Integrals of Some Particular Functions 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 Integrals of Some Particular Functions with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Integrals of Some Particular Functions questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Integrals of Some Particular Functions with Solutions
1.
$\int\left(\frac{4e^{2}-25}{2e^{x}-5}\right)dx = Ax+B \,\,log |2e^{x}-5|+c$ then- $ A = 5$, and $B = 3$
- $ A = 5$, and $B = - 3 $
- $A = - 5$, and $B = 3$
- $ A = - 5$, and $B = - 3$
2.
$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $- $log a.a^{x+tan^{-1}x}+c$
- $\frac{\left(x+tan^{-1}x\right)}{log\,a}+c$
- $\frac{a^{x+tan^{-1}x}}{log\,a}+c$
- $log \,a(x + tan^{-1}x) + c$
3.
Evaluate the integral: \( \int \sin^5 x \, dx \)- \( -\frac{1}{5} \cos x (5 - 10 \sin^2 x + \sin^4 x) + C \)
- \( -\cos x + \frac{\cos^3 x}{3} - \frac{\cos^5 x}{5} + C \)
- \( \frac{1}{5} \sin^5 x + C \)
- \( \int \sin^5 x \, dx = \int \sin^3 x \cdot \sin^2 x \, dx \)
4.
If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $- $-1$
- $\frac{1}{2} $
- $ - \frac{1}{2} $
- $1$
5.
$\int \frac{1}{\sqrt{8+2x-x^{2}}} dx$ is equal to- $\frac{1}{3} sin^{-1} \left(\frac{x-1}{3}\right) +c$
- $sin^{-1} \left(\frac{x+1}{3}\right) +c$
- $\frac{1}{3}sin^{-1} \left(\frac{x+1}{3}\right) +c$
- $sin^{-1} \left(\frac{x-1}{3}\right) +c$
6.
If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $- $\frac{\pi}{2} \log ( 1/2) $
- $ 1 - \frac{\pi}{2} \log ( 1/2) $
- $ 1 + \frac{\pi}{2} \log ( 1/2) $
- $\frac{\pi}{2} \log \, 2 $
7.
$\int^1_0 x \, \tan^{-1} x\,dx = $- $\frac{\pi}{4} + \frac{1}{2}$
- $\frac{\pi}{4} - \frac{1}{2}$
- $\frac{1}{2} - \frac{\pi}{4} $
- $ - \frac{\pi}{4} - \frac{1}{2}$
8.
If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$- $cot\,x$
- $tan\,x$
- $sec\,x$
- $cosec\,x$
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