Binomial Expansion: JEE Questions & Solutions

If the coefficient of x in the expansion of (ax²+bx+c)(1-2x)²⁶ is -56 and the coefficients of x² and x³ are both zero, then a+b+c is equal…

The sum of all possible values of n ∈ ℕ, so that the coefficients of x, x² and x³ in the expansion of (1+x²)²(1+x)ⁿ are in arithmetic…

Let α, β, γ and δ be the coefficients of x⁷, x⁵, x³, x respectively in the expansion of (x + √(x³ - 1))⁵ + (x - √(x³ - 1))⁵, x > 1. If α u…

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:

For some n ≠ 10, let the coefficients of the 5^th, 6^th, and 7^th terms in the binomial expansion of (1 + x)ⁿ⁺⁴ be in A.P. Then the largest…

Suppose A and B are the coefficients of the 30th and 12th terms respectively in the binomial expansion of (1 + x)^(2n - 1). If 2A = 5B,…

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

The term independent of x in the expansion of ( (x + 1)/(x^(2/3) + 1 - x^(1/3)) - (x - 1)/(x - x^(1/2)))¹⁰, x > 1, is:

If Σ_(r=0)¹⁰ ( (10^(r+1) - 1)/10^r) · ¹¹C_(r+1) = (α¹¹ - 11¹¹)/10¹⁰, then α is equal to:

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

The coefficient of x²⁰¹² in the expansion of (1 - x)²⁰⁰⁸(1 + x + x²)²⁰⁰⁷ is:

In the expansion of (1 + x)(1 - x²)(1 + 3/x + 3/x² + 1/x³)⁵, x ≠ 0, the sum of the coefficient of x³ and x⁻¹³ is equal to:

Let the sum of the coefficients of the first three terms in the expansion of (x - 3/x²)ⁿ, x ≠ 0, n ∈ ℕ, be 376. Then the coefficient of x⁴…

Suppose the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)ⁿ are in the ratio 2: 5: 8. Then the coefficient…

The remainder when 19²⁰⁰ + 23²⁰⁰ is divided by 49, is:

Let the sixth term in the binomial expansion of ( √2^log₂(10 - 3^x) + 5-root √2^((x-2)log₂ 3))^m, in the increasing powers of 2^((x-2)log₂…

If the coefficients of x and x² in (1 + x)^p(1 - x)^q are 4 and -5 respectively, then 2p + 3q is equal to:

The mean of the coefficients of x, x², …, x⁷ in the binomial expansion of (2 + x)⁹ is: