1
JEE Main 2025 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A board has 16 squares as shown in the figure :

JEE Main 2025 (Online) 23rd January Evening Shift Mathematics - Probability Question 14 English

Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

A
$\frac{3}{5}$
B
$\frac{4}{5}$
C
$\frac{23}{30}$
D
$\frac{7}{10}$
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

A
$\frac{2}{3}$
B
$\frac{3}{5}$
C
$\frac{4}{9}$
D
$\frac{1}{2}$
3
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12 x^2-7 x+1=0$, then the value of $\frac{P(\bar{A} \cup \bar{B})}{P(\bar{A} \cap \bar{B})}$ is :

A
$\frac{4}{3}$
B
$\frac{7}{4}$
C
$\frac{9}{4}$
D
$\frac{5}{3}$
4
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of $X$, then the value of $64\left(\mu+\sigma^2\right)$ is:

A
64
B
32
C
51
D
48
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