1
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1
Out of Syllabus

The random variable $$\mathrm{X}$$ follows binomial distribution $$\mathrm{B}(\mathrm{n}, \mathrm{p})$$, for which the difference of the mean and the variance is 1 . If $$2 \mathrm{P}(\mathrm{X}=2)=3 \mathrm{P}(\mathrm{X}=1)$$, then $$n^{2} \mathrm{P}(\mathrm{X}>1)$$ is equal to :

A
15
B
12
C
11
D
16
2
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $$\mathrm{X}$$ denotes the number of tosses of the coin, then the mean of $$\mathrm{X}$$ is :

A
$$\frac{81}{64}$$
B
$$\frac{37}{16}$$
C
$$\frac{21}{16}$$
D
$$\frac{15}{16}$$
3
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

Two dice A and B are rolled. Let the numbers obtained on A and B be $$\alpha$$ and $$\beta$$ respectively. If the variance of $$\alpha-\beta$$ is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are co-prime, then the sum of the positive divisors of $$p$$ is equal to :

A
48
B
31
C
72
D
36
4
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

Let $$S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$$ be a sample space and $$A=\{M \in S: M$$ is invertible $$\}$$ be an event. Then $$P(A)$$ is equal to :

A
$$\frac{47}{81}$$
B
$$\frac{49}{81}$$
C
$$\frac{50}{81}$$
D
$$\frac{16}{27}$$
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