Class 11

Math

JEE Main Questions

Binomial Theorem

Using binomial theorem, evaluate : $(99)_{5}$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Using the principle of mathematical induction, prove that $(2_{3n}−1)$ is divisible by $7$ for all $n∈N$

If $x_{p}$ occurs in the expansion of $(x_{2}+1/x)_{2n}$ , prove that its coefficient is $[31 (4n−p)]![31 (2n+p)]!(2n)! $ .

Find the sum of the last 30 coefficients in the expansion of $(1+x)_{59},$ when expanded in ascending powers of $x˙$

Find the coefficient of $x_{k}∈1+(1+x)+(1+x)_{2}++(1+x)_{n}(0≤k≤n)˙$

There are two bags each of which contains $n$ balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag $is_{2n}C_{n}−1.$

If the sum of coefficient of first half terms in the expansion of $(x+y)_{n}is256$ , then find the greatest coefficient in the expansion.

The number of terms in the expansion of $(1+x)_{101}(1+x_{2}−x)_{100}$ in powers of x is

Find the coefficient of $x_{5}$ in the expansioin of the product $(1+2x)_{6}(1−x)_{7}˙$