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

The sum of the infinite series $\cot ^{-1}\left(\frac{7}{4}\right)+\cot ^{-1}\left(\frac{19}{4}\right)+\cot ^{-1}\left(\frac{39}{4}\right)+\cot ^{-1}\left(\frac{67}{4}\right)+\ldots$. is :

A
$\frac{\pi}{2}+\cot ^{-1}\left(\frac{1}{2}\right)$
B
$\frac{\pi}{2}-\cot ^{-1}\left(\frac{1}{2}\right)$
C
$\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{2}\right)$
D
$\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{2}\right)$
2
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
$\frac{\pi}{4}+\sin ^{-1} x$
3
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

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

4
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
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