1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$ y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^2 $$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

A
$2 \mathrm{n}(\mathrm{n}+1)$
B
$\mathrm{n}(\mathrm{n}+1)$
C
 $\frac{\mathrm{n}(\mathrm{n}+1)}{2}$
D
$\left(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\right)^2$
2
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

For the probability distribution

$x :$ 0 1 2 3 4 5
$p(x):$ $\mathrm{k}$ 0.3 0.15 0.15 0.1 2$\mathrm{k}$

The expected value of X is

A
1.45
B
2.45
C
1.55
D
2.55
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{\mathrm{d} x}{7+6 x-x^2}$ is equal to

A
$\frac{1}{4} \log \left(\frac{1+x}{7-x}\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{1}{8} \log \left(\frac{7-x}{1+x}\right)+\mathrm{c}$, ( where c is a constant of integration)
C
$\frac{1}{4} \log \left(\frac{7-x}{1+x}\right)+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{8} \log \left(\frac{1+x}{7-x}\right)+\mathrm{c}$, (where c is a constant of integration)
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is equal to }\end{aligned}$

A
$\cos 54^{\circ}$
B
$\cos 36^{\circ}$
C
$\sin 54^{\circ}$
D
$\sin 36^{\circ}$
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