Binomial Theorem

If the term independent of x in the expansion of ( ax2 + 12x3 )10 is 105, then a2 is equal to :

1. 6
2. 4
3. 2
4. 9

If the second, third and fourth terms in the expansion of (x + y)n are 135, 30 and 103, respectively, then 6 (n3 + x2 + y ) is equal to .

If the constant term in the expansion of (1 + 2x - 3x3 ) ( 32x2 - 13x )9 is p, then 108p is equal to .

If the constant term in the expansion of ( [5]3x + 2x [3]5 )12, x 0, is 28 [5]3, then 25 is equal to :

1. 724
2. 742
3. 693
4. 639

The sum of all rational terms in the expansion of (2 15+5 13 )15 is equal to :

1. 633
2. 6131
3. 3133
4. 931

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 .