1
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$e^{-y} \cdot y=x$$, then $$\frac{d y}{d x}$$ is

A
$$\frac{y}{1-y}$$
B
$$\frac{1}{x y(1-y)}$$
C
$$\frac{1}{x(1-y)}$$
D
$$\frac{y}{x(1-y)}$$
2
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\beta)=$$

A
$$\frac{h}{a+b}$$
B
$$\frac{2 h}{a+b}$$
C
$$\frac{\mathrm{h}}{\mathrm{a}-\mathrm{b}}$$
D
$$\frac{2 h}{a-b}$$
3
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The vertices of triangle $$\mathrm{ABC}$$ are $$\mathrm{A} \equiv(3,0,0) ; \mathrm{B} \equiv(0,0,4) ; \mathrm{C} \equiv(0,5,4)$$. Find the position vector of the point in which the bisector of angle A meets B C is

A
$$5 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}$$
B
$$\frac{5 \hat{\mathrm{j}}+12 \hat{\mathrm{k}}}{3}$$
C
$$\frac{5 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}}{13}$$
D
$$\frac{5 \hat{\mathrm{i}}-12 \hat{\mathrm{j}}}{3}$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles, then $\lambda=$

A
$$\frac{-70}{11}$$
B
$$\frac{70}{11}$$
C
$$\frac{11}{70}$$
D
$$\frac{-11}{70}$$
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