Differentiation · Mathematics · NDA
MCQ (Single Correct Answer)
1
The derivative of ln(x + sin x) with respect to (x + cos x) is
NDA 2015 Paper 2
2
If $$y = {\cot ^{ - 1}}\left[ {{{\sqrt {1 + \sin x} + \sqrt {1 - \sin x} } \over {\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }}} \right]$$, where $$0 < x < {\pi \over 2}$$, then $${{dy} \over {dx}}$$ is equal to
NDA 2015 Paper 2
3
The function $$f(x) = {{{x^2}} \over {{e^x}}}$$ is monotonically increasing, if
NDA 2015 Paper 2
4
If $${x^a}{y^b} = {(x - y)^{a + b}}$$, then the value of $${{dy} \over {dx}} - {y \over x}$$ is equal to
NDA 2015 Paper 2
5
If $$s = \sqrt {{t^2} + 1} $$, then $${{{d^2}s} \over {d{t^2}}}$$ is equal to
NDA 2015 Paper 2
6
What is f'(x) equal to when x > 1 ?
NDA 2016 Paper 2
7
What is f'(x) equal to when 0 < x < 1 ?
NDA 2016 Paper 2
8
Which of the following equations is/are correct?
I. f($$-$$2) = f(5)
II. f''($$-$$2) + f''(0.5) + f''(3) = 4
Select the correct answer using the code given below.
I. f($$-$$2) = f(5)
II. f''($$-$$2) + f''(0.5) + f''(3) = 4
Select the correct answer using the code given below.
NDA 2016 Paper 2
9
What is the value of f'(0) ?
NDA 2016 Paper 1
10
What is the value of p for which f''(0) = 0 ?
NDA 2016 Paper 1
11
If $$y = {\log _{10}}x + {\log _x}10 + {\log _x}x + {\log _{10}}10$$, then what is $${\left( {{{dy} \over {dx}}} \right)_{x = 10}}$$ equal to ?
NDA 2016 Paper 1
12
What is f(1) equal to ?
NDA 2016 Paper 1
13
What is f'(1) equal to ?
NDA 2016 Paper 1
14
What is f'''(10) equal to ?
NDA 2016 Paper 1
15
What is f'(4) equal to?
NDA 2016 Paper 1
16
What is f''(2.5) equal to ?
NDA 2016 Paper 1
17
If $$y = {(\cos x)^{{{(\cos x)}^{(\cos x)\infty }}}}$$, then $${{dy} \over {dx}}$$ is equal to
NDA 2017 Paper 2
18
Consider the following statements
1. Derivative of f(x) may not exist at some point.
2. Derivative of f(x) may exist finitely at some point.
3. Derivative of f(x) may be infinite (geometrically) at some point.
Which of the above statements are correct?
1. Derivative of f(x) may not exist at some point.
2. Derivative of f(x) may exist finitely at some point.
3. Derivative of f(x) may be infinite (geometrically) at some point.
Which of the above statements are correct?
NDA 2017 Paper 2
19
If $$y = {\cos ^ - }\left( {{{2x} \over {1 + {x^2}}}} \right)$$, then $${{dy} \over {dx}}$$ is equal to
NDA 2017 Paper 2
20
What is $${{{d^2}x} \over {d{y^2}}}$$ equal to ?
NDA 2017 Paper 1
21
What is the derivative of $${\log _{10}}(5{x^2} + 3)$$ with respect to x ?
NDA 2017 Paper 1
22
Suppose the function f(x) = xn, n $$\ne$$ 0 is differentiable for all x. Then n can be any element of the interval
NDA 2017 Paper 1
23
If $$y = {\tan ^{ - 1}}\left( {{{5 - 2\tan \sqrt x } \over {2 + 5\tan \sqrt x }}} \right)$$, then what is $${{dy} \over {dx}}$$ equal to ?
NDA 2018 Paper 2
24
If $$u = {e^{ax}}\sin bx$$ and $$v = {e^{ax}}\cos bx$$, then what is $$u{{du} \over {dx}} + v{{dv} \over {dx}}$$ equal to ?
NDA 2018 Paper 2
25
If $$y = \sin (\ln x)$$, then which one of the following is correct?
NDA 2018 Paper 2
26
If $$y = {\left| {\sin x} \right|^{\left| x \right|}}$$, then what is the value of $${{dy} \over {dx}}$$ at $$x = - {\pi \over 6}$$ ?
NDA 2018 Paper 2
27
What is $${d \over {dx}}\sqrt {1 - \sin 2x} $$ equal to, where $${\pi \over 4} < x < {\pi \over 2}$$ ?
NDA 2018 Paper 2
28
If $$y = {e^{{x^2}}}\sin 2x$$, then what is $${{dy} \over {dx}}$$ at x = $$\pi$$ equal to ?
NDA 2018 Paper 1
29
What is the derivative of $${2^{{{(\sin x)}^2}}}$$ with respect to sin x?
NDA 2019 Paper 2
30
Let $$f(x) = {x^2} + 2x - 5$$ and $$g(x) = 5x + 30$$. If $$h(x) = 5f(x) - xg(x)$$, then what is the derivative of h(x)?
NDA 2019 Paper 2
31
What is $${{dy} \over {dx}}$$ at x = 1 equal to ?
NDA 2019 Paper 2
32
What is $${{{d^2}y} \over {d{x^2}}}$$ at x = 1 equal to ?
NDA 2019 Paper 2
33
What is the derivative of $${\sec ^2}({\tan ^{ - 1}}x)$$ with respect to x ?
NDA 2019 Paper 1
34
If f(x) = sin (cos x), then f'(x) is equal to
NDA 2019 Paper 1
35
What is $\frac{d^{2}y}{dx^{2}}$ at x = 0 equal to?
NDA Mathematics 14th September 2025
36
If x = sin $\theta$ then what is $\frac{dy}{dx}$ equal to?
NDA Mathematics 14th September 2025
37
What is f'(-1) equal to?
NDA Mathematics 14th September 2025
38
What is $\frac{dy}{dx}$ at x = 3.5 equal to?
NDA Mathematics 14th September 2025
39
What is $(\frac{dy}{dx})^2$ equal to?
NDA Mathematics 13 April 2025
40
What $\left[ \frac{x^2+4}{y^2+4} \frac{dy}{dx} \left( x^2+4 \frac{d^2y}{dx^2} - 16y \right) \right] $ equal to?
NDA Mathematics 13 April 2025
41
The derivative of y with respect to x
NDA Mathematics 13 April 2025
42
If , then what is $\frac{dy}{dx}$ equal to?
NDA Mathematics 13 April 2025
43
What is h’(0) equal to?
NDA Mathematics 1st September 2024
44
What is g’(0) equal to?
NDA Mathematics 1st September 2024
45
Consider the following statements :
1. $f''(e) = \frac{1}{e}$
2. $f(x)$ attains local minimum value at $x = e$
3. A local minimum value of $f(x)$ is $e$
Which of the statements given above are correct ?
NDA Mathematics 21 April 2024
46
What is $f''(x)$ equal to?
NDA Mathematics 21 April 2024
47
If f is differentiable, then what is f'(0.5) equal to?
NDA Mathematics 3 September 2023
48
If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?
NDA Mathematics 3 September 2023
49
If f'(x) = cos (In x) and $y=f\left(\frac{2 x-3}{x}\right)$, then what is $\frac{d y}{d x}$ equal to ?
NDA Mathematics 3 September 2023
50
What is f'(0) equal to ?
NDA Mathematics 16 April 2023
51
What is the derivative of f(x) at x = 0.5 ?
NDA Mathematics 16 April 2023
52
What is the derivative of f(x) at x = 2 ?
NDA Mathematics 16 April 2023
53
What is the derivative of fof(x), where 1 < x < 2 ?
NDA Mathematics 16 April 2023
54
What is the derivative of cosec(x°) ?
NDA Mathematics 16 April 2023
55
If y = $\frac{x \sqrt{x^2−16}}{2} − 8 \ln\left|x + \sqrt{x^2−16}\right|$, then what is $\frac{\text{dy}}{\text{dx}}$ equal to ?
NDA Mathematics 4 September 2022
56
If y = (xx)x, then which one of the following is correct ?
NDA Mathematics 4 September 2022
57
Let f(x) be a function such that f'(x) = g(x) and f''(x) = −f(x). Let h(x) = {f(x)}2 + {g(x)}2. Then consider the following statements :
1. h'(3) = 0
2. h(1) = h(2)
Which of the statements given above is/are correct ?
NDA Mathematics 4 September 2022
58
If y = ln2$\left(\frac{x^2−x+1}{x^2+x+1}\right)$, then what is $\frac{\text{dy}}{\text{dx}}$ at x = 0 equal to ?
NDA Mathematics 4 September 2022
59
If $\frac{d}{d x}\left(\frac{1+x^4+x^8}{1−x^2+x^4}\right)$ = ax + bx3, then which one of the following is correct?
NDA Mathematics 4 September 2022
60
If xyyx = 1, then what is $\frac{dy}{dx}$ at (1, 1) equal to?
NDA Mathematics 10 April 2022
61
If y = (xx)x, then what is the value of $\frac{dy}{dx}$ at x = 1?
NDA Mathematics 10 April 2022
62
If y = (1 + x)(1 + x2)(1 + x4)(1 + x8)(1 + x16) then what is $\frac{dy}{dx}$ at x = 0 equal to?
NDA Mathematics 14 November 2021
63
If y = cos x ⋅ cos 4x ⋅ cos 8x, then what is $\rm \frac{1}{y}\frac{dy}{dx}$ at $\rm x = \frac{\pi}{4}$ equal to?
NDA Mathematics 14 November 2021
64
Let f(x) be a polynomial function such that f ∘ f(x) = x4. What is f'(1) equal to ?
NDA Mathematics 14 November 2021
65
What is the derivative of $\rm e^{e^x}$ with respect to ex?
NDA Mathematics 14 November 2021
66
What is the derivative of ex with respect to xe?
NDA Mathematics 18 April 2021
67
What is the derivative of sin(ln x) + cos(ln x) with respect to x at x = e?
NDA Mathematics 18 April 2021
68
If x = et cost and y = et sint, then what is $\dfrac{dx}{dy}$ at t = 0 equal to?
NDA Mathematics 18 April 2021