Class 11 Mathematics Functions MCQs Set 07

Question. \( f : A \rightarrow B \) is a function then A, B are respectivley.
(a) domain, range
(b) domain, co domain
(c) co domain, range
(d) range, domain
Answer: (b) domain, co domain

Question. \( f : A \rightarrow B \) then f(A) is called
(a) domain
(b) co domain
(c) range
(d) function
Answer: (c) range

Question. If \( f : A \rightarrow B \) is a function then
(a) \( f(A) = B \)
(b) \( f(A) \subset B \)
(c) \( f(A) \subseteq B \)
(d) \( B \subseteq f(A) \)
Answer: (c) \( f(A) \subseteq B \)

Question. If \( f : A \rightarrow B \) is surjective then
(a) No two elements of A have the same image in B
(b) Every element in A has an image in B
(c) Every element of B has at least one pre-image in A
(d) A and B are finite non empty sets
Answer: (c) Every element of B has at least one pre-image in A

Question. A constant function \( f : A \rightarrow B \) will be one-one if
(a) \( n(A) = n(B) \)
(b) \( n(A) = 1 \)
(c) \( n(B) = 1 \)
(d) \( n(A) < n(B) \)
Answer: (b) \( n(A) = 1 \)

Question. If \( f : A \rightarrow B \) is a constant function which is onto then B is
(a) a singleton set
(b) a null set
(c) an infinite set
(d) a finite set
Answer: (a) a singleton set

Question. If \( n \ge 2 \) then the number of surjections that can be defined from \( \{1,2,3,....n\} \) onto \( \{1, 2\} \) is
(a) \( n^2 - n \)
(b) \( n^2 \)
(c) \( 2^n \)
(d) \( 2^n - 2 \)
Answer: (d) \( 2^n - 2 \)

Question. If f and g are functions such that fog is onto then
(a) f is onto
(b) g is onto
(c) gof is onto
(d) Neither f nor g is onto
Answer: (a) f is onto

Question. If f and g are functions such that fog is one - one then
(a) g must be onto
(b) g must be one - one
(c) f must be one-one
(d) f, g need not one-one
Answer: (b) g must be one - one

Question. To have inverse for the function f, f should be
(a) one-one
(b) onto
(c) one-one and onto
(d) Identity function
Answer: (c) one-one and onto

Question. If \( f : A \rightarrow B \) is a bijection then \( f^{-1}of = \)
(a) \( fof^{-1} \)
(b) \( f \)
(c) \( f^{-1} \)
(d) \( I_A \)
Answer: (d) \( I_A \)

Question. \( f : A \rightarrow B \) is a bijection then \( fof^{-1} = \)
(a) \( I_A \)
(b) \( I_B \)
(c) \( f \)
(d) \( f^{-1} \)
Answer: (b) \( I_B \)

Question. Let \( f(x) = ax^2 + bx + c \), where a,b,c are rational and \( f : Z \rightarrow Z \) where Z is the set of integers. Then \( a + b \) is
(a) a negative integer
(b) an integer
(c) non integral rational number
(d) Real number
Answer: (b) an integer

Question. The graph of the function \( y = f(x) \) is symmetrical about the line \( x = 2 \). Then
(a) \( f(x+2) = f(x-2) \)
(b) \( f(2+x) = f(2-x) \)
(c) \( f(x) = f(-x) \)
(d) \( f(x) = -f(-x) \)
Answer: (b) \( f(2+x) = f(2-x) \)

Question. The graph of odd function is
(a) symmetric about origin
(b) symmetric about y-axis
(c) parallel to x-axis
(d) parallel to y-axis
Answer: (a) symmetric about origin

Question. The graph of even function is
(a) symmetric in opp quadrtants
(b) symmetric about y-axis
(c) parallel to x-axis
(d) parallel to y-axis
Answer: (b) symmetric about y-axis

Question. The graph of Identify function is
(a) Straight line passing through origin
(b) symmetric about y-axis
(c) parallel to x-axis
(d) parallel to y-axis
Answer: (a) Straight line passing through origin

Question. The graph of |x| is
(a) Straight line passing through origin
(b) symmetric about y-axis
(c) parallel to x-axis
(d) parallel to y-axis
Answer: (b) symmetric about y-axis

Question. The fucntion \( f(x) = \{x\} \) is
(a) even funciton
(b) odd function
(c) periodic funciton with period 1
(d) periodic function but no fundamental period
Answer: (c) periodic funciton with period 1

Question. Let f be a strictly decreasing function with range \( [a,b] \) then domain of the function \( f^{-1} \) is
(a) \( [f^{-1}(b), f^{-1}(a)] \)
(b) \( [b, a] \)
(c) \( [f^{-1}(a), f^{-1}(b)] \)
(d) \( (b, a) \)
Answer: (a) \( [f^{-1}(b), f^{-1}(a)] \)

Question. If \( f(x) = x^2 + \lambda x + \mu \) be an integral function of the integral variable x then
(a) \( \lambda \) is an integer and \( \mu \) is a rational fraction
(b) \( \lambda \) and \( \mu \) are integers
(c) \( \mu \) is an integer and \( \lambda \) is a rational fraction
(d) \( \lambda \) and \( \mu \) are rational fractions
Answer: (b) \( \lambda \) and \( \mu \) are integers

Real valued functions :

Question. Let \( f : \{(1,1),(2,3),(0,-1),(-1,-3)\} \) be a function from z to z defined by \( f(x) = ax+b \),for some integers a,b then (a,b) =
(a) (-1,2)
(b) (2,-1)
(c) (3,-2)
(d) (0,3)
Answer: (b) (2,-1)

Question. If \( e^{f(x)} = \frac{10+x}{10-x}, x \in (-10,10) \) and \( f(x) = k.f\left(\frac{200x}{100+x^2}\right) \) then k =
(a) 0.5
(b) 0.6
(c) 0.7
(d) 0.8
Answer: (a) 0.5

Question. \( f : R \rightarrow R \) is defined as \( f(x) = 2x + |x| \) then \( f(3x) - f(-x) - 4x = \)
(a) \( f(x) \)
(b) \( -f(x) \)
(c) \( f(-x) \)
(d) \( 2f(x) \)
Answer: (d) \( 2f(x) \)

Question. \( f(1) = 1, n \ge 1 \)
\( \implies \) \( f(n+1) = 2f(n) + 1 \) then \( f(n) = \) 
(a) \( 2^{n+1} \)
(b) \( 2^n \)
(c) \( 2^n - 1 \)
(d) \( 2^{n-1} - 1 \)
Answer: (c) \( 2^n - 1 \)

Question. If \( f(x) = \frac{7^{1+\ln x}}{x^{\ln 7}} \) then f(2015) =
(a) 20
(b) 7
(c) 2015
(d) 100
Answer: (b) 7

Question. If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in R \) then f(2016) =
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1

Question. If \( f = \{(-2,4),(0,6),(2,8)\} \) and \( g = \{(-2,-1),(0,3),(2,5)\} \), then \( \left(\frac{2f}{3g} + \frac{3g}{2f}\right)(0) = \)
(a) 1/12
(b) 25/12
(c) 5/12
(d) 13/12
Answer: (b) 25/12

Question. If f(x) = \sin (\log x) then f(xy) + \( f\left(\frac{x}{y}\right) \) -2f(x) \cos (\log y) =
(a) \cos (\log x)
(b) \sin (\log y)
(c) \cos (\log (xy))
(d) 0
Answer: (d) 0

Question. If \( f(x+y, x-y) = xy \) then the arithmetic mean of \( f(x,y) \) and \( f(y,x) \) is
(a) x
(b) y
(c) 0
(d) xy
Answer: (c) 0

Even and odd functions :

Question. Let \( f(x) = \frac{x}{e^x - 1} + \frac{x}{2} + 1 \), then f is
(a) an odd funciton
(b) an even function
(c) both odd and even
(d) neitheer odd nor even
Answer: (b) an even function

Question. Which of the following is an even function
(a) \( f(x) = \frac{a^x + a^{-x}}{a^x - a^{-x}} \)
(b) \( f(x) = \frac{a^x + 1}{a^x - 1} \)
(c) \( f(x) = x \frac{a^x - 1}{a^x + 1} \)
(d) \( f(x) = \log_2(x + \sqrt{x^2 + 1}) \)
Answer: (c) \( f(x) = x \frac{a^x - 1}{a^x + 1} \)

Periodic functions:

Question. The period of \( \cos x^2 \) is
(a) \( 2\pi \)
(b) \( \sqrt{2\pi} \)
(c) \( 4\pi^2 \)
(d) does not exist
Answer: (d) does not exist

Question. Period of \( f(x) = e^{\cos \{x\}} + \sin \pi [x] \) is (\([\cdot]\) and \(\{\cdot\}\) denote the greatest integer function and fractional part function respectively)
(a) 1
(b) 2
(c) \( \pi \)
(d) \( 2\pi \)
Answer: (a) 1

Question. Let \( f(x) \) be periodic and k be a positive real number such that \( f(x+k) + f(x) = 0 \) for all \( x \in R \). Then the period of \( f(x) \) is
(a) k
(b) 2k
(c) 4k
(d) 8k
Answer: (b) 2k

Question. The period of \( f(x) = \sqrt{x - [x]} \) is
(a) no fundamental period
(b) \( \frac{1}{2} \)
(c) 1
(d) 2
Answer: (c) 1

Domain of the function:

Question. The domain of \( f(x) = \frac{x^2 + 2x + 1}{x^2 - x - 6} \)
(a) \( R - \{3, -2\} \)
(b) \( R - \{-3, 2\} \)
(c) \( R - \{3, -2] \)
(d) \( R - (3, -2) \)
Answer: (a) \( R - \{3, -2\} \)

Question. The domain of \( f(x) = \frac{1}{\log |x|} \) is
(a) \( R - \{0\} \)
(b) \( R - \{0,1\} \)
(c) \( R - \{-1, 0, 1\} \)
(d) \( (-\infty, \infty) \)
Answer: (c) \( R - \{-1, 0, 1\} \)

Question. The domain of \( f(x) = \frac{3^x + 3^{-x}}{3^x - 3^{-x}} \) is
(a) \( (-\infty, \infty) \)
(b) \( (-\infty, 0) \cup (0, \infty) \)
(c) \( (0, \infty) \)
(d) \( (0, 1) \)
Answer: (b) \( (-\infty, 0) \cup (0, \infty) \)

Question. The domain of the function \( f(x) = \sqrt{\log_{16} x^2} \) is
(a) x = 0
(b) \( |x| \ge 4 \)
(c) \( |x| \ge 1 \)
(d) \( |x| \ge 2 \)
Answer: (c) \( |x| \ge 1 \)