Class 11 Mathematics Relations and Functions MCQs

Question. Domain of √a²-x²(a > 0) is
(a) (– a, a)
(b) [– a, a]
(c) [0, a]
(d) (– a, 0]

Answer : B
 

Question. If A is the null set and B is an infinite set, then what is A×B ?
(a) Infinite set
(b) f
(c) Undefined
(d) A singleton set

Answer :  C
 

Question. The domain and range of the real function f defied by f(x) = 4-x /x-4 is given by
(a) Domain = R, Range = {–1, 1}
(b) Domain = R – {1}, Range = R
(c) Domain = R – {4}, Range = {–1}
(d) Domain = R – {– 4}, Range = {–1, 1}

Answer : C


Question. If A = {1, 2, 3}, B = {1, 2} and C = {2, 3}, which one of the following is correct ?
(a) (A´B)Ç(B´A) = (A´C)Ç(B´C)
(b) (A´B)Ç(B´A) = (C´A)Ç(C´B)
(c) (A´B)È(B´A) = (A´B)È(B´C)
(d) (A´B)È(B´A) = (A´B)È(A´C)

Answer : C
 

Question. If f (x) = x³-1/x³ , then f (x) +f(1/x) is equal to
(a) 2 x³
(b) 2. 1/x³
(c) 0
(d) 1

Answer : C


Question. Consider the following statements :
(i) If n (A) = p and n (B) = q then n (A × B) = pq
(ii) A × f = f
(iii) In general, A × B ¹ B × A
Which of the above statements are true ?
(a) only (i)
(b) only (ii)
(c) only (iii)
(d) All the above

Answer : D


Question. If A × B = { (5, 5), (5, 6), (5, 7), (8, 6), (8, 7), (8, 5)},then the value A.
(a) {5}
(b) {8}
(c) {5, 8}
(d) {5, 6, 7, 8}

Answer : C


Question. Let y2 = 4ax, a ¹ 0 , Now consider the following statements:
(1) y = 2 ax expresses y as a function of x
(2) y = – 2 ax expresses y as a function of x
(3) y = ± 2 ax expresses y as a function of x
Which of these is/are correct ?
(a) 1 and 2
(b) 1 and 3
(c) 2 and 3
(d) 3 only

Answer : A


Question. Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is
(a) mn
(b) nm – 1
(c) mn – 1
(d) 2mn – 1

Answer : D


Question. If aN = {ax : x Î N} and bN Ç cN = dN, where b, c Î N are relatively prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None

Answer :  A


Question. Let R = {(2, 3), (3, 4)} be relation defined on the set of natural numbers. The minimum number of ordered pairs required to be added in R so that enlarged relation becomes an equivalence relation is :
(a) 3
(b) 5
(c) 7
(d) 9

Answer : D
 

Question. If the domain of the function f(x) = x2 – 6x + 7 is (– ∞, ∞), then the range of function is:
(a) [– 2, ∞)
(b) (– ∞, ∞)
(c) (– 2, + 1)
(d) (– ∞, – 2)

Answer : A

Question. Which of the following relation is a function ?
(a) {(a, b) (b, e) (c, e) (b, x)}
(b) {(a, d) (a, m) (b, e) (a, b)}
(c) {(a, d) (b, e) (c, d) (e, x)}
(d) {(a, d) (b, m) (b, y) (d, x)}

Answer : C


Question. If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7,then the number of relations from A to B is
(a) 29
(b) 92
(c) 32
(d) 29 – 1

Answer : A
 

Question. The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}is given
(a) {(1, 4), (2, 5), (3, 6),.....}
(b) {(4, 1), (5, 2), (6, 3),.....}
(c) {(1, 3), (2, 6), (3, 9),.....}
(d) none of these

Answer : B

Question. The range of the function f(x) = ^{7- x} P _x-3 is
(a) {1, 2, 3, 4, 5}
(b) {1, 2, 3, 4, 5,6}
(c) {1, 2, 3, 4,}
(d) {1, 2, 3,}

Answer : D
 

Question. The range of the function 
f(x) = √(x -1)(3 - x) is :
(a) [– 1, 1]
(b) (– 1, 1)
(c) (– 3, 3)
(d) (– 3, 1)

Answer : A
 

Question. If f (x) = 3x4 – 5x2 + 9, then value of f (x – 1) is
(a) 3x4 + 12x³ + 13x² + 2x + 7
(b) 3x4 – 12x³ – 13x² – 2x – 7
(c) 3x4 – 12x³ + 13x² – 2x + 7
(d) 3x4 – 12x³ – 13x² + 2x + 7

Answer : C
 

Question. If f(x) = (x – 1) (x – 3)(x – 4)(x – 6) + 19 for all real value of x is
(a) positive
(b) negative
(c) zero
(d) none of these

Answer : A


Question. If f : R ® R is defined by f(x) = 3x + | x | , then f(2x) – f (– x) – 6x =
(a) f(x)
(b) 2f(x)
(c) – f(x)
(d) f(– x)

Answer : A


Question. Let R be a relation in the set of real numbers defined as a R b iff | a – b | ≥ 1/2 . Then the relation R is:
(a) an equivalence relation
(b) reflexive and symmetric but not transitive
(c) symmetric and transitive but not reflexive
(d) symmetric but neither reflexive nor transitive

Answer : D
 

Question. If P, Q and R are subsets of a set A, then R × (PC È QC)C equals.
(a) (R´ P)Ç(R´Q)
(b) (R´Q)Ç(R´ P)
(c) (R´ P)È(R´Q)
(d) None of these

Answer : A
 

Question. If g(x) = 1 +√x and f [g (x)] = 3 + 2√x + x , then
f(x) =
(a) 1 + 2x²
(b) 2 + x²
(c) 1 + x
(d) 2 + x

Answer : B
 

Question. If f(x) = 2x + 2-x/2  , then f(x + y). f(x – y) =
(a) 1/2 [f(2x) + f (2y)]
(b) 1/4[f (2x) f (2y)]
(c) 1/2[f (2x) f (2y)]
(d) 1/4[f (2x) f (2y)]

Answer : A 
 

Question. If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function described by the formula, g (x) = a x + b then what values should be assigned to a and b ?
(a) a = 1, b = 1
(b) a = 2, b = – 1
(c) a = 1, b = – 2
(d) a = – 2, b = – 1

Answer : B 

Question. The range of the function f (x) = ^7–xP_x–3 is :
(a) {1, 2, 3, 4}
(b) {1, 2, 3, 4, 5}
(c) {1, 2, 3}
(d) {1, 2, 3, 4, 5, 6}

Answer : C
 

Question. Domain of the function
f (x) =√( 2 - 2x - x²) is :
(a) - √3 ≤ x ≤ + √3
(b) -1- √3 ≤ x ≤ -1+ √3
(c) -2 ≤ x ≤ 2
(d) -2 + √3 ≤ x ≤-2 -√3

Answer : B
 

Question. f (x) = √(x 1) (x 3) /(x 2) = is a real valued function in the domain
(a) (-∞, -1] ∪ [3,∞)
(b) (-∞, -1] ∪ (2,3]
(c) [-1, 2) ∪ [3, ∞)
(d) none of these

Answer : C


Question. Total number of equivalence relations defined in the set S = {a, b, c } is :
(a) 5
(b) 3!
(c) 23
(d) 33

Answer : A
 

Question. For the following relation
R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0),
(0, 2), (0, 1)}
(a) domain = {0, 1}
(b) range = {0, 1, 2}
(c) both correct
(d) none of these

Answer : B
 

Question. Which one of the following is the domain of the relation R defined on the set N of natural numbers as R = {(m, n): 2m + 3n = 30 m , nÎN}?
(a) {2, 4, 6, 8}
(b) {3, 7, 11, 15}
(c) {3, 6, 9, 12}
(d) {3, 6, 9, 12, 15}

Answer : C