1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals } $$

A
$$\frac{-2 x}{\sqrt{1-x^2}}$$
B
$$\frac{-1}{\sqrt{1+x^2}}$$
C
$$\frac{1}{\sqrt{1-x^2}}$$
D
$$\frac{2 x}{\sqrt{1-x^2}}$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=f^{\prime}(x)$$ and $$f(1)=2$$, then $$f(3)$$ is

A
$$2 e^3$$
B
$$\log 8-3$$
C
$$2 e^2$$
D
6
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to } $$

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

$$ \text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is } $$

A
$$ \frac{2}{1+4 x^2} $$
B
$$ -\frac{4}{1+4 x^2} $$
C
$$ -\frac{2}{1+4 x^2} $$
D
$$ \frac{1}{1+4 x^2} $$
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