JEE Main 2025 — Binomial Theorem Questions with Solutions

If α=1+₌₁⁶(-3)r⁻¹ ¹² C₂ r₋₁, then the distance of the point (12, √(3)) from the line α x-√(3) y+1=0 is _________.

In the expansion of ([3]2+1[3]3 )ⁿ, n N, if the ratio of 15at term from the beginning to the 15th term from the end is…

If ₌₀¹⁰ (10r⁺¹-110r ) · ¹¹ Cr₊₁=α¹¹-11¹¹10¹⁰, then α is equal to :

If in the expansion of (1+x)p(1-x)q, the coefficients of x and x² are 1 and -2 , respectively, then p²+q² is equal to :

If ₌₁⁹ (r+32r ) . ⁹ Cr=α ((3)/(2) )⁹-β, α, β N, then (α+β)² is equal to

If ₌₀⁵ ¹¹ C₂r₊₁2 r+2=mn, gcd(m, n)=1, then m-n is equal to _______

Let the coefficients of three consecutive terms Tr, Tr₊₁ and Tr₊₂ in the binomial expansion of (a+b)¹² be in a G.P. and…

The number of integral terms in the expansion of (5⁽¹⁾/⁽²⁾+7⁽¹⁾/⁽⁸⁾ )¹⁰¹⁶ is

The product of the last two digits of (1919)¹⁹¹⁹ is

Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)² ⁿ⁻¹. If 2…