JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 10th April Evening ShiftQuestion 1

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution $x_i$ : $0,1,2,3,4,5$ $f_i$ : $k+2,\ 2k,\ k^{2}-1,\ k^{2}-1,\ k^{2}+1,\ k-3$ where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\le x$, then $\left[\mu^{2}+\sigma^{2}\right]$ is equal to

Statistics

$6$$7$$8$$9$

JEE Main 2024 (Online) 31st January Evening ShiftQuestion 2

Let the mean and the variance of $6$ observations $a,b,68,44,48,60$ be $55$ and $194$, respectively. If $a>b$, then $a+3b$ is

Statistics

$180$$190$$200$$210$

JEE Main 2024 (Online) 27th January Morning ShiftQuestion 3

Let $a_1,a_2,\ldots,a_{10}$ be $10$ observations such that $\sum_{k=1}^{10}a_k=50$ and $\sum_{\forall k<j}a_k\cdot a_j=1100$. Then the standard deviation of $a_1,a_2,\ldots,a_{10}$ is equal to :

Statistics

$5$$10$$\sqrt{5}$$\sqrt{115}$

JEE Main 2026 (Online) 4th April Evening ShiftQuestion 4

For $10$ observations $x_1,x_2,\ldots,x_{10}$, if $\sum_{i=1}^{10}(x_i+2)^{2}=180$ and $\sum_{i=1}^{10}(x_i-1)^{2}=90$, then their standard deviation is:

Statistics

$2$$\sqrt{3}$$2\sqrt{2}$$3$

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 5

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively. A new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding $2$ to each element of $B$. Then the sum of the mean and variance of the elements of $C$ is :

Statistics

$38$$32$$36$$40$