1
JEE Main 2025 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

If A and B are two events such that $P(A) = 0.7$, $P(B) = 0.4$ and $P(A \cap \overline{B}) = 0.5$, where $\overline{B}$ denotes the complement of B, then $P\left(B \mid (A \cup \overline{B})\right)$ is equal to

A

$\frac{1}{3}$

B

$\frac{1}{2}$

C

$\frac{1}{4}$

D

$\frac{1}{6}$

2
JEE Main 2025 (Online) 7th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $n^2 - m^2$ is equal to :

A

64

B

80

C

60

D

72

3
JEE Main 2025 (Online) 7th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let a random variable X take values 0, 1, 2, 3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X2)=2E(X). Then the value of 8p−1 is :

A

2

B

0

C

3

D

1

4
JEE Main 2025 (Online) 4th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

A
$\frac{129}{182}$
B
$\frac{17}{26}$
C
$\frac{19}{26}$
D
$\frac{103}{182}$
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