Binomial Theorem · Question 28

The term independent of x in the expansion of ( (x + 1)(x2/3 + 1 - x1/3) - (x - 1)(x - x1/2) )10, x > 1, is :

1. 240
2. 120
3. 150
4. 210

If r=010 ( 10r+1 - 110r ) 11Cr+1 = 11 - 11111010, then is equal to :

1. 11
2. 20
3. 24
4. 15

The least value of n for which the number of integral terms in the Binomial expansion of ( [3]7 + [12]11)n is 183, is :

1. 2184
2. 2172
3. 2196
4. 2148

If = 1 + r=16(-3)r-1 12C2r-1, then the distance of the point (12, 3) from the line x - 3y + 1 = 0 is .

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