PYQSide
ExamsMy practice
If r=19 ( r+32r ) 9Cr = ( 32 )9 - , , N, then ( + )2 is equal to
(2) 81
S = r=19 r 9Cr ( 12 )r + 3 r=19 9Cr ( 12 )r
r 9Cr = 9 8Cr-1
r=19 r 9Cr ( 12 )r = 92 r=19 8Cr-1 ( 12 )r-1 = 92 ( 32 )8 = 3 ( 32 )9
r=19 9Cr ( 12 )r = ( 32 )9 - 1
S = 3 ( 32 )9 + 3 ( 32 )9 - 3 = 6 ( 32 )9 - 3
= 6, = 3
( + )2 = 92 = 81
Answer: (2)
Let (1 + x + x2 )10 = a0 + a1x + a2x2 + + a20x20. If (a1 + a3 + a5 + + a19) - 11a2 = 121k, then k is equal to .
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 :
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 :
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: