1
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
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Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denote the number of defective oranges, then the variance of $x$ is

A
$26 / 75$
B
$14/25$
C
$18 / 25$
D
$28 / 75$
2
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
$\frac{5}{8}$
3
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
$\frac{9}{17}$
4
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
$\frac{7}{10}$
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