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 =

⁽²ⁿ⁺¹⁾C₀-⁽²ⁿ⁺¹⁾C₁+…………. -⁽²ⁿ⁺¹⁾C_2n =

The coefficient of x² in (1+x)²(8-x)^-1/3 is

C₀²+3.C₁²+5.C₂²+……….+(2n+1).C_n² =

1.ⁿC₀+4¹.ⁿC₁+4².ⁿC₂+4³.ⁿC₃+……..+4ⁿ.ⁿC_n =

3.C₀+7.C₁+11.C₂+……..+(4n+3).C_n =