If `(1+x)^n=C_0+C_1x+C_2x^2++C_n x^n ,t h e nC_0C_2+C_1C_3+C_2C_4++C_(n-2)C_n=` `((2n)!)/((n !)^2)` b. `((2n)!)/((n-1)!(n+1)!)` c. `((2n)!)/((n-2)!(n+2)!)` d. none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

If (1+x)^n=C_0+C_1x+C2x2++C_n x^n , n in N ,t h e nC_0-C_1+C_2-+(-1)^(n-1)C_(m-1), is equal to (mltn)

If (1+x)^n=C_0+C_1x+C2x2++C_n x^n , t h e n 'C_0-(C_0+C_1+)+(C_0+C_1+C_2)-(C_0+C_1+C_2+C_3)+(-1)^(n-1)(C_0+C_1+ C_(n-1))',w h e r e n is

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

If (1-x)^(-n)=a_0+a_1x+a_2x^2++a_r x^r+ ,t h e na_0+a_1+a_2++a_r is equal to (a) (n(n+1)(n+2)(n+r))/(r !) (b) ((n+1)(n+2)(n+r))/(r !) (c) (n(n+1)(n+2)(n+r-1))/(r !) (d)none of these

Prove that C_(0)^(2) + C_(1)^(2) + C_(2)^(2) +…+C_(n)^(2) = (2n!)/(n!)^(2)

Prove that ^n C_0 ^(2n)C_n- ^n C_1 ^(2n-2)C_n+ ^n C_2^(2n-4)C_n-=2^ndot

The value of (lim_(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s 1 (b) -1 (c) 0 (d) none of these

Find the sum 3^n C_0-8^n C_1+13^n C_2 - 18^n C_3+..