1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The order and degree of differential equation of all tangent lines to the parabola $x^2=4 y$ is respectively.
A
$1,2$
B
$2,2$
C
$3,1$
D
$4,1$
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability distribution of a discrete random variable X is

$\mathrm{X}$ 0 1 2 3 4
$\mathrm{P(X=}x)$ $\mathrm{2k}$ $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{4k}$ $\mathrm{k}$

If $\mathrm{a}=\mathrm{P}(x<3)$ and $\mathrm{b}=\mathrm{P}(2 \leq \mathrm{X}<4)$, then

A
$\mathrm{a}=\mathrm{b}$
B
$a>b$
C
a $<$ b
D
$\mathrm{a}=\frac{1}{2} \mathrm{~b}$
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If a random variable $X$ has the p.d.f. $f(x)=\left\{\begin{array}{cc}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0< x< \infty \\ 0 & , \text { otherwise }\end{array}\right.$ then c.d.f. of X is
A
$2 \tan ^{-1} x$
B
$\frac{\pi}{2} \tan ^{-1} x$
C
$\frac{2}{\pi} \tan ^{-1} x$
D
$\tan ^{-1} x$
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $y=y(x)$ satisfies $\left(\frac{2+\sin x}{1+y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=-\cos x$ such that $y(0)=2$, then $y\left(\frac{\pi}{2}\right)$ is equal to
A
4
B
3
C
2
D
1

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