1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 30^{\circ}=0.8660$

A
0.8778
B
0.7666
C
0.7916
D
0.8616
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

A
$\frac{24}{169}$
B
$\frac{52}{169}$
C
$\frac{25}{169}$
D
$\frac{49}{169}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

A
$\frac{\mathrm{e}^x}{(x+1)}+\mathrm{c}$, (where c is constant of integration)
B
$\frac{\mathrm{e}^{\mathrm{x}}}{(x+1)^2}+\mathrm{c}$, (where c is constant of integration)
C
$\frac{-\mathrm{e}^x}{(x+1)}+\mathrm{c}$, (where c is constant of integration)
D
$\frac{-\mathrm{e}^x}{(x+1)^2}+\mathrm{c}$, (where c is constant of integration)
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{P}(2,3,6)$ be a point in space and Q be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+4 z=1$ is

A
$\frac{13}{6}$
B
$-\frac{6}{13}$
C
$\frac{6}{13}$
D
$-\frac{13}{6}$
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