1
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$

A
$$1, \frac{2}{5}$$
B
10
C
2
D
$$\frac{2}{3}, 40$$
2
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the p.m.f of a. r.v. $$X$$ is given by

$$P(X=x)=\frac{{ }^5 C_x}{2^5}$$

if $$x=0,1,2, \ldots \ldots . .5=0$$,

0 , otherwise,

then which of the following is not true?

A
$$P(X \leq 2)=P(X \geq 3)$$
B
$$P(X \leq 1)=P(X \geq 4)$$
C
$$P(X \leq 2) \geq P(X \geq 4)$$
D
$$P(X \leq 3) \leq P(X \geq 3)$$
3
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

The radius of the circle passing through the points $$(5,7),(2,-2)$$ and $$(-2,0)$$ is

A
2 units
B
5 units
C
3 units
D
4 units
4
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is

A
$$e^{\tan ^{-1} x}$$
B
$$-e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}$$
C
$$-e^{\tan ^{-1} x}$$
D
$$e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}$$
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