JEE MAIN Probability Distribution Previous Year Question Paper and Solution with PDF

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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Probability Distribution PYQ

Qus : 1 JEE MAIN PYQ

Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$. Then the mean of the distribution and P(X is positive and even) respectively are :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and ${{37} \over 4}$ respectively, then (a $-$ b)² is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 July Morning Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ when the throw results in the sum of $9$, and loses Rs. $6$ for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

A six faced die is biased such that

$3 \times P(\text{a prime number}) = 6 \times P(\text{a composite number}) = 2 \times P(1).$

Let $X$ be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of $X$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Evening Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

Let 9 distinct balls be distributed among 4 boxes, B₁, B₂, B₃ and B₄. If the probability than B₃ contains exactly 3 balls is $k{\left( {{3 \over 4}} \right)^9}$ then k lies in the set :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 February Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

A random variable X has the following probability distribution :

The value of P(1 < X < 4 | X $\le$ 2) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Evening Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let a random variable $X$ take values $0,1,2,3$ with $P(X=0)=P(X=1)=p$, $P(X=2)=P(X=3)$ and $E(X^2)=2E(X)$. Then the value of $8p-1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

The probability that the random variable $X$ takes 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 $P(X \ge 2)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Three defective oranges are accidentally 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 $x$ denotes the number of defective oranges, then the variance of $x$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is ${1 \over n}$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

A fair die is thrown until $2$ appears. Then, the probability that $2$ appears in an even number of throws is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be ${1 \over 2}$ and probability of occurrence of 0 at the odd place be ${1 \over 3}$. Then the probability that '10' is followed by '01' is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $\displaystyle \frac{dy}{dx}=\frac{\tan x + y}{\sin x}$, $x\in\left(0,\frac{\pi}{2}\right)$, satisfying $y\!\left(\frac{\pi}{4}\right)=2$. Then $y\!\left(\frac{\pi}{3}\right)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Three rotten apples are mixed accidentally with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and $\sigma^{2}$ represent the mean and variance of $X$, respectively, then $10(\mu^{2}+\sigma^{2})$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a² + b² is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Evening Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and ${{20} \over 3}$, respectively, then the value of | a $-$ b | is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Evening Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

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(\mu+\sigma^2) is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $99%$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

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 $P(X\ge 3)$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $\sqrt {13.44} $, then the standard deviation of the second sample is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Morning Shift) PYQ

Solution

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