Chapter-2 Relations and Functions MCQs QUESTIONS WITH ANSWERS

 Chapter-2 Relations and Functions

Q1. If f(x) = (a – x)^1/n, a > 0 and n ∈ N, then the value of f(f(x)) is
(a) 1/x
(b) x
(c) x²
(d) x^1/2

Q2. The domain of the definition of the real function f(x) = √(log₁₂ x² ) of the real variable x is
(a) x > 0
(b) |x| ≥ 1
(c) |x| > 4
(d) x ≥ 4

Q3. If f(x) = e^x and g(x) = log_e x then the value of fog (1) is
(a) 0
(b) 1
(c) -1
(d) None of these

Q4. Two functions f and g are said to be equal if f
(a) the domain of f = the domain of g
(b) the co-domain of f = the co-domain of g
(c) f(x) = g(x) for all x
(d) all of above

Q5. A function f(x) is said to be an odd function if
(a) f(-x) = f(x)
(b) f(-x) = -f(x)
(c) f(-x) = k * f(x) where k is a constant
(d) None of these

Q6. If f(x) is an odd differentiable function on R, then df(x)/dx is a/an
(a) Even function
(b) Odd function
(c) Either even or odd function
(d) Neither even nor odd function

Q7. The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period
(a) 4
(b) 6
(c) 12
(d) 24

Q8. If f(x) = log₃ x and A = (3, 27) then f(A) =
(a) (1, 1)
(b) (3, 3)
(c) (1, 3)
(d) (2, 3)

Q9. The domain of tan^-1 (2x + 1) is
(a) R
(b) R -{1/2}
(c) R -{-1/2}
(d) None of these

Q10. the function f(x) = x – [x] has period of
(a) 0
(b) 1
(c) 2
(d) 3

Q11. If f(x) =(3x – 2)/(2x – 3) then the value of f(f(x)) is
(a) x
(b) x²
(c) x³
(d) None of these

Q12. Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to
(a) 2x + 1
(b) 2x² + 1
(c) (2x + 1)²
(d) None of these

Q13. A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is
(a) (0, 4, 4)
(b) (0, -4, 4)
(c) (0, -4, -4)
(d) None of these

Q14. The number of binary operations on the set {a, b} are
(a) 2
(b) 4
(c) 8
(d) 16

Q15. If f is an even function and g is an odd function the fog is a/an
(a) Even function
(b) Odd function
(c) Either even or odd function
(d) Neither even nor odd function

Q16. The domain of the function f(x) = 1/(x² – 3x + 2) is
(a) {1, 2}
(b) R
(c) R – {1, 2}
(d) R – {1, -2}

Q17. The domain of the function f(x) = sin^-1 (tan x) is
(a) -π/4 ≤ x ≤ π/4
(b) nπ – π/4 ≤ x ≤ nπ + π/4
(c) nπ – π/3 ≤ x ≤ nπ + π/3
(d) -π/3 ≤ x ≤ π/3

Q18. Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is
(a) {7, -5, -3}
(b) {-7, 5, -3}
(c) {-7, -5, 3}
(d) {-7, -5, -3}

Q19. The range of the function ^7-xP_x-3 is
(a) {1, 2, 3, 4, 5}
(b) {3, 4, 5}
(c) None of these
(d) {1, 2, 3}

Q20. The period of the function f(x) = sin⁴ 3x + cos⁴ 3x is
(a) π/2
(b) π/3
(c) π/4
(d) π/6

Answer key

Q's	1	2	3	4	5	6	7	8	9	10
Ans	b	b	b	d	b	a	a	c	a	b
Q's	11	12	13	14	15	16	17	18	19	20
Ans	a	b	b	d	a	c	b	d	d	d