Application of Derivatives · Mathematics · NDA

Start Practice

MCQ (Single Correct Answer)

1
Consider the following statements

1. The function f(x) = x2 + 2 cos x is increasing in the interval (0, $$\pi$$).

2. The function $$f(x) = \ln (\sqrt {1 + {x^2}} - x)$$ is decreasing in the interval ($$-$$ $$\infty$$, $$\infty$$)

Which of the above statements is/are correct?
NDA 2015 Paper 2
2
Consider the following statements

1. f(x) = ln x is an increasing function on (0, $$\infty$$).

2. f(x) = ex $$-$$ x(ln x) is an increasing function on (1, $$\infty$$).

Which of the above statements is/are correct?
NDA 2015 Paper 2
3
At what value of x does the function attain maximum value?
NDA 2015 Paper 2
4
The maximum value of the function is
NDA 2015 Paper 2
5
The function f(x) is an increasing function in the interval
NDA 2015 Paper 2
6
The function f(x) is a decreasing function in the interval
NDA 2015 Paper 2
7
Which one of the following statements is correct in respect of the function f(x) = x3 sin x?
NDA 2016 Paper 2
8
Which of the following statements is/are correct?

I. f(x) is increasing in the interval {$$-$$1, 2}.

II. f(x) is decreasing in the interval {2, 3}.

Select the correct answer using the code given below.
NDA 2016 Paper 2
9
Which of the following statements are correct?

I. f(x) is continuous at x = 2.

II. f(x) attains greatest value at x = 2.

III. f(x) is differentiable at x = 2.

Select the correct answer using the code given below.
NDA 2016 Paper 2
10
Let $$f(x) = \left\{ {\matrix{ {{{{e^x} - 1} \over x},} & {x > 0} \cr {0,} & {x = 0} \cr } } \right.$$ be a real valued function. Which one of the following statements is correct?
NDA 2016 Paper 2
11
Which one of the following statements is correct?
NDA 2016 Paper 1
12
Which one of the following statements is correct?
NDA 2016 Paper 1
13
Which one of the following is correct in respect of the function

$$f(x) = x(x - 1)(x + 1)$$ ?
NDA 2017 Paper 2
14
The maximum value of $${{\ln x} \over x}$$ is
NDA 2017 Paper 2
15
A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is
NDA 2017 Paper 2
16
What is the length of the longest interval in which the function $$f(x) = 3\sin x - 4{\sin ^3}x$$ is increasing?
NDA 2017 Paper 1
17
Let $$f(x) = x + {1 \over x}$$, where x$$\in$$ (0, 1). Then which one of the following is correct?
NDA 2017 Paper 1
18
Let the slope of the curve y = cos$$-$$1 (sin x) be tan$$\theta$$. Then, the value of $$\theta$$ in the interval (0, $$\pi$$) is
NDA 2018 Paper 2
19
Which one of the following is correct in respect of the function $$f(x) = x\sin x + \cos x + {1 \over 2}{\cos ^2}x$$ ?
NDA 2018 Paper 2
20
In which one of the following intervals is the function $$f(x) = {x^2} - 5x + 6$$ decreasing?
NDA 2018 Paper 2
21
A flower-bed in the form of a sector has been fenced by a wire of 40 m length. If the flower-bed has the greatest possible area, then what is the radius of the sector?
NDA 2018 Paper 2
22
What is the minimum value of $${[x(x - 1) + 1]^{{1 \over 3}}}$$, where 0 $$\le$$ x $$\le$$ 1 ?
NDA 2018 Paper 2
23
If the area of the trapezium is the maximum possible, then what is $$\alpha$$ equal to?
NDA 2018 Paper 1
24
If the area of the trapezium is maximum, what is the length of the fourth side?
NDA 2018 Paper 1
25
What is the maximum area of the trapezium?
NDA 2018 Paper 1
26
What is the slope of the curve at the point of intersection P?
NDA 2019 Paper 2
27
How much angle does the tangent at P make with y-axis?
NDA 2019 Paper 2
28
What is the equation of tangent to the curve at P?
NDA 2019 Paper 2
29
If $$f(x) = {{{x^3}} \over 3} - {{5{x^2}} \over 2} + 6x + 7$$ increases in the interval T and decreases in the interval S, then which one of the following is correct?
NDA 2019 Paper 2
30
In which one of the following intervals is the function increasing?
NDA 2019 Paper 2
31
In which one of the following intervals is the function decreasing?
NDA 2019 Paper 2
32
A given quantity of metal is to be case into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is
NDA 2019 Paper 1
33
The minimum distance from the point (4, 2) to y2 = 8x is equal to
NDA 2019 Paper 1
34
What is the minimum value of a2x + b2y where xy = c2 ?
NDA 2019 Paper 1
35

The non-negative values of $b$ for which the function $\frac{16x^3}{3} - 4bx^2 + x$ has neither maximum nor minimum in the range $x>0$ is

NDA Mathematics 21 April 2024
36

What is $\varphi(a)$ equal to?

NDA Mathematics 21 April 2024
37

What is $\varphi'(a)$ equal to?

NDA Mathematics 21 April 2024
38

Which of the following is/are correct?

1. $f'(0) = 0$

2. $f''(0) < 0$

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024
39

The function $y$ has a relative maxima at $x = 0$ for

NDA Mathematics 21 April 2024
40
What is the maximum value of y?
NDA Mathematics 3 September 2023
41
What is the maximum value of xy ?
NDA Mathematics 3 September 2023
42

Consider the following statements :

1. f(x) = In x is increasing in (0, ∞)

2. $g(x)=e^x+e^{\frac{1}{x}} $ is decreasing in (0, ∞)

Which of the statements given above is/are correct ?  

NDA Mathematics 16 April 2023
43
What is the derivative of sin2 x with respect to cos2x ?  
NDA Mathematics 16 April 2023
44
Under which one of the following conditions does the function f(x) = (p sec x)2 + (q cosec x)2 attain minimum value ?
NDA Mathematics 4 September 2022
45
Where does the function f(x) = $\displaystyle\sum_{j=1}^7$(x − j)2 attain its minimum value ?
NDA Mathematics 4 September 2022
46
How many extreme values does sin4x + 2x, where $0 < x < \frac{\pi}{2} $ have ?
NDA Mathematics 10 April 2022
47
If the derivative of the function$f(x) =\frac{m}{x} +2nx + 1$ vanishes at x = 2, then what is the value of m + 8n ?
NDA Mathematics 10 April 2022
48
If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y ?
NDA Mathematics 10 April 2022
49

Consider the following statements in respect of the function f(x) = sin x:

1. f(x) increases in the interval (0, π).

2. f(x) decreases in the interval $\left(\dfrac{5\pi}{2},3\pi\right).$

Which of the above statements is/are correct?

NDA Mathematics 18 April 2021
50
The curve y = -x3 + 3x2 + 2x - 27 has the maximum slope at:
NDA Mathematics 18 April 2021
51
If x + y = 20 and P = xy, then what is the maximum value of P?
NDA Mathematics 18 April 2021
52
What is the maximum value of sin 2x ⋅ cos 2x?
NDA Mathematics 18 April 2021
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12