CBSE Class 12 Mathematics Relations And Functions Assignment Set C

Question. If R be a relation < from A = {1,2, 3, 4} to B = {1, 3, 5} i.e., (a, b) ∈ R ⇔ a < b, then RoR⁻¹ is:
a. {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
b. {(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
c. {(3, 3), (3, 5), (5, 3), (5, 5)}
d. {(3, 3) (3, 4), (4, 5)}
Answer : C

Question.

a. 7/6
b. 5/6
c. 6/7
d. 5/7
Answer : C

Question. The domain of the function √log(x² − 6x + 6) is:
a. (−∞,∞)
b. (−∞,3 − √3) ∪ (3+ √3,∞)
c. (−∞,1] ∪ [5,∞)
d. (−∞,1] ∪ [3,∞)
Answer : C

Question. If A contains 10 elements then total number of functions defined from A to A is:
a. 10
b. 2¹⁰
c. 10¹⁰
d. 2^{10 –}
Answer : C

Question. If f (y) = log y, then f(1/y) + f(1/y) is equal to:
a. 2
b. 1
c. 0
d. –1
Answer : C

Question. The domain of the derivative of the function

a. R −{0}
b. R −{1}
c. R −{−1}
d. R −{−1, 1}
Answer : C

Question. The domain of the function f(x) = log_3+x  (x² −1) is:
a. (−3, − 1) ∪ (1,∞)
b. [−3, − 1) ∪ [1,∞)
c. (−3,−2) ∪ (−2, − 1) ∪ (1,∞)
d. [−3, − 2) ∪ (−2, − 1) ∪ [1,∞]
Answer : C

Question. Domain of definition of the function

Answer : A

Question. The function f : R → R defined by f (x) = (x −1)(x − 2)(x − 3) is:
a. One-one but not onto
b. Onto but not one-one
c. Both one-one and onto
d. Neither one-one nor onto
Answer : B

Question. The function f : R → R defined by x f(x) = e is:
a. Onto
b. Many-one
c. One-one and into
d. Many one and onto
Answer : C

Question. Range of the function f(x) = x² + x + 2 / x² + x + 1; x ∈ R is:
a. (1,∞)
b. (1,11/ 7)
c. (1, 7 / 3]
d. (1, 7 / 5]
Answer : C

Question. Function f : N → N, f (x) = 2x + 3 is:
a. One-one onto
b. One-one into
c. 0 Many-one onto
d. Many –one into
Answer : B

Question. Which of the following is an even function?
a. x(a^x - 1 / a^x + 1)
b. tan x
c. a^x - a-x
d. a^x + 1 / a^x - 1
Answer : A

Question. The function f(x) = sin πx/2 + 2cos (πx/3) - tan (πx/4) is periodic with period:
a. 6
b. 3
c. 4
d. 12
Answer : D

Question. The period of | sin 2x | is:
a. π/4
b. π/2
c. π
d. 2π
Answer : B

Question. The period of the function f(x) = sin² x is:
a. π/2
b. π
c. 2π
d. 3π
Answer : B

Question. Which of the following is an even function?
a. f(x) = a^x + 1 / a^x - 1
b. f(x) = x (a^x - 1 / a^x + 1)
c. a^x - a^-x / a^x - a^-x
d. f (x ) = sin x
Answer : B

Question. The period of the function f(x) = 2 cos 1/3  (x − π) is:
a. 6π
b. 4π
c. 2π
d. π
Answer : A

Question. If f : R → R, f(x) = 2x − 1 and g : R → R, g(x) = x² then (gof )(x) equals?
a. x² − 1
b. (2x − 1)²
c. 4x² − 2x + 1
d. x² + 2x − 1
Answer : B

Question. f(x) sin² x + sin² (x + n/3) + cos x cos (x + n/3) and g (5/4) = 1, then (gof )(x) is equal to:
a. 1
b. –1
c. 2
d. – 2
Answer : A

Question. Suppose that g(x) = 1 + √x and f (g(x)) = 3 + 2√x + x, then f(x) is:
a. 1 + 2x²
b. 2 + x²
c. 1 + x
d. 2 + x
Answer : B

Question. The period of f(x) = x − [x], if it is periodic, is:
a. f(x) is not periodic
b. 1/2
c. 1
d. 2
Answer : C

Question. The period of f(x) = sin (πx/n-1) + cos (πx/n), n ∈ Z, n > 2 is:
a. 2πn(n − 1)
b. 4n (n − 1)
c. 2n(n −1)
d. None of these'
Answer : C

Question. If S is the set of all real x such that 2x - 1/2x³ + 3x² + x is positive, then S contains:
a. (−∞, − 3/2)
b. (- 3/2, − 1/4)
c. (− 1/4, 1/2)
d. (1/2, 3)
Answer : AD

Question. If g(x)x² + x – 2 and 1/2 (gof) (x) = 2x² – 5x + 2, then f (x ) is equal to:
a. 2x − 3
b. 2x + 3
c. 2x² + 3x + 1
d. 2x² − 3x − 1
Answer : A

Question. If(x) = 2x - 3 / c - 2 , then [f{f(x)}] equals:
a. x
b. –x
c. x/2
d. - 1/x
Answer : A

Question. Let g(x) be a function defined on [–1,1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and [x, g(x)] is √3 / 4, then the function g(x) is:

Answer : BC

Question. If f : R→ R is given by f (x) = 3x − 5, then f^-1(x) ?
a. Is given by 1/3x −5
b. Is given by x + 5/3
c. Does not exist because f is not one-one
d. Does not exist because f is not onto
Answer : B

Question. Let f : R → R be defined by f(x) = 3x − 4, then f^-1(x) is:
a. 3x + 4
b. 1/3 x − 4
c. 1/3 (x + 4)
d. 1/3(x - 4)
Answer : C

Question. If y = f(x) = x + 2/x - 1, then:
a. x = f(y)
b. f(1) = 3
c. y increases will x for x < 1
d. f is a rational function of x
Answer : AD

Question. If f(x) = cos[π²]x + cos[−π²]x, where [x] stands for the greatest integer function, then:
a. f (π / 2) = −1
b. f (π ) = 1
c. f (−π ) = 0
d. f (π / 4) = 1
Answer : AC

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