1
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be two events such that $$P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$$ and $$P(A \cap B)=\frac{1}{9} \cdot$$ Consider

(S1) $$P\left(A^{\prime} \cup B\right)=\frac{5}{6}$$,

(S2) $$P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$$

Then

A
Both (S1) and (S2) are true
B
Both (S1) and (S2) are false
C
Only (S1) is true
D
Only (S2) is true
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Out of $$60 \%$$ female and $$40 \%$$ male candidates appearing in an exam, $$60 \%$$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :

A
$$\frac{2}{3}$$
B
$$\frac{11}{16}$$
C
$$\frac{23}{32}$$
D
$$\frac{13}{16}$$
3
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
4
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
$$\frac{8}{11}$$
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