1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sin ^{-1}\left(\frac{1}{\sqrt{x+1}}\right)$ then $\frac{d y}{d x}=$
A
$\frac{1}{2 \sqrt{1-x}}$
B
$\frac{1}{2 \sqrt{x}(1+\sqrt{x})}$
C
$\frac{1}{2 x(1+\sqrt{x})}$
D
$-\frac{1}{2 \sqrt{x}(1+x)}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$ is equal to
A
$\pi$
B
$2 \pi$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The range of $x$ for which the equation $\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)=2 \tan ^{-1} x$ holds true
A
$|x| \leq 1$
B
$\forall x \in R$
C
$x \geq 0$
D
$|x| \geq 1$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A spherical snowball is melting such that its volume is decreasing at the rate of $1 \mathrm{~cm}^3 / \mathrm{min}$. The rate at which the diameter is decreasing when the diameter is 10 cm is
A
$\frac{11}{75 \pi} \mathrm{~cm} / \mathrm{min}$
B
$\frac{1}{50 \pi} \mathrm{~cm} / \mathrm{min}$
C
$\frac{2}{75 \pi} \mathrm{~cm} / \mathrm{min}$
D
$\frac{1}{25 \pi} \mathrm{~cm} / \mathrm{min}$
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