Functions · Mathematics · NDA
MCQ (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
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
45
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
46
What is $g[f(x) - 3x]$ equal to?
NDA Mathematics 21 April 2024
47
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
48
What is $f(x)$ equal to?
NDA Mathematics 21 April 2024
49
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
50
Which one of the following is a possible expression for g(x)?
NDA Mathematics 3 September 2023
51
What is g(15) equal to ?
NDA Mathematics 3 September 2023
52
What is the range of the function?
NDA Mathematics 3 September 2023
53
What is the domain of the function?
NDA Mathematics 3 September 2023
54
What is the greatest value of the function?
NDA Mathematics 3 September 2023
55
At what value of x does the function attain minimum value ?
NDA Mathematics 16 April 2023
56
What is the minimum value of the function ?
NDA Mathematics 16 April 2023
57
What is f(0) equal to ?
NDA Mathematics 16 April 2023
58
What is $f\left(\frac{\pi}{2}\right)$ equal to ?
NDA Mathematics 16 April 2023
59
What is $f\left(\frac{\pi}{4}\right)$ equal to ?
NDA Mathematics 16 April 2023
60
If f(x) = x2 + 2 and g(x) = 2x - 3, then what is (fog)(1) equal to ?
NDA Mathematics 16 April 2023
61
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
62
What is $\displaystyle\sum_{x=1}^5$f(2x − 1) equal to ?
NDA Mathematics 4 September 2022
63
What is $\displaystyle\sum_{x=1}^6$2x f(x) equal to ?
NDA Mathematics 4 September 2022
64
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
65
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
66
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
67
What is the domain of the function $f(x) =\sqrt{1 - (x-1)^2} \ ?$
NDA Mathematics 10 April 2022
68
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
69
If f(x) = 4x + 3, then what is f o f o f(-1) equal to?
NDA Mathematics 10 April 2022
70
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
71
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
72
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
73
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
74
What is the domain of the function f(x) = 3x?
NDA Mathematics 18 April 2021