If n is even then C₀²-C₁²+C₂²-……….+(-1)ⁿ C_n² =

The number of non-zero terms in the expansion of (1+3√2x)⁹+(1+3√2x)⁹is equal to:

If the coefficient of rth term and (r + l)th term in the expansion of (1 + x)²⁰ are in the ratio 1 : 2, then r is equal to:

C₀+C₁/2+C₂/2²+C₃/2³+.....C_n/2ⁿ

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