1
JEE Main 2025 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is :

A
$\frac{3}{8}$
B
$\frac{1}{8}$
C
$\frac{3}{16}$
D
$\frac{5}{8}$
2
JEE Main 2025 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$A$ and $B$ alternately throw a pair of dice. A wins if he throws a sum of 5 before $B$ throws a sum of 8 , and $B$ wins if he throws a sum of 8 before $A$ throws a sum of 5 . The probability, that A wins if A makes the first throw, is

A
$\frac{8}{19}$
B
$\frac{9}{19}$
C
$\frac{8}{17}$
D
$\frac{9}{17}$
3
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 5 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
$\frac{7}{10}$
4
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
$\frac{1}{2}$
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