1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The number of solutions, of $2^{1+|\cos x|+|\cos x|^2+\ldots \ldots \cdots \cdots}=4$ in $(-\pi, \pi)$, is

A
2
B
3
C
4
D
6
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10< x<10$, where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to

A
10
B
9
C
6
D
8
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overline{\mathrm{c}}=\hat{\mathrm{a}}+2 \hat{\mathrm{~b}}$ and $\overline{\mathrm{d}}=5 \hat{\mathrm{a}}+4 \hat{\mathrm{~b}}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

A
$\frac{\pi}{6}$
B
$\cos ^{-1}\left(\frac{13}{14}\right)$
C
$\frac{\pi}{3}$
D
$\cos ^{-1}\left(\frac{-13}{14}\right)$
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Integrating factor of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+y=\frac{1+y}{x}$ is

A
$\frac{x}{\mathrm{e}^x}$
B
$x e^x$
C
$e^x$
D
$\frac{\mathrm{e}^x}{x}$
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