JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 1

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in $2\times2$ matrices. The probability that such formed matrices have all different entries and are non-singular, is :

Probability

$\frac{45}{162}$$\frac{22}{81}$$\frac{23}{81}$$\frac{43}{162}$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 2

A dice is thrown twice. If $A$ is the event that the sum of numbers appearing on them is $7$ and $B$ is the event that number $5$ appears at least once, then $P(B|A)$ is equal to

Probability

$\frac{1}{2}$$\frac{1}{3}$$\frac{2}{11}$$\frac{2}{5}$

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 3

Let in a Binomial distribution, consisting of $5$ independent trials, probabilities of exactly $1$ and $2$ successes be $0.4096$ and $0.2048$ respectively. Then the probability of getting exactly $3$ successes is equal to :

Probability

$\frac{40}{243}$$\frac{80}{243}$$\frac{128}{625}$$\frac{32}{625}$

JEE Main 2021 (Online) 4th August Morning ShiftQuestion 4

Two players $A$ and $B$ play a game. Player $A$ first throws a fair die and if $5$ or $6$ appears, he wins; otherwise player $B$ throws a fair coin and wins if head comes. The process continues till someone wins. The probability that $B$ wins after completion of $3$ or more throws of the die, is

Probability

$\frac{1}{18}$$\frac{1}{9}$$\frac{4}{9}$$\frac{1}{2}$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 5

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :

Probability

$\frac{1}{27}$$\frac{1}{8}$$\frac{3}{8}$$\frac{3}{4}$