1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^{\frac{\pi}{4}} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x=$$

A
$\frac{\pi}{2} \log 2$
B
$\frac{\pi}{4} \log 2$
C
$\frac{\pi}{6} \log 2$
D
$\frac{\pi}{8} \log 2$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$A$ and $B$ are independent events with $P(A)=\frac{3}{10}$, $\mathrm{P}(\mathrm{B})=\frac{2}{5}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}\right)$ has the value

A
$\frac{41}{50}$
B
$\frac{41}{125}$
C
$\frac{7}{25}$
D
$\frac{7}{50}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=(x-1)(x-2)(x-3), x \in[0,4]$. Values of C will be __________ if L.M.V.T. (Lagrange's Mean Value Theorem) can be applied.

A
$\frac{4-2 \sqrt{3}}{3}, \frac{4+2 \sqrt{3}}{3}$
B
$\frac{6-2 \sqrt{3}}{3}, \frac{6+2 \sqrt{3}}{3}$
C
$\frac{6-\sqrt{3}}{3}, \frac{6+\sqrt{3}}{3}$
D
$2-\sqrt{3}, 2+\sqrt{3}$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\sin x+\cos x}{1+y \log y}\right)$ is

A
$\mathrm{e}^y \log y=\mathrm{e}^{\mathrm{x}} \sin x+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
C
$\log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
D
$y \log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
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