Binomial Theorem Questions

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

If the coefficients of x7 & x8 in the expansion of are equal, then the value of n is -...

If n is a positive integer, then is :

Given positive integers r > 1, n > 2and the coefficient of (3r) th and (r + 2) th term in the binomial expansion of (1 + x)2n are equal. Then,

The coefficient of x4 in is

If Cr stands for nCr, then the sum of the series [Co2 - 2C12 + 3C22 - .... + (- 1)r (n + 1)Cn2] where n is an even positive integer, is equal to...

The expression [x + (x3 -1)1/2]5 + [x - (x3 -1)1/2]5 is a polynomial of degree

If an = , then equals

If in the expansion of (1+ x)m (1 - x)n, the coefficients of x and x2 are 3 and - 6respectively, then m is

For 2 ≤ r ≤ n, is equal to

In the binomial expansion of (a - b)n, n ≥ 5 the sum of the 5th and 6th terms is zero. Then, a / b equals

Let Tn denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1 - Tn = 21, then n equals...

The sum , where = 0 if p ? q, is maximum when m is

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then equals...

If the coefficients of rth, (r + 1)th and (r + 2)th terms in the binomial expansion of (1 + y)m are in A.P., then m and r satisfy the equation

The coefficient of the middle term in the binomial expansion in powers of x of $(1 + \alpha x)^4$ and of $(1 - \alpha x)^6$ is the same if $\alpha$ equals

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The sum of the binomial coefficients of is equal to 256. The constant term in the expansion is -

The sum of the co-efficients in the expansion of (1 - 2x + 5x2)n is ′a′ and the sum of the co-efficients in the expansion of (1 + x)2n is b. Then -...

Given that the term of the expansion (x1/3 - x-1/2 )15 which does not contain x is 5 m where m ∈ N, then m is equal to -