1
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $$P(X>n-3)=\frac{k}{2^{n}}$$, then k is equal to :

A
528
B
529
C
629
D
630
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

A six faced die is biased such that

$$3 \times \mathrm{P}($$a prime number$$)\,=6 \times \mathrm{P}($$a composite number$$)\,=2 \times \mathrm{P}(1)$$.

Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

A
$$\frac{3}{11}$$
B
$$\frac{5}{11}$$
C
$$\frac{7}{11}$$
D
$$\frac{8}{11}$$
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Let $$S$$ be the sample space of all five digit numbers. It $$p$$ is the probability that a randomly selected number from $$S$$, is a multiple of 7 but not divisible by 5 , then $$9 p$$ is equal to

A
1.0146
B
1.2085
C
1.0285
D
1.1521
4
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

Let $$X$$ be a binomially distributed random variable with mean 4 and variance $$\frac{4}{3}$$. Then, $$54 \,P(X \leq 2)$$ is equal to

A
$$\frac{73}{27}$$
B
$$\frac{146}{27}$$
C
$$\frac{146}{81}$$
D
$$\frac{126}{81}$$
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