The coefficient of x² in1+x²/(1-x)³ is

If p and q are the coefficients of xⁿ in (1+x)^2n-1 and (1+x)²ⁿ respectively then 2p=

C₀+C₁/2+C₃/3+ …………C_n/n+1+ =

The positive integer which is just greater than (1+0.0001)¹⁰⁰⁰⁰ is

The coefficient of x¹⁰ in 1-2x+3x²/1-x is

C₁/1 – C₂/2 + C₃/3 – C₄/4 +………. +(-1)^n-1 C_n/n =

The coefficient of x⁵ in the expression of (1+x)²¹+(1+x)²²+……+(1+x)³⁰ is

The coefficient of x⁷ in (ax²-1/bx)¹¹  is equal to the coefficient of x^-7 in (ax-1/bx²) then ab=

The number of non zero terms in the expansion of (8+2)¹⁰¹ - (8-2)¹⁰¹ is

The coefficients of three consecutive terms in the expansion of (1+x)ⁿ are in the ratio 1:7:42, then n=