Binomial Theorem

If the coefficients of x4, x5 and x6 in the expansion of (1 + x)n are in the arithmetic progression, then the maximum value of n is:

1. 28
2. 21
3. 7
4. 14

If the coefficient of x30 in the expansion of (1+ 1x )6 (1+x2 )7 (1-x3 )8; x 0 is , then | | equals .

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 .