Differentiation · Mathematics · NDA
MCQ (Single Correct Answer)
1
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
2
What is $f''(x)$ equal to?
NDA Mathematics 21 April 2024
3
If f is differentiable, then what is f'(0.5) equal to?
NDA Mathematics 3 September 2023
4
If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?
NDA Mathematics 3 September 2023
5
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
6
What is f'(0) equal to ?
NDA Mathematics 16 April 2023
7
What is the derivative of f(x) at x = 0.5 ?
NDA Mathematics 16 April 2023
8
What is the derivative of f(x) at x = 2 ?
NDA Mathematics 16 April 2023
9
What is the derivative of fof(x), where 1 < x < 2 ?
NDA Mathematics 16 April 2023
10
What is the derivative of cosec(x°) ?
NDA Mathematics 16 April 2023
11
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
12
If y = (xx)x, then which one of the following is correct ?
NDA Mathematics 4 September 2022
13
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
14
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
15
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
16
If xyyx = 1, then what is $\frac{dy}{dx}$ at (1, 1) equal to?
NDA Mathematics 10 April 2022
17
If y = (xx)x, then what is the value of $\frac{dy}{dx}$ at x = 1?
NDA Mathematics 10 April 2022
18
What is the derivative of ex with respect to xe?
NDA Mathematics 18 April 2021
19
What is the derivative of sin(ln x) + cos(ln x) with respect to x at x = e?
NDA Mathematics 18 April 2021
20
If x = et cost and y = et sint, then what is $\dfrac{dx}{dy}$ at t = 0 equal to?
NDA Mathematics 18 April 2021