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 :
(4) 210
x + 1 = (x1/3 + 1)(x2/3 - x1/3 + 1) x + 1x2/3 + 1 - x1/3 = x1/3 + 1
x - 1x - x1/2 = ( x - 1)( x + 1) x( x - 1) = 1 + x-1/2
Expression = (x1/3 - x-1/2 )10
Tr+1 = 10Cr (x1/3)10 - r(-x-1/2)r
Power of x: 10 - r3 - r2 = 0 20 - 5r = 0 r = 4
T5 = 10C4 (-1)4 = 210
Answer: (4)
If r=010 ( 10r+1 - 110r ) 11Cr+1 = 11 - 11111010, then is equal to :
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 :
The remainder, when 7103 is divided by 23, is equal to:
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:
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:
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:
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 :
If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .