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

Let L be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If L makes an angle $\alpha$ with the positive X -axis, then $\cos \alpha$ equals

A
1
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{\sqrt{3}}$
D
$\frac{1}{2}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group if there are two specific girls A and B , who refuse to be the members of the same team, is

A
350
B
300
C
200
D
500
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the mean and the variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to

A
$\frac{5}{16}$
B
$\frac{11}{16}$
C
$\frac{12}{16}$
D
$\frac{15}{16}$
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}$ is

A
$\sin ^{-1} y=\log x+c$, where c is a constant of integration.
B
$\frac{y}{x}=\sin ^{-1} x+\mathrm{c}$, where c is a constant of integration.
C
$\frac{y}{x}=\sqrt{x^2-y^2}+\mathrm{c}$, where c is a constant of integration.
D
$\sin ^{-1}\left(\frac{y}{x}\right)=\log x+\mathrm{c}$, where c is a constant of integration.
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