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Practice QuestionsMCQ (Single Correct Answer)
1
If $$g(x) = {1 \over {f(x)}}$$ and f(x) = x, x $$\ne$$ 0, then which one of the following is correct?
NDA 2015 Paper 2
2
The domain of the function $$f(x) = {1 \over {\sqrt {|x| - x} }}$$ is
NDA 2015 Paper 2
3
If f : R $$\to$$ R, g : R $$\to$$ R are two functions given by f(x) = 2x $$-$$ 3 and g(x) = x3 + 5, then (fog)$$-$$1 (x) is equal to
NDA 2015 Paper 2
4
f(xy) = f(x) + f(y) is true for all
NDA 2015 Paper 2
5
Consider the following statements :
Statement I The function f : R $$\to$$ R such that f(x) = x3 for all x$$\in$$R is one-one.
Statement II f(a) = f(b) $$\Rightarrow$$ a = b for all a, b $$\in$$R, if the function f is one-one.
Which one of the following is correct in respect of the above statements ?
Statement I The function f : R $$\to$$ R such that f(x) = x3 for all x$$\in$$R is one-one.
Statement II f(a) = f(b) $$\Rightarrow$$ a = b for all a, b $$\in$$R, if the function f is one-one.
Which one of the following is correct in respect of the above statements ?
NDA 2015 Paper 2
6
If $$f({x_1}) - f({x_2}) = f\left( {{{{x_1} - {x_2}} \over {1 - {x_1}{x_2}}}} \right)$$ for x1, x2 $$\in$$($$-$$1, 1), then what is f(x) equal to ?
NDA 2016 Paper 1
7
What is the range of the function $$y = {{{x^2}} \over {1 + {x^2}}}$$ where x$$\in$$R ?
NDA 2016 Paper 1
8
How many solutions does the function f(x) = 1 have ?
NDA 2016 Paper 1
9
How many solutions does the function f(x) = $$-$$ 1 have?
NDA 2016 Paper 1
10
The inverse of the function y = 5ln x is
NDA 2017 Paper 2
11
The function f(x) = | x | $$-$$ x3 is
NDA 2017 Paper 2
12
If x is any real number, then $${{{x^2}} \over {1 + {x^4}}}$$ belongs to which one of the following intervals?
NDA 2017 Paper 2
13
If $$f(x) = {x \over 2} - 1$$, then on the interval [0, $$\pi$$] which one of the following is correct?
NDA 2017 Paper 2
14
Which one of the following graph represents the function $$f(x) = {x \over x},x \ne 0$$ ?
NDA 2017 Paper 2
15
Let $$f(n) = \left[ {{1 \over 4} + {n \over {1000}}} \right]$$, where [x] denote the integral part of x. Then the value of $$\sum\limits_{n = 1}^{1000} {f(n)} $$ is
NDA 2017 Paper 2
16
If $$f(x) = {{4x + {x^4}} \over {1 + 4{x^3}}}$$ and $$g(x) = \ln \left( {{{1 + x} \over {1 - x}}} \right)$$, then what is the value of $$(fog)\left( {{{e - 1} \over {e + 1}}} \right)$$ equal to ?
NDA 2017 Paper 2
17
If $$f(x) = {x \over {x - 1}}$$, then what is $${{f(a)} \over {f(a + 1)}}$$ equal to ?
NDA 2017 Paper 1
18
Let f : [$$-$$6, 6] $$\to$$ R be defined by f(x) = x2 $$-$$ 3. Considered the following :
1. $$(f \circ f \circ f)( - 1) = (f \circ f \circ f)(1)$$
2. $$(f \circ f \circ f)( - 1) - 4(f \circ f \circ f)(1)$$
$$ = (f \circ f)(0)$$
Which of the above is/are correct?
1. $$(f \circ f \circ f)( - 1) = (f \circ f \circ f)(1)$$
2. $$(f \circ f \circ f)( - 1) - 4(f \circ f \circ f)(1)$$
$$ = (f \circ f)(0)$$
Which of the above is/are correct?
NDA 2017 Paper 1
19
Let f(x) = px + q and g(x) = mx + n. Then, f(g(x)) = g(f(x)) is equivalent to
NDA 2017 Paper 1
20
Which one of the following functions is neither even nor odd?
NDA 2017 Paper 1
21
Let $$f(a) = {{a - 1} \over {a + 1}}$$ consider the following :
1. $$f(2a) = f(a) + 1$$
2. $$f\left( {{1 \over a}} \right) = - f(a)$$
Which of the above is/are correct?
1. $$f(2a) = f(a) + 1$$
2. $$f\left( {{1 \over a}} \right) = - f(a)$$
Which of the above is/are correct?
NDA 2017 Paper 1
22
Let $$f(x):\left\{ {\matrix{
{x,} & {x\,is\,rational} \cr
{0,} & {x\,is\,irrational} \cr
} } \right.$$
and $$g(x):\left\{ {\matrix{ {x,} & {x\,is\,rational} \cr {0,} & {x\,is\,irrational} \cr } } \right.$$
if $$f:R \to R$$ and $$g:R \to R$$, then (f $$-$$ g) is
and $$g(x):\left\{ {\matrix{ {x,} & {x\,is\,rational} \cr {0,} & {x\,is\,irrational} \cr } } \right.$$
if $$f:R \to R$$ and $$g:R \to R$$, then (f $$-$$ g) is
NDA 2017 Paper 1
23
If $$f(x) = {{\sqrt {x - 1} } \over {x - 4}}$$, defines a function on R, then what is its domain?
NDA 2018 Paper 2
24
When one of the following is correct in respect of the function f : R $$\to$$ R+ defined as f(x) = |x + 1| ?
NDA 2018 Paper 1
25
Suppose f : R $$\to$$ R is defined by $$f(x) = {{{x^2}} \over {1 + {x^2}}}$$. What is the range of the function?
NDA 2018 Paper 1
26
For f to be a function, what is the domain of f, if $$f(x) = {1 \over {\sqrt {|x| - x} }}$$ ?
NDA 2018 Paper 1
27
What is the period of the function f(x) = sin x?
NDA 2018 Paper 1
28
If f(x) is an even function, where f(x) $$\ne$$ 0, then which one of the following is correct?
NDA 2018 Paper 1
29
If f : R $$\to$$ S defined by f(x) = 4 sin x $$-$$ 3 cos x + 1 is onto, then what is S equal to ?
NDA 2018 Paper 1
30
For $$x = {{\sqrt \pi } \over 2}$$, what is the value of $$[ho(gof)](x)$$ ?
NDA 2019 Paper 2
31
What is $$[fo(fof)](2)$$ equal to ?
NDA 2019 Paper 2
32
What is the period of the function g(x)?
NDA 2019 Paper 2
33
What is the period of the function h(x)?
NDA 2019 Paper 2
34
What is the period of the function f(x) ?
NDA 2019 Paper 2
35
What are the roots of the equation $$g[(f(x)] = 0$$ ?
NDA 2019 Paper 2
36
Consider the following statements :
1. f[g(x)] is a polynomial of degree 3.
2. g[g(x)] is a polynomial of degree 2.
Which of the above statements is/are correct?
1. f[g(x)] is a polynomial of degree 3.
2. g[g(x)] is a polynomial of degree 2.
Which of the above statements is/are correct?
NDA 2019 Paper 2
37
A function f defined by $$f(x) = \ln \left( {\sqrt {{x^2} + 1} - x} \right)$$ is
NDA 2019 Paper 1
38
The domain of the function f defined by
f(x) = logx 10 is
f(x) = logx 10 is
NDA 2019 Paper 1
39
For r > 0, f(r) is the ratio of perimeter to area of a circle of radius r. Then, f(1) + f(2) is equal to
NDA 2019 Paper 1
40
If f(x) = 31 + x, then f(x) f(y) f(z) is equal to
NDA 2019 Paper 1
41
The domain of the function
$$f(x) = \sqrt {(2 - x)(x - 3)} $$ is
$$f(x) = \sqrt {(2 - x)(x - 3)} $$ is
NDA 2019 Paper 1
42
If $$f(x) = {{x - 2} \over {x + 2}}$$, x $$\ne$$ $$-$$2, then what is f$$-$$1(x) equal to ?
NDA 2019 Paper 1
43
If f(x) = log10 (1 + x), then what is 4f(4) + 5f(1) $$-$$ log10 2 equal to ?
NDA 2019 Paper 1
44
Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?
NDA Mathematics 1st September 2024
45
If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?
NDA Mathematics 1st September 2024
46
What is the minimum value of the function f(x) = log10(x2 + 2x + 11)?
NDA Mathematics 1st September 2024
47
If f(2x) = 4x2 + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?
NDA Mathematics 1st September 2024
48
Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?
NDA Mathematics 1st September 2024
49
Which one of the following is f(x)?
NDA Mathematics 1st September 2024
50
Which one of the following is g(x)?
NDA Mathematics 1st September 2024
51
What is f(0.999) + f(1.001) equal to
NDA Mathematics 1st September 2024
52
Consider the following statements :
I. f(t) is an odd function.
Il. g(t) is an odd function.
Which of the statements given above is/are correct?
NDA Mathematics 1st September 2024
53
If $f(x)=ax-b$ and $g(x)=cx+d$ are such that $f(g(x))=g(f(x))$, then which one of the following holds?
NDA Mathematics 21 April 2024
54
Which one of the following is correct in respect of $f(x) = \frac{1}{\sqrt{|x| - x}}$ and $g(x) = \frac{1}{\sqrt{x - |x|}}$?
NDA Mathematics 21 April 2024
55
What is $g[f(x) - 3x]$ equal to?
NDA Mathematics 21 April 2024
56
Consider the following statements:
1. $f(x)$ is differentiable for all $x < 0$
2. $g(x)$ is continuous at $x = 0.0001$
3. The derivative of $g(x)$ at $x = 2.5$ is 1
Which of the statements given above are correct?
NDA Mathematics 21 April 2024
57
What is $f(x)$ equal to?
NDA Mathematics 21 April 2024
58
A function satisfies $f(x-y)=\frac{f(x)}{f(y)}$, where f(y) ≠ 0. If f(1) = 0.5, then what is f(2) + f(3) + f(4) + f(5) + f(6) equal to ?
NDA Mathematics 3 September 2023
59
Which one of the following is a possible expression for g(x)?
NDA Mathematics 3 September 2023
60
What is g(15) equal to ?
NDA Mathematics 3 September 2023
61
What is the range of the function?
NDA Mathematics 3 September 2023
62
What is the domain of the function?
NDA Mathematics 3 September 2023
63
What is the greatest value of the function?
NDA Mathematics 3 September 2023
64
At what value of x does the function attain minimum value ?
NDA Mathematics 16 April 2023
65
What is the minimum value of the function ?
NDA Mathematics 16 April 2023
66
What is f(0) equal to ?
NDA Mathematics 16 April 2023
67
What is $f\left(\frac{\pi}{2}\right)$ equal to ?
NDA Mathematics 16 April 2023
68
What is $f\left(\frac{\pi}{4}\right)$ equal to ?
NDA Mathematics 16 April 2023
69
If f(x) = x2 + 2 and g(x) = 2x - 3, then what is (fog)(1) equal to ?
NDA Mathematics 16 April 2023
70
What is the range of the function f(x) = x + |x| if the domain is the set of real numbers ?
NDA Mathematics 16 April 2023
71
What is $\displaystyle\sum_{x=1}^5$f(2x − 1) equal to ?
NDA Mathematics 4 September 2022
72
What is $\displaystyle\sum_{x=1}^6$2x f(x) equal to ?
NDA Mathematics 4 September 2022
73
If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?
NDA Mathematics 4 September 2022
74
Consider the following statements in respect of the function f(x) = $\left\{\begin{array}{rc}|x|+1, & 0<|x| \leqslant 3 \\ 1, & x = 0\end{array}\right.$
1. The function attains maximum value only at x = 3
2. The function attains local minimum only at x = 0
Which of the statements given above is/are correct ?
NDA Mathematics 4 September 2022
75
Consider the following statements in respect of the function y = [x], x ∈ (-1, 1) where [.] is the greatest integer function:
1. Its derivative is 0 at x = 0.5
2. It is continuous at x = 0
Which of the above statements is/are correct?
NDA Mathematics 10 April 2022
76
What is the domain of the function $f(x) =\sqrt{1 - (x-1)^2} \ ?$
NDA Mathematics 10 April 2022
77
If $4f(x) - f \left(\frac{1}{x}\right)=\left(2x+\frac{1}{x}\right)\left(2x-\frac{1}{x}\right),$ then what is f(2) equal to?
NDA Mathematics 10 April 2022
78
If f(x) = 4x + 3, then what is f o f o f(-1) equal to?
NDA Mathematics 10 April 2022
79
Consider the following in respect of the function f(x) = 10x :
1. Its domain is (-∞, ∞)
2. It is a continuous function
3. It is differentiable at x = 0
Which of the above statements are correct?
NDA Mathematics 10 April 2022
80
In which one of the following intervals is the function $f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5$ decreasing?
NDA Mathematics 10 April 2022
81
What is the period of the function f(x) = ln(2 + sin2x)?
NDA Mathematics 14 November 2021
82
What is the range of the function f(x) = 1 - sinx defined on entire real line?
NDA Mathematics 14 November 2021
83
Consider the following statements:
1. A function f : Z → Z, defined by f(x) = x + 1, is one-one as well as onto.
2. A function f : N → N, defined by f(x) = x + 1, is one-one but not onto.
Which of the above statements is/are correct?
NDA Mathematics 18 April 2021
84
If
$f(x)=\left|\begin{array}{ccc}1 & 1 & x+1 \\ 2 x & x(x-1) & x(x+1) \\ 3 x(x-1) & 2(x-1)(x-2) & x(x+1)(x-1)\end{array}\right|$
then what is f(-1) + f(0) + f(1) equal to?
NDA Mathematics 18 April 2021
85
What is the domain of the function f(x) = 3x?
NDA Mathematics 18 April 2021