Binomial Theorem

Suppose 2-p, p, 2- , are the coefficients of four consecutive terms in the expansion of (1+x)n. Then the value of p2- 2+6 +2p equals

1. 8
2. 4
3. 6
4. 10

Let = k=0n ( ( n Ck )2k+1 ) and = k=0n-1 ( n Ck n Ck+1k+2 ). If 5 =6 , then n equals .

If 11C12+ 11C23+ + 11C910= nm with (n,m)=1, then n+m is equal to .

Remainder when 643232 is divided by 9 is equal to .

If A denotes the sum of all the coefficients in the expansion of (1-3x+10x2 )n and B denotes the sum of all the coefficients in the expansion of (1+x2 )n, then :

1. B=A3
2. 3A=B
3. A=3B
4. A=B3

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