1
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
2
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
$$\frac{2}{x^2}$$
3
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
$$\frac{1}{1+4 x^2}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0$$

A
1
B
sec a
C
cos a
D
$$-1$$
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