Binomial Theorem9 questions8 PYQ

Binomial Theorem — JEE Maths Practice Questions & Solutions

9 questions on Binomial Theorem with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

mediumPYQ · JEE Main 2026

If the coefficients of the middle terms in the binomial expansions of

(1+\alpha x)^{26}

and

(1-\alpha x)^{28}

\alpha\ne0

, are equal, then the value of

\alpha

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mediumPYQ · JEE Advanced 2026

Let

p_n

denote the total number of triangles formed by joining the vertices of an

n

-side regular polygon. If

p_{n+1}-p_n=66

, then the sum of all distinct prime divisors of

n

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mediumPYQ · JEE Main 2026

The number of elements in the set

S=\left\{(r,k):k\in\mathbb{Z}\ \text{and}\ {}^{36}C_{r+1}=\dfrac{6\left({}^{35}C_r\right)}{k^2-3}\right\}

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mediumPYQ · JEE Main 2026

Let the smallest value of

k\in\mathbb{N}

, for which the coefficient of

x^3

(1+x)^3+(1+x)^4+(1+x)^5+\cdots+(1+x)^{99}+(1+kx)^{100}

x\ne0

, is

\left(43n+\dfrac{101}{4}\right)\big({}^{100}C_3\big)

for some

n\in\mathbb{N}

, be

p

. Then the value of

p+n

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mediumPYQ · JEE Main 2026

The coefficient of

x^2

in the expansion of

\left(2x^2+\dfrac{1}{x}\right)^{10}

x\neq0

, is:

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easyPYQ · JEE Main 2026

If for

3\le r\le 30

{}^{30}C_{30-r}+3\,{}^{30}C_{31-r}+3\,{}^{30}C_{32-r}+{}^{30}C_{33-r}={}^{m}C_r,

then

m

equals

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easyPYQ · JEE Main 2026

In the expansion of

\left(9x-\dfrac{1}{3\sqrt{x}}\right)^{18}

x>0

, if the term independent of

x

(221)k

, then

k

is equal to

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easyPYQ · JEE Main 2026

If the sum of the coefficients of

x^7

and

x^{14}

in the expansion of

\left(\dfrac{1}{x^3}-x^4\right)^n

x\ne0

, is zero, then the value of

n

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medium

Let

t_1=7

t_2=7^7

t_3=7^{7^7}

, and so on. The digit at the tens place of

t_{1000}

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