Binomial Theorem

Let , , and be the coefficients of x7,x5,x3 and x respectively in the expansion of (x+ x3-1 )5+ (x- x3-1 )5, x>1. If u and v satisfy the equations u+ v=18, u+ v=20, then u+v equals :

1. 4
2. 3
3. 5
4. 8

If r=130 r2 (30Cr )230Cr-1= 229, then is equal to .

The coefficient of x70 in x2(1 + x)98 + x3(1 + x)97 + x4(1 + x)96 + + x54(1 + x)46 is 99Cp - 46Cq. Then a possible value of p + q is :

1. 61
2. 83
3. 55
4. 68

The remainder when 4282024 is divided by 21 is .

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