CUET Mathematics - If e^3 x(x^4+1)^-1dx = m/n(x^4+1)+C, where C is an arbitrary constant, m and n are positive integers such that g.c.d (m,n)=1, then (4m^2+n^2) is equal to | PYQs + Solutions

CUET Mathematics 2026 18th May Shift 1

Calculus

Medium

applied

✅ Correct Option: 1

Related questions:

29th May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\displaystyle\int_{-2}^{2}\cos^4x\sin^5x\,dx$	(I) $\pi$
(B) $\displaystyle\int_{-1}^{1}\lvert x \rvert dx$	(II) $\dfrac{\pi}{4}$
(C) $\displaystyle\int_0^{\pi/2}\cos^2x\,dx$	(III) 0
(D) $\displaystyle\int_{-\pi/2}^{\pi/2}(x^3+x\cos x+\tan^5x+1)dx$	(IV) 1

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14th May Shift 2

If C is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\int a^x \, dx$	I.	$\sin^{-1}\dfrac{x}{a} + C$
B.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 - x^2}}$	II.	$\log_e \vert x + \sqrt{x^2 - a^2} \vert + C$
C.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 + x^2}}$	III.	$\dfrac{a^x}{\log_e a} + C$
D.	$\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}}$	IV.	$\log_e \vert x + \sqrt{a^2 + x^2} \vert + C$

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30th May Shift 2

The value of integral $\int_{-\pi/2}^{\pi/2} \frac{1}{1+e^{\sin x}}dx$ is

CUET Mathematics 2026 18th May Shift 1 PYQs