Relation & Function
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JEE Mains Pattern
Mathematics : Relation and Function
Practice Paper – 02
sin 1 3 x
1. The domain of the function f x is
ln(| x | 2)
(A) 2, 4 (B) (2,3) (3,4] (C) [2, ) (D) (, 3) [2, )
2. The domain of f x log | logx | is
(A) 0, (B) 1, (C) 0,1 1, (D) ,1
3. The domain of the function
1
f x contains the points
10
Cx 1 3 Cx
10
(A) 9, 10, 11 (B) 9, 10,12
(C) all natural numbers (D) none of these
4.
The range of the function f x cot 1 2x x 2 is
(A) (0, ) (B) 0, (C) , (D) ,
4 4 4 2
x2 1
5. The range of sin 1 2 is
x 2
(A) 0, / 2 (B) 0, / 6 (C) [ / 6, / 2) (D) none of these
sec1 x
6. The function f x , where [x] denotes the greatest integer less than or equal
x x
to x, is defined for all x
(A) R (B) R 1,1 n : n N
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(C) R 0,1 (D) R n : n N
2 | x | 1
7. The domain of f(x) = cos1 log 3 x is
4
(A) 2,6 (B) [6,2) 2,3 (C) 6, 2 (D) 2, 2 2,3
1
8. The domain of the function f(x) = log is
| sin x |
(A) R , (B) R n : n Z
(C) R 2n : n Z (D) ,
The domain of the function f x x 2 x , where [x] = greatest integer less than or
2
9.
equal to x, is
(A) R (B) [0, ) (C) (,0] (D) none of these
10. If f(x) = ax7 + bx3 + cx – 5; a, b, c are real constants and f 7 7 , then the range of
f(7) + 17 cos x is
(A) 34,0 (B) 0,34 (C) 34,34 (D) none of these
e x e|x|
11. The range of the function f x x |x|
e e
(A) , (B) [0, 1) (C) (1,0] (D) 1,1
1
12. The domain of the function f x , where {.} denotes the
sin x sin x
fractional part, is
n
(A) R ~ n (B) R ~ 2n (C) R (D) R ~
2
13. The range of the function f defined by
1
f x [where [.] and {.}, respectively, denote the greatest integer and the
sin x
fractional part] is
(A) I, the set of integers (B) N, the set of natural numbers
(C) W, the set of whole numbers (D) {2, 3, 4, ……}
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14. Let f x | x | x , (where {.} denotes the fractional part of x and X, Y are its
domain and range, respectively), then
1 1
(A) X , and Y ,
2 2
1 1
(B) X , [0, ) and Y ,
2 2
1
(C) X , [0, ) and Y 0,
2
(D) none of these
15.
The domain of the function : f x ln (|x|1) x 2 4x 4 is
(A) 3, 1 1,2 (B) 2, 1 [2, )
(C) (, 3] (2, 1) 2, (D) none of these
16. The domain of the function f x sin cos x is
(A) R (B) 2n , 2n
2 2
3
(C) 2n , 2n (D) 2n, 2n
2 2 2
2x 3x 1 , where {.} denotes the fractional part in 1,1
2
17. The domain of f(x) =
, is
1 1 1
(A) 1,1 ,1 (B) 1, 0, 1
2 2 2
1 1
(C) 1, (D) ,1
2 2
1 1
18. The range of sin 1 x 2 cos 1 x 2 , where [.] denotes the greater integer
2 2
function, is
(A) , (B) (C) (D) none of these
2 2
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19. The domain of f(x) = sin 1 2x 2 3 , where [.] denotes the greatest integer function, is
3 3 3 5 5
(A) , (B) , 1 ,
2 2 2 2 2
5 5 5 5
(C) , (D) , 1 1,
2 2 2 2
20. The range of f(x) = | sin x | | cos x | , where [.] denotes the greatest integer function, is
(A) {0} (B) {0, 1} (C) {1} (D) none of these
x2 e
21. If f x log e 2 , then the range of f(x) is
x 1
(A) (0, 1) (B) [0, 1] (C) [0, 1) (D) (0, 1]
22. The range of f(x) = sin x cos x tan x sec x , x 0, , where [.] denote the
4
greatest integer function x , is
(A) {0,1} (B) 1,0,1 (C) 1 (D) none of these
23. Let A = {1, 2, 3} and let R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}. Then R is
(A) reflexive and symmetric but not transitive
(B) reflexive and transitive but not symmetric
(C) symmetric and transitive but not reflexive
(D) an equivalence relation
24. Let A = {a, b, c} and let R = {(a, a)(a, b), (b, a)}. Then, R is
(A) reflexive and symmetric but not transitive
(B) reflexive and transitive but not symmetric
(C) symmetric and transitive but not reflexive
(D) an equivalence relation.
25. Let A = {1, 2, 3} then total number of relations in A A is
(A) 23 (B) 26 (C) 29 (D) 212
26. Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b
a b. Then, R is
(A) reflexive but neither symmetric nor transitive
(B) symmetric but neither reflexive nor transitive
(C) transitive but neither reflexive nor symmetric
(D) an equivalence relation
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27. Let S be the set of all real numbers and let R be a relation on S, defined by a R b |a –
b| 1. Then, R is
(A) reflexive and symmetric but not transitive
(B) reflexive and transitive but not symmetric
(C) symmetric and transitive but not reflexive
(D) an equivalence relation.
28. Let W denote the words in the English dictionary. Define the relation R by
R = {(x, y)W × W| the words x and y have at least one letter in common}. Then, R is
(A) reflexive, symmetric and not transitive
(B) reflexive, symmetric and transitive
(C) reflexive, not symmetric and transitive
(D) not reflexive and symmetric
29. Let R = {(3, 3), (6, 6), (9, 9), (3,6), (3, 9), (9, 12), (3,12), (6, 12), (12, 12)}, be a relation
on the set
A = {3, 6, 9, 12} Then the relation is
(A) reflexive only (B) reflexive and transitive only
(C) reflexive and symmetric only (D) an equivalence relation
30. Let R be a relation on the set A of ordered pairs of positive integers defined by
(x, y)R(u, v) if and only if xv = yu, then
(A) R is equivalence (B) R is reflexive but not transitive
(C) R transitive but not reflexive (D) R is not symmetric
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