1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

In a triangle ABC with usual notations if, $\tan \left(\frac{\mathrm{B}-\mathrm{C}}{2}\right)=x \cot \frac{\mathrm{~A}}{2}$, then $x=$

A
$\frac{c-a}{c+a}$
B
$\frac{a-b}{a+b}$
C
$\frac{\mathrm{b}-\mathrm{c}}{\mathrm{b}+\mathrm{c}}$
D
$\frac{a+b}{a-b}$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

A coin is tossed until one head appears or a tail appears 4 times in succession. The probability distribution of the number of tosses is

A

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{8} & \frac{1}{8} & \frac{1}{2} & \frac{1}{4} \\ \hline \end{array} $$

B

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \\ \hline \end{array} $$

C

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} & \frac{1}{2} \\ \hline \end{array} $$

D

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{8} \\ \hline \end{array} $$

3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The degree of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+3\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2=x^2 \log \left(\frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right)$ is

A
1
B
2
C
3
D
Not defined
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the sum of the squares of the distances of a point $\mathrm{P}(x, y, z)$ from the three co-ordinate axes is 324 , then the distance of point P from the origin is ….

A
18
B
162
C
$9 \sqrt{2}$
D
324
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