Find the term independent of x in the expansion of (2x - 1/x)¹⁰

the second, third and fourth term of the binomial expansion (x+a)n  (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)ⁿ are in AP, then find values of n???

the coefficient of x⁴ in the expansion of (1+x+x²+x³)¹¹ is :

a) 900 b)909

c) 990 d)999

if 4th term in the expansion of ( ax+1/x)ⁿ is 5/2, then the values of a and n :

a) 1/2,6 b) 1,3

c) 1/2,3

The coefficients of three consecutive terms in the expansion of(1+x)ⁿ are in the ratio 1:7:42. find  n. 

 Show that the middle term in the expansion of(1+x)raise to power 2n is = 1.3.5.......(2n-1) . 2n.xraise to power n upon n! , where nis a +ve integer.

Using Binomial theoram, prove that 2³ⁿ - 7n-1 is divisible by 49 where n is a Natural number

 solve this    

if the coefficients of (r-5)^th and (2r-1)^th term in the expansion of (1+x)³⁴ are equal, fiind r

using binomial therorem, 3²ⁿ⁺²-8n-9 is divisible by 64, n belongs to N

Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn