1
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}$$ and $$\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ are three vectors such that $$\vec{a}=x \vec{b}+y \vec{c}$$, then $$x+y=$$

A
$$-1$$
B
$$-2$$
C
5
D
1
2
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$\frac{x-2}{1}=\frac{y+m}{2}=\frac{z-2}{1}$$ intersect each other, then value of m is

A
1
B
$$-$$2
C
2
D
$$-$$1
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The length of perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\overline{\mathrm{r}}=(11 \hat{i}-2 \hat{j}-8 \hat{k})+\lambda(10 \hat{i}-4 \hat{j}-11 \hat{k})$$ is

A
$$\sqrt{14}$$ units
B
14 units
C
237 units
D
$$\sqrt{237}$$ units
4
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \text { If } u=\cos ^3 x, v=\sin ^3 x \text {, then }\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}} \text { is equal to } $$

A
$$-$$2
B
2
C
1
D
$$-$$1
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