1
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x=\sqrt{\mathrm{e}^{\sin ^{-1} t}}$$ and $$y=\sqrt{\mathrm{e}^{\cos ^{-1} t}}$$, then $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ is

A
$$\frac{-y}{x^2}$$
B
$$\frac{y^2}{2 x^2}$$
C
$$\frac{2 y}{x^2}$$
D
$$\frac{-2 y}{x^2}$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is

A
$$\frac{100}{101}$$
B
$$\frac{51}{50}$$
C
$$\frac{50}{51}$$
D
$$\frac{101}{102}$$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is :

A
$$\mathrm{e}^x\left(\frac{x}{x+4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\mathrm{e}^x\left(\frac{4}{x+4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\mathrm{e}^x\left(\frac{x}{(x+4)^2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\mathrm{e}^x\left(\frac{4}{(x+4)^2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The diagonal of a square is changing at the rate of $$0.5 \mathrm{~cm} / \mathrm{sec}$$. Then the rate of change of area when the area is $$400 \mathrm{~cm}^2$$ is equal to

A
$$20 \sqrt{2} \mathrm{~cm}^2 / \mathrm{sec}$$
B
$$10 \sqrt{2} \mathrm{~cm}^2 / \mathrm{sec}$$
C
$$\frac{1}{10 \sqrt{2}} \mathrm{~cm}^2 / \mathrm{sec}$$
D
$$\frac{10}{\sqrt{2}} \mathrm{~cm}^2 / \mathrm{sec}$$
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