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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}, \quad$ then $2 x y \frac{d y}{d x}$ is equal to
A
$x+\frac{a}{x}$
B
$\frac{x^2+a^2}{a x}$
C
$\frac{x}{a}-\frac{a}{x}$
D
$\frac{a}{x}-\frac{x}{a}$
2
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
$-\frac{1}{2 \sqrt{x}(1+x)}$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=f(x), \quad p=\frac{d y}{d x} ; q=\frac{d^2 y}{d x^2} \text { then } \frac{d^2 x}{d y^2} \text { is equal to } $$

A
$$-\frac{q}{p^2}$$
B
$$\frac{q}{p}$$
C
$$-\frac{q}{p^3}$$
D
$$\frac{q}{p^2}$$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\sqrt{\sin x+y} \text { then find } \frac{d y}{d x} \text { at } x=0, \quad y=1 $$

A
0
B
1
C
2
D
$$-$$1
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