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

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1\end{array}\right]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

A
6
B
$-$14
C
14
D
$-$6
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to

A
$\frac{1}{3} x^3 \psi\left(x^3\right)-3 \int x^3 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^3 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{1}{3} x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 80 thousand in 40 years, then the population in another 40 years will be

A
180000
B
128000
C
160000
D
256000
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If X is a random variable with distribution given below

$\mathrm{X}=x_{\mathrm{i}}:$ 0 1 2 3
$\mathrm{P}\left(\mathrm{X}=x_{\mathrm{i}}\right):$ $\mathrm{k}$ $\mathrm{3k}$ $\mathrm{3k}$ $\mathrm{k}$

Then the value of $k$ and its variance are respectively given by

A
$\frac{1}{8}, \frac{22}{27}$
B
$\frac{1}{8}, \frac{23}{27}$
C
$\frac{1}{8}, \frac{8}{9}$
D
$\frac{1}{8}, \frac{3}{4}$
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