C₀-2. C₁+3. C₂………..+(-1)ⁿ(n+1).C_n =

If the 2^nd term in the expansion (13√a+a/√a^-1) is 14a^5/2, then the value of ⁿC₃/ⁿC₂ is

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 =