1
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is

A
$$\frac{3}{13}$$
B
$$\frac{5}{13}$$
C
$$\frac{6}{13}$$
D
$$\frac{8}{13}$$
2
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ and $$\bar{b}=\hat{i}-\hat{j}-\hat{k}$$, then the projection of $$\bar{b}$$ in the direction of $$\bar{a}$$ is

A
$$\frac{1}{\sqrt{29}}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$\frac{5}{\sqrt{3}}$$
D
$$\frac{3}{\sqrt{29}}$$
3
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherwise }\end{array}\right.$$, then $$\int_\limits{-2}^3 \mathrm{f}(x) \mathrm{d} x$$ is equal to

A
0
B
2
C
1
D
3
4
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the line passing through the point $$(-1,3,-2)$$ and perpendicular to each of the lines $$\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$$ and $$\frac{x+2}{-3}=\frac{y-1}{2}=\frac{z+1}{5}$$ is

A
$$\frac{x+1}{2}=\frac{y-3}{7}=\frac{z+2}{4}$$
B
$$\frac{x+1}{2}=\frac{y-3}{-7}=\frac{z+2}{4}$$
C
$$\frac{x-1}{2}=\frac{y+3}{-7}=\frac{z+2}{4}$$
D
$$\frac{x-1}{2}=\frac{y+3}{7}=\frac{z-2}{4}$$
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