1
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to } $$

A
$$ \left[0, \frac{2}{3}\right] $$
B
$$ \left(0, \frac{2}{3}\right) $$
C
$$ \left(-\frac{2}{3}, \frac{2}{3}\right) $$
D
$$ \left[-\frac{2}{3}, \frac{2}{3}\right] $$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The solution of the differential equation $$\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x$$

A
$$ y e^{\sin x}=e^{\sin x}(\sin x+1)+c $$
B
$$ y e^{\sin x}=e^{\sin x}(\sin x-1)+c $$
C
$$ y e^{\sin 2 x}=e^{\sin 2 x}(\sin x-1)+c $$
D
$$ y e^{\cos x}=e^{\sin x}(\cos x-1)+c $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The area bounded by the curve $$y^2=4 a^2(x-1)$$ and the lines $$x=1, y=4 a$$ is

A
$$ \frac{16}{3} a \text { sq units } $$
B
$$ \frac{16}{3} a^2 \text { squnits } $$
C
$$ 16 a^2 \text { squnits } $$
D
$$ 4 a^2 \text { sq units } $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to } $$

A
$$ 2 \log 2 $$
B
$$ \frac{2}{3} \log 2 $$
C
0
D
$$ \log 2 $$
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