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

A random variable $$X$$ has the following probability distribution

$$\mathrm{X}=x$$ 0 1 2
$$\mathrm{P(X}=x)$$ $$\mathrm{4k-10k^2}$$ $$\mathrm{5k-1}$$ $$\mathrm{3k^3}$$

then P(X < 2) is

A
$$\frac{2}{9}$$
B
$$\frac{5}{9}$$
C
$$\frac{8}{9}$$
D
$$\frac{4}{9}$$
2
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{X}$$ be random variable having Binomial distribution $$B(7, p)$$. If $$P[X=3]=5 P[X=4]$$, then variance of $$\mathrm{X}$$ is

A
$$\frac{7}{6}$$
B
$$\frac{35}{36}$$
C
$$\frac{77}{36}$$
D
$$\frac{1}{36}$$
3
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If a continuous random variable $$\mathrm{X}$$ has probability density function $$\mathrm{f}(x)$$ given by

$$f(x)=\left\{\begin{array}{cl} a x & , \text { if } 0 \leq x<1 \\ a & , \text { if } 1 \leq x<2 \\ 3 a-a x & , \text { if } 2 \leq x \leq 3 \\ 0 & , \text { otherwise } \end{array}\right.$$,

then a has the value

A
$$\frac{1}{5}$$
B
$$\frac{1}{3}$$
C
$$\frac{1}{2}$$
D
1
4
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
$$\frac{8}{13}$$
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