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

In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are $10^4$ at the end of 3 hours and $4 \cdot 10^4$ at the end of 5 hours, then there were _________ the beginning.

A
$10^4$
B
$\frac{10^4}{4}$
C
$410^4$
D
$\frac{10^4}{8}$
2
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
3
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
4
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
$\cos ^{-1}\left(\frac{-13}{14}\right)$
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