Binomial Theorem

Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of ( 13x 13+ 12x 23 )18. Then ( nm ) 13 is :

1. 19
2. 14
3. 49
4. 94

In the expansion of (1+x) (1-x2 ) (1+ 3x+ 3x2+ 1x3 )5, x 0, the sum of the coefficients of x3 and x-13 is equal to .

Let the coefficient of xr in the expansion of (x+3)n-1+(x+3)n-2(x+2)+(x+3)n-3(x+2)2+ +(x+2)n-1 be r. If r=0n r= n- n, , N, then the value of 2+ 2 equals .

Number of integral terms in the expansion of \7 ( 12 )+11 ( 16 ) \824 is equal to .

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 .