Binomial Theorem

The sum of the coefficients of x2/3 and x-2/5 in the binomial expansion of (x2/3 + 12x-2/5 )9 is

1. 19/4
2. 69/16
3. 63/16
4. 21/4

Let = r=0n (4r2 + 2r + 1 )nCr and = ( r=0n nCrr + 1 ) + 1n + 1. If 140 < 2 < 281, then the value of n is .

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