Integral Calculus is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.
This article gives you a full set of MHT CET PYQs for Integral Calculus with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Integral Calculus questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Integral Calculus with Solutions
1.
Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$- \( \frac{1}{3} \ln \left( e^{3x} + 1 \right) + C \)
- \( \frac{1}{3} \ln \left( e^{3x} - 1 \right) + C \)
- \( \frac{1}{3} \ln \left( e^{3x} + e^x \right) + C \)
- \( \frac{1}{2} \ln \left( e^{3x} + 1 \right) + C \)
2.
The surface area of a spherical balloon is increasing at the rate of \( 2 \, \text{cm}^2/\text{sec} \). Then the rate of increase in the volume of the balloon, when the radius of the balloon is \( 6 \, \text{cm} \), is:- \( 4 \, \text{cm}^3/\text{sec} \)
- \( 16 \, \text{cm}^3/\text{sec} \)
- \( 36 \, \text{cm}^3/\text{sec} \)
- \( 6 \, \text{cm}^3/\text{sec} \)
3.
If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is:- \( \frac{y^2 \cot x}{1 - y \log (\sin x)} \)
- \( \frac{y^2 \cot x}{1 - y \log (x)} \)
- \( \frac{y^2 \cot x}{1 + y \log (\sin x)} \)
- \( \frac{y^2 \cot x}{1 + y \log (x)} \)
4.
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:- \( (-8, 3) \)
- \( (-3, 8) \)
- \( (3, 8) \)
- \( (-8, -3) \)
5.
The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is:- \( e^x(x-1) + \cos \frac{y}{x} + c = 0 \)
- \( x e^x + \cos \frac{y}{x} + c = 0 \)
- \( e^x(x+1) + \cos \frac{y}{x} + c = 0 \)
- \( e^x x - \cos \frac{y}{x} + c = 0 \)
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