VITEEE PYQs for Application of derivatives with Solutions: Practice VITEEE Previous Year Questions

Updated 3+ months ago

Application of derivatives is an important topic in the Mathematics section in VITEEE exam. Practising this topic will increase your score overall and make your conceptual grip on VITEEE exam stronger.

This article gives you a full set of VITEEE PYQs for Application of derivatives with explanations for effective preparation. Practice of VITEEE Mathematics PYQs including Application of derivatives questions regularly will improve accuracy, speed, and confidence in the VITEEE 2026 exam.

VITEEE PYQs for Application of derivatives with Solutions

1.
Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$
- $ \pi^2 $
- $ \frac{\pi^2}{2} $
- 0
- $ 2\pi^2 $
View Solution
2.
If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is
- $k$
- $3k$
- $\frac{k}{3}$
- None of these
View Solution
3.
The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is
- $\frac{5}{18} cm/sec$
- $\frac{1}{4} cm/sec$
- $\frac{5}{16} cm/sec$
- None of these
View Solution
4.
The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is
- 25
- 4
- does not exist
- None of these
View Solution
5.
The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is
- $\frac{1}{e}$
- $\frac{1}{ 2 e}$
- $\frac{1}{e^2}$
- $\frac{4}{e^4}$
View Solution
6.
On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point
- $0$
- $ \frac{1}{4}$
- $ \frac{1}{2}$
- $ \frac{1}{3}$
View Solution
7.
The minimum value of $\frac{x}{\log \, x}$ is
- $e$
- $\frac{1}{e}$
- $e^2$
- $e^3$
View Solution
8.
A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is
- 10$\pi$
- 100$\pi$
- 200$\pi$
- 50$\pi$
View Solution
9.
If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \left(a > b\right)$ and $x^{2} - y^{2} = c^{2}$ cut at right angles, then
- $a^2 + b^2 = 2c^2$
- $ b^2 - a^2 = 2c^2$
- $a^2 - b^2 = 2c^2$
- $a^2 b^2 = 2c^2$
View Solution

View more VITEEE Questions

SHARE ON FACEBOOK SHARE ON TWITTER

Comments

No Comments To Show

SUBSCRIBE TO OUR NEWS LETTER

COLLEGE NOTIFICATIONS

EXAM NOTIFICATIONS

NEWS UPDATES

Download the Collegedunia app on

VITEEE PYQs for Application of derivatives with Solutions

1.Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$

2.If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

3.The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is

4.The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is

5.The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

6.On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

7.The minimum value of $\frac{x}{\log \, x}$ is

8.A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is

9.If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \left(a > b\right)$ and $x^{2} - y^{2} = c^{2}$ cut at right angles, then

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$

2.
If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

3.
The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is

4.
The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is

5.
The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

6.
On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

7.
The minimum value of $\frac{x}{\log \, x}$ is

8.
A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is

9.
If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \left(a > b\right)$ and $x^{2} - y^{2} = c^{2}$ cut at right angles, then