Binomial Theorem

Let the coefficients of three consecutive terms Tr, Tr+1 and Tr+2 in the binomial expansion of (a + b)12 be in a G.P. and let p be the number of all possible values of r. Let q be the sum of all rational terms in the binomial expansion of ( [4]3 + [3]4)12. Then p + q is equal to:

1. 295
2. 283
3. 299
4. 287

For some n 10, let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of (1+x)n+4 be in A.P. Then the largest coefficient in the expansion of (1+x)n+4 is:

1. 10
2. 35
3. 70
4. 20

Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)2n-1. If 2A=5B, then n is equal to:

1. 20
2. 19
3. 22
4. 21

The sum of all rational terms in the expansion of (1+21/3+31/2 )6 is equal to .

If in the expansion of (1+x)p(1-x)q, the coefficients of x and x2 are 1 and -2, respectively, then p2+q2 is equal to :

1. 8
2. 20
3. 13
4. 18

If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .

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 .