k.C₀+k².C₁/2+K². C₂/3+.…………+kⁿ⁺¹.C_n/n+1 =

If x+y=1, then ².ⁿC_rx^r.y^n-r =

2.C₂+6.C₃+12.C₄+……….+n(n-1)C_n =

If the sum of the coefficients of (1+2x)ⁿ is 6561, then the greatest coefficient is

If (1+x+x²)ⁿ =Σ_{r=0²ⁿ r}x^r then a₀+a₂+a₄+……….+a_2n=

If n is a positive integer, then value of (3n+2)ⁿC₀+(3n-1) ⁿC₁+(3n-4) ⁿC₂+……..+ 2(ⁿC_n) is

The middle term of (1-3x+3x²-x³)²ⁿ is

(1.03)¹⁹ =

x^2n-1+y^2n-1 is divisible by x+y if n is

If (1+x+x²)ⁿ = a₀+a₁x+a₂x²+……..+a_2nx²ⁿ then a₀²-a₁²+a₂²-……….+a_2n² =