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

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

A
$\frac{11}{15}$
B
$\frac{2}{15}$
C
$\frac{3}{5}$
D
$\frac{28}{75}$
2
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the probability that the random variable $X$ takes the value $x$ is given by

$P(X=x)=k(x+1) 3^{-x}, x=0,1,2,3 \ldots$, where $k$ is a constant, then $P(X \geq 3)$ is equal to

A
$\frac{1}{9}$
B
$\frac{8}{27}$
C
$\frac{7}{27}$
D
$\frac{4}{9}$
3
JEE Main 2025 (Online) 2nd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $$

$$ \begin{array}{lccc} & \text { Red } & \text { Blue } & \text { Green } \\ \text { Bag I } & 3 & 2 & 5 \\ \text { Bag II } & 4 & 3 & 3 \\ \text { Bag III } & 5 & 1 & 4 \end{array} $$

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:
A
6
B
9
C
7
D
8
4
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $ \frac{29}{45} $, then n is equal to:

A

5

B

6

C

4

D

3

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