JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 8th April Evening ShiftQuestion 1

The absolute difference of the coefficients of $x^{10}$ and $x^{7}$ in the expansion of $\left(2x^{2}+\frac{1}{2x}\right)^{11}$ is equal to

Binomial Theorem · Coefficient of a Given Power / Term Independent of x

$11^{3}-11$$12^{3}-12$$10^{3}-10$$13^{3}-13$

JEE Main 2023 (Online) 6th April Evening ShiftQuestion 2

If the coefficients of $x^{7}$ in $\left(ax^{2}+\frac{1}{2bx}\right)^{11}$ and $x^{-7}$ in $\left(ax-\frac{1}{3bx^{2}}\right)^{11}$ are equal, then

Binomial Theorem · Coefficient of a Given Power / Term Independent of x

$32ab=729$$64ab=243$$243ab=64$$729ab=32$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 3

If $26\bigg(\frac{2^{3}}{3}\left({}^{12}C_{2}\right)+\frac{2^{5}}{5}\left({}^{12}C_{4}\right)+$ $\frac{2^{7}}{7}\left({}^{12}C_{6}\right)+\ldots+\frac{2^{13}}{13}\left({}^{12}C_{12}\right)\bigg)$ $=3^{13}-\alpha$, then $\alpha$ is equal to :

Binomial Theorem · Properties and Sums of Binomial Coefficients

$45$$48$$51$$54$

JEE Main 2025 (Online) 3rd April Morning ShiftQuestion 4

If $\sum_{r=1}^{9}\left(\frac{r+3}{2^{r}}\right)\cdot{}^{9}C_r=\alpha\left(\frac{3}{2}\right)^{9}-\beta$, $\alpha,\beta\in\mathbb{N}$, then $(\alpha+\beta)^{2}$ is equal to

Binomial Theorem · Properties and Sums of Binomial Coefficients

$27$$18$$9$$81$

JEE Main 2023 (Online) 15th April Morning ShiftQuestion 5

Let $\left(a+bx+cx^{2}\right)^{10}=\sum_{i=0}^{20}p_ix^{i}$, $a,b,c\in\mathbb{N}$. If $p_1=20$ and $p_2=210$, then $2(a+b+c)$ is equal to

Binomial Theorem · Multinomial Expansion

$6$$8$$12$$15$