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1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int_1^4 \log [x] \mathrm{d} x$, where $[x]$ is the greatest integer function less than or equal to $x$ is equal to
A
$\log 5$
B
$\log 6$
C
$\log 2$
D
$\log 3$
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$$\int_1^e \frac{\mathrm{e}^x}{x}(1+x \log x) \mathrm{d} x=$$
A
$\mathrm{e}^{\mathrm{e}}$
B
$e^e-e$
C
$e^e+e$
D
$e$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $[x]$ denotes the greatest integer function, then $$\int_\limits0^5 x^2[x] d x=$$

A
$\frac{244}{3}$
B
$\frac{316}{3}$
C
$\frac{200}{3}$
D
$\frac{400}{3}$
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^2 x}{1+2^x} d x$ is

A
$\frac{\pi}{4}$
B
$\frac{\pi}{8}$
C
$\frac{\pi}{2}$
D
$4 \pi$
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