JEE Mathematics Relation and Functions MCQs Set D

Question. If a function f : [2, ∞) →B defined by f(x) = x² – 4x + 5 is a bijection, then B is equal to:
(a) [1, ∞)
(b) [5, ∞)
(c)   R
(d) [2, ∞)

Answer: A

Question. Let Φ(x)= ax-b/x-a, the range being all real numbers except a, and b = a². Then its inverse is:
(a) (ax – b)/(x – a)
(b) (bx – a)/(x – a)
(c) (x – a)/(ax – b)
(d) (a – bx)/(1 – ax)

Answer: A

Question. The domain of f(x) = cos^–1 (3x – 1) is :
(a) f (x)= 1-x/1+x
(b) f (x) = 3^{log x}
(c) f (x) = 3^x(x+1)
(d) none of these

Answer: A

Question. Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x) =x-2/x+3 Then :
(a) f is bijective
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) none of these

Answer: A

Question. The function f : R → R defined by f (x) = (x – 1) (x – 2) (x – 3) is
(a) onto but not one-one
(b) neither one-one nor onto
(c) one-one but not onto
(d) both one-one and onto

Answer: A

Question. Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the number of ordered pairs which when added to R make the R an equivalence relation is :
(a) 6
(b) None of these
(c) 5
(d) 7

Answer: A

Question. The function f : R → R defined by f (x) = sin x is :
(a) many one
(b) onto
(c) into
(d) one-one

Answer: A

Question. If the number of elements in set A is m and number of element in set B is n then find number of relation defined from A to B
(a) 2^mn
(b) 2^m+n
(c) 2^m–n
(d) 2^m/n

Answer: A

Question. In the above question, find Domain of R
(a) {9, 6, 3}
(b) {6, 4, 3}
(c) {9, 5, 3}
(d) {8, 1, 3}

Answer: A

Question. In the above question, find Range of R
(a) {1, 2, 3}
(b) {9, 5, 3}
(c) {9, 6, 3}
(d) {6, 4, 3}

Answer: A

Question. Which of the following is a function?
(a) { (1,2), (2,2), (3,2), (4,2)}
(b) { (1,2), (3,3), (2,3), (1,4)}
(c) {(1,4), (2,5), (1,6) , (3,9)}
(d) {(2,1), (2,2), (2,3), (2,4)}

Answer: A

Question. Function f (x) = x^–2 + x^–3 is-
(a) a rational function
(b) an inverse function
(c) None of these
(d) an irrational function

Answer: A

Question. If f(x) = 2|x – 2| – 3|x – 3|, then the value of f(x) when 2 < x < 3 is
(a) 5x – 13
(b) 5 – x
(c) x – 5
(d) None of these

Answer: A

Question. The relation R = { (1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is :
(a) reflexive only
(b) an equivalence relation
(c) transitive only
(d) symmetric only

Answer: A

Question. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. Then R^–1 is
(a) {(8, 11), (10, 13)}
(b) {(10, 13), (8, 11)}
(c) {(11, 18), (13, 10)}
(d) None of these

Answer: A

Question. If f : [0, 2]→ [0, 2] is a bijective function defined by f (x) = ax² + bx + c, where a, b, c are non-zero real numbers then Which of the following is one of the roots f (x) = 0 ?
(a) 1/a
(b) 1/b
(c) 1/c
(d) None of these

Answer: A

Question. If f : [0, 2]→ [0, 2] is a bijective function defined by f (x) = ax² + bx + c, where a, b, c are non-zero real numbers then
Which of the following is not a value of a ?
(a) 1
(b) 1/2
(c) –1/4
(d) – 1/2

Answer: A

Question. Find the range of f (x) = x– [x]
(a) [0, 1)
(b) (0, 1)
(c) [0, 1]
(d) [–1, 0)

Answer: A

Question. Range of f (x) = 3 + x – [x+2] will be
(a) [1, 2)
(b) [0, 2)
(c) [0, 1]
(d) [–1, 0)

Answer: A

Question. If X = {x1, x2, x3}, Y = (x1, x2, x3,x4,x5} and R1, is a relation from X to Y, then which of the followings are reflexive relation? (1) R1 : {(x1, x1), (x2, x2), (x3, x3)} (2) R1 : {(x1, x1), (x2, x2)} (3) R1 : {(x1, x1), (x2, x2),(x3, x3),(x1, x3),(x2, x4)} (4) R1 : {(x1, x1), (x2, x2),(x3, x3),(x4, x4)}
(a) 1 and 3 are correct
(b) 1 and 2 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct

Answer: A

Question. If X = {a, b, c} and Y = {a, b, c, d, e, f} then find which of the following relation are symmetric relation?
(1) R₁ : { } i.e. void relation
(2) R₃ : {(a, b), (b, a)(a, c)(c, a)(a, a)}
(3) Every null relation
(4) R₂ : {(a, b)}
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct

Answer: A

Question. If X = {a, b, c} and Y = {a, b, c, d, e} then which of thefollowing are transitive relation.
(1) R₁ = { }
(2) R₂ = {(a, a)}
(3) R₃ = {(a, a).(c, d)}
(4) R₄ = {(a, b), (b, c)(a, c)}
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct

Answer: A