1
MHT CET 2026 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If $3\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) - 4\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right) + 2\tan^{-1}\left(\dfrac{2x}{1 - x^2}\right) = \dfrac{\pi}{3}$ then $x = ?$
A
$\sqrt{3}$
B
$1$
C
$\dfrac{1}{\sqrt{3}}$
D
$-1$
2
MHT CET 2026 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If $2\sin^{-1}x - 3\cos^{-1}x = 4$, then $2\sin^{-1}x + 3\cos^{-1}x =$
A
$\dfrac{6\pi - 4}{5}$
B
$\dfrac{6\pi + 4}{5}$
C
$\dfrac{5\pi - 4}{6}$
D
$\dfrac{5\pi + 4}{6}$
3
MHT CET 2026 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $a_1, a_2, a_3, \ldots, a_n$ are in arithmetic progression with common difference d, then $\tan\left[\tan^{-1}\left(\dfrac{d}{1 + a_1 a_2}\right) + \tan^{-1}\left(\dfrac{d}{1 + a_2 a_3}\right) + \ldots + \tan^{-1}\left(\dfrac{d}{1 + a_{n-1} a_n}\right)\right] = $ ____
A
$\dfrac{a_1 - a_n}{1 + a_1 a_n}$
B
$\dfrac{a_n - a_1}{1 - a_1 a_n}$
C
$\dfrac{a_n - a_1}{1 + a_1 a_n}$
D
$\dfrac{a_1 + a_n}{1 + a_1 a_n}$
4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=\tan ^{-1}\left\{\frac{\sqrt{1+t^2}-1}{t}\right\}, y=\cos ^{-1}\left\{\frac{1-t^2}{1+t^2}\right\}, \quad$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A

2

B

$\frac{1}{2}$

C

4

D

$\frac{1}{4}$

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