1
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Considering only the principal values of inverse function, the set

$$A=\left\{x \geq 0 / \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\right\}$$

A
is an empty set.
B
is a singleton set.
C
contains more than two elements.
D
contains two elements.
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The number of real solutions of

$\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

A
zero.
B
one.
C
two.
D
infinite.
3
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\sin \left(2 \cos ^{-1}\left(-\frac{3}{5}\right)\right)$ is

A
$\frac{24}{25}$
B
$-\frac{24}{25}$
C
$\frac{8}{25}$
D
$-\frac{8}{25}$
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is

A
$$\frac{100}{101}$$
B
$$\frac{51}{50}$$
C
$$\frac{50}{51}$$
D
$$\frac{101}{102}$$
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