2,2), (–1,1), (0,0), (1, –2), (1,2), (2,–1), (2,–2)} 3) {(0,0), (1,1), (2,2)} 4) {(–2,2), (–1,1), (0,0), (1,1), (2,2)}

23A/TP/M 2 JEE-MATHS 13. If A  {2, 4} and B  {3, 4,5} , then A  BA  B is 1) {(2,2), (3,4), (4,2), (5,4)} 2) {(2,3), (4,3), (4,5)} 3) {(2,4), (3,4), (4,4), (4,5)} 4) {(4,2), (4,3), (4,4), (4,5} 14. If A  {1, 2,3}, B = {4,5,6}, which of the following is not a relation fromAto B 1) R = {(1,4), (1,5), (1,6)} 2) R = {(1,5), (2,4), (3,6)} 1 2 3) R = {(1,4), (1,5), (3,6), (2,6), (3,4)} 4) R = {(4,2), (2,6), (5,1), (2,4)} 3 4 15. Let R be a relation in N defined by R  {(x, y) : x  2y  8}. The range is 1) {2,4,6} 2) {1,2,3} 3) {1,2,3,4,6} 4) {1,2} 16. Let A {1, 2,3} . The total number of distinct relations which can be defined over A is 1) 6 2) 8 3) 29 4) 210 17. Range of the relation R  , a ,, b,c,  1) ,, , a, b, c 2) ,,  3) a, b,  4) ,, c 2x when x  3  f  x    x 2 when 1  x  3 18. 3x when x  1 Then f 1  f 2  f 4 is 1) 9 2) 14 3) 5 4) 3 19. If n(A) = p and n(B) = q. Number of relations from A to B is 32, then p2 + q2 1) 5 2) 17 3) 26 4) 37 20. Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is 1) 10! 2) 1010 3) 210 4) 210 1 In part II (5 Questions) answer to each question is a numerical figure from 0 to 999 both inclusive.No negative mark for incorrect answers. 21. If a function F is such that F (o) = 2, F (1) = 3, F (n + 2) = 2F (n) – F(n + 1) for n 0 , then F (5) is equal to | x| 22. If f(x) = x and e is any real number not equal to zero; then |f(e) - f(-e)| = ......: 23. If f (x) is a polynomial satisfying f ( x ). f  1   f (x)  f  1  and f (3) = 28, then f (4) is given by  x   x  24. If n A  B C  36 and n A  3, n(B)  2, the n(C)  25. Let Aand B are two sets having 3 elements in common. If n(A) =5 and n (B) =4, then nAB BA is equal to

Name ................................................ ONLINE JEE MAIN OBJECTIVE EXAM Batch.................... Roll No. ............... Relation functions Batch: LT.2023 (GROUP-1) 03- 07- 2021 23A/TP/M 1. 4 2. 1 since (3, 2), (7, 5), (8, 5)  A  B ; we have 3, 7, 8 A and 2, 5, 8 B 3. 4 R1   y, x;x, y  R  3,1,5, 2,3,3 4. 2 f x  is defined only when x  3  0, ie, when x  3 Df   R 3 5. 3 6. 1 7. 4 8. 3 n A  B  B A  n A  BB  A = nA  B nB  A = 44 44 1936 9. 3 f  x  1    x  1 2  3  f (x)  x2  3  x   x  10. 3 R = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}=Ax B 11. 3 Df  x  R : x2  x 1  0 ;   R : x  1  3i   R x   2 12. 4 13. 4 14. 4 R4  A  B 15. 2 16. 2 17. 3 18. 1 19. 3 2pq = 3n Þ pq = 5 Þ p2 + q2 = 1 + 25 = 26 20. 2 The total number of functions from A to A containing distinct elements is nn. Hence required number of functions = 1010. 21. 13 F (2) = 2F (0) – F (1) = 22 31 ; similarly F(3) 5 , F(4)   3 F(5)  2F(3)  F(4)  253 = 10+ 3 = 13 22. 2 23. 65 24. 6 25. 9


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