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

The number of all values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ satisfying the equation $(1-\tan \theta)(1+\tan \theta) \sec ^2 \theta+2 \tan ^2 \theta=0$ is

A
1
B
0
C
2
D
infinitely many.
2
MHT CET 2024 3rd May Evening 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 kings obtained in the two drawn cards. Then $\mathrm{P}(x=1)+\mathrm{P}(x=2)$ equals

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

The curve $y=a x^3+b x^2+c x+5$ touches the $x$-axis at $(-2,0)$ and cuts the $y$-axis at a point Q where its gradient is 3 , then the value of $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is

A
$\frac{7}{8}$
B
$\frac{7}{4}$
C
$\frac{7}{2}$
D
$\frac{7}{12}$
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{L}_1$ $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+1}{1}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y+2}{1}=\frac{z-3}{3}$ be the given lines. Then the unit vector perpendicular to $L_1$ and $L_2$ is

A
$\frac{-5 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}}{\sqrt{78}}$
B
$\frac{5 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{5 \sqrt{3}}$
C
$\frac{5 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{5 \sqrt{3}}$
D
$\frac{5 \hat{i}+7 \hat{j}-\hat{k}}{5 \sqrt{3}}$
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