1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)$$ is a function satisfying $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$ with $$\mathrm{f}(0)=1$$ and $$\mathrm{g}(x)$$ is a function that satisfies $$\mathrm{f}(x)+\mathrm{g}(x)=x^2$$. Then the value of the integral $$\int_\limits0^1 f(x) g(x) d x$$ is

A
$$e-\frac{e^2}{2}-\frac{5}{2}$$
B
$$\mathrm{e}+\frac{\mathrm{e}^2}{2}-\frac{3}{2}$$
C
$$\mathrm{e}-\frac{\mathrm{e}^2}{2}-\frac{3}{2}$$
D
$$\mathrm{e}+\frac{\mathrm{e}^2}{2}+\frac{5}{2}$$
2
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$

A
$$\log \left|\frac{27}{32}\right|$$
B
$$\log \left|\frac{3}{4}\right|$$
C
$$\log \left|\frac{8}{9}\right|$$
D
$$\log \left|\frac{32}{27}\right|$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$

A
1
B
2
C
$$-$$1
D
0
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$$

A
$$\frac{\pi}{4}$$
B
$$\frac{2}{\pi}$$
C
0
D
$$\frac{\pi}{2}$$
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