Binomial Expansion: JEE Questions & Solutions

If the coefficient of x in the expansion of (ax^2+bx+c)(1-2x)^26 is -56 and the coefficients of x^2 and x^3 are both zero, then a+b+c is…

The sum of all possible values of n N, so that the coefficients of x, x^2 and x^3 in the expansion of (1+x^2)^2(1+x)^n are in arithmetic…

Let,, and be the coefficients of x^7, x^5, x^3, x respectively in the expansion of (x + x^3 - 1)^5 + (x - x^3 - 1)^5, x 1. If u + v = 18, u…

If in the expansion of (1 + x)^p (1 - x)^q, the coefficients of x and x^2 are 1 and -2, respectively, then p^2 + q^2 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…

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, then…

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 let p be the…

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

If r=0^10 ( 10^r+1 - 1) 10r = ^11 - 1 then is equal to:

The number of integral terms in the expansion of ( 5^ 12 + 7^ 18)^1016 is:

The coefficient of x^2012 in the expansion of (1 - x)^2008(1 + x + x^2)^2007 is:

In the expansion of (1 + x)(1 - x^2)^(1 + 3x + 3x^2 + 1x^3), x 0, the sum of the coefficient of x^2 and x^-13 is equal to:

Number of integral terms in the expansion of ( 7z + 16 z)^824 is equal to:

Let the sum of the coefficients of the first three terms in the expansion of (x - 3x^2)^n, x 0, n N, be 376. Then the coefficient of x^4 is:

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 19^200 + 23^200 is divided by 49, is:

Let the sixth term in the binomial expansion of ( 2^ 2(10 - 3^x) + 5 2^(x-2) 2 3)^m, in the increasing powers of 2^(x-2) 2 3, be 21. If the…

Mathematics Section-A If the coefficients of x and x^2 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^n, x^n+1,, x^r in the binomial expansion of (2 + x)^r is: