1
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The surface area of a spherical balloon is increasing at the rate $$2 \mathrm{~cm}^2 / \mathrm{sec}$$. Then rate of increase in the volume of the balloon is , when the radius of the balloon is $$6 \mathrm{~cm}$$.

A
$$4 \mathrm{~cm}^3 / \mathrm{sec}$$.
B
$$16 \mathrm{~cm}^3 / \mathrm{sec}$$.
C
$$36 \mathrm{~cm}^3 / \mathrm{sec}$$.
D
$$6 \mathrm{~cm}^3 / \mathrm{sec}$$.
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The p.m.f. of a random variable X is $$\mathrm{P(X = x) = {1 \over {{2^5}}}\left( {_x^5} \right),x = 0,1,2,3,4,5}=0$$ then

A
$$\mathrm{P}(\mathrm{X} \leq 2)<\mathrm{P}(\mathrm{X} \geq 3)$$
B
$$\mathrm{P}(\mathrm{X} \leq 2)>\mathrm{P}(\mathrm{X} \geq 3)$$
C
$$\mathrm{P}(\mathrm{X} \leq 2)=2 \mathrm{P}(\mathrm{X} \geq 3)$$
D
$$\mathrm{P}(\mathrm{X} \leq 2)=\mathrm{P}(\mathrm{X} \geq 3)$$
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=4,|\overline{\mathrm{c}}|=3$$ and each is perpendicular to the sum of the other two, then $$|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|^2=$$

A
60
B
12
C
47
D
50
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\frac{n !}{2 !(n-2) !}$$ and $$\frac{n !}{4 !(n-4) !}$$ are in the ratio $$2: 1$$, then $$n=$$

A
6
B
4
C
5
D
3
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