1
JEE Main 2025 (Online) 4th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Considering the principal values of the inverse trigonometric functions, $\sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^2}\right),-\frac{1}{2}< x<\frac{1}{\sqrt{2}}$, is equal to

A
$\frac{-5 \pi}{6}-\sin ^{-1} x$
B
$\frac{5 \pi}{6}-\sin ^{-1} x$
C
$\frac{\pi}{6}+\sin ^{-1} x$
D
$\frac{\pi}{4}+\sin ^{-1} x$
2
JEE Main 2025 (Online) 28th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let [x] denote the greatest integer less than or equal to x. Then the domain of $ f(x) = \sec^{-1}(2[x] + 1) $ is:

A

$(-\infty, \infty)$

B

$(-\infty, \infty)- \{0\}$

C

$(-\infty, -1] \cup [0, \infty)$

D

$(-\infty, -1] \cup [1, \infty)$

3
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)$ is equal to:

A
$\frac{33}{65}$
B
1
C
$\frac{32}{65}$
D
0
4
JEE Main 2025 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\alpha>\beta>\gamma>0$, then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^2\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^2\right)}{(\beta-\gamma)}\right\}+\cot ^{-1}\left\{\alpha+\frac{\left(1+\alpha^2\right)}{(\gamma-\alpha)}\right\}$ is equal to :

A
$3 \pi$
B
$\frac{\pi}{2}-(\alpha+\beta+\gamma)$
C
$\pi$
D
0
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