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

If $$\int \frac{x^2}{\sqrt{1-x}} \mathrm{~d} x=\mathrm{p} \sqrt{1-x}\left(3 x^2+4 x+8\right)+\mathrm{c}$$ where $$\mathrm{c}$$ is a constant of integration, then the value of $$p$$ is

A
$$\frac{-2}{15}$$
B
$$\frac{2}{15}$$
C
$$\frac{4}{15}$$
D
$$\frac{-4}{15}$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\mathrm{d} x}{\cot ^2 x-1}=\frac{1}{\mathrm{~A}} \log |\sec 2 x+\tan 2 x|-\frac{x}{\mathrm{~B}}+\mathrm{c}$$, (where $$\mathrm{c}$$ is constant of integration), then $$\mathrm{A}+\mathrm{B}=$$

A
$$-$$6
B
6
C
$$-$$5
D
5
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$I=\int \frac{d x}{\sin (x-a) \sin (x-b)}$$, then I is given by

A
$$\frac{1}{\sin (b-a)} \log |\sin (x-a) \sin (x-b)|+c$$, where $$c$$ is a constant of integration.
B
$$\log \left|\frac{\sin (x-a)}{\sin (x-b)}\right|+c$$, where $$c$$ is a constant of integration.
C
$$\frac{1}{\sin (b-a)} \log \left|\frac{\sin (x-a)}{\sin (x-b)}\right|+c$$, where $$c$$ is a constant of integration.
D
$$\frac{1}{\sin (b-a)} \log \left|\frac{\sin (x-b)}{\sin (x-a)}\right|+c$$, where $$c$$ is a constant of integration.
4
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\sin 2 x\left(1-\frac{3}{2} \cos x\right)}{e^{\sin ^2 x+\cos ^3 x}} d x=$$

A
$$\mathrm{e}^{\sin ^2 x+\cos ^3 x}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\mathrm{-e}^{-(\sin ^2 x+\cos ^3 x)}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\mathrm{e}^{-(\sin ^2 x+\cos ^3 x)^2}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\mathrm{e}^{\sin ^2 x+\cos x}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
MHT CET Subjects
EXAM MAP