If `(nC_0)/(2^n)+2.(nC_1)/2^n+3.(nC_2)/2^n+....(n+1)(nC_n)/2^n=16` then the value of 'n' is

If nC_(16)=20C_(n+2), then the value of n is

(nC_(0))^(2)+(nC_(1))^(2)+(nC_(2))^(2)+......+(nC_(n))^(2)

(nC_(0))^(2)-(nC_(1))^(2)+(nC_(2))^(2)+....+(-1)^(n)(nC_(n))^(2)

If 3^n is a factor of the determinant |{:(1,1,1),(.^nC_1,.^(n+3)C_1,.^(n+6)C_1),(.^nC_2, .^(n+3)C_2, .^(n+6)C_2):}| then the maximum value of n is ……..

The value of (nC_(0))/(n)+(nC_(1))/(n+1)+(nC_(2))/(n+2)+......+(nC_(n))/(2n) is equal to

If .^nC_0+3.^nC_1+5^nC_2+7^nC_3+ . . .till (n+1) term=2^100*101 then the value of 2[(n-1)/2] where [.] is G.I.F)

If S_n=^nC_0.^nC_1+^nC_1.^nC_2+.....+^nC_(n-1).^nC_n and if S_(n+1)/S_n=15/4 , then the sum of all possible values of n is (A) 2 (B) 4 (C) 6 (D) 8

If _(nC_(r)+4nC_(r+1)+6nC_(r+2)+4nC_(r+3)+nC_(r+4))nC_(r)+3nC_(r+1)+3nC_(r+2)+nC_(r+3)=(n+k)/(r+k) then the value of k is :

nC_(0)-(1)/(2)(^(^^)nC_(1))+(1)/(3)(^(^^)nC_(2))-....+(- 1)^(n)(nC_(n))/(n+1)=