मान ज्ञात कीजिएः ` ""^(12)C_(1)+""^(12)C_(2)+""^(12)C_(3)+.....+""^(12)C_(11)`

If ""^(12)C_(0)""^(12)C_(1).....""^(12)C_(12) are the binomial coefficients of the expansion (1+x)^(12),"them" ""^(12)C_(0)-""^(12)C_(1)+""^(12C_(2-""^(12)C_(3)+......""^(12)C_(12= ____________

The value of |{:(""^(10)C_(4), ""^(10)C_(5), ""^(11)C_(m)), (""^(11)C_(6), ""^(11)C_(7), ""^(12)C_(m+2)), (""^(12)C_(8), ""^(12)C_(9), ""^(13)C_(m+4)):}|=0 when m is equal to :

Evaluate: (i) .^(12)C_(1)+.^(12)C_(2)+.^(12)C_(3)+ . . .+.^(12)C_(12) (ii) .^(19)C_(3)+.^(19)C_(5)+.^(19)C_(7)+ . . .+^(19)C_(19) .

If ""^(12)C_(r+1)=""^(12)C_(3r-5), find r.

Evaluate the ""^12C_0 + ""^12C_2 + ""^12C_4 +………….+""^12C_12

If ""^(12)C_(5) =^(12)C_(r) then r=_____

Determine n if (i) ""^(2n)C_(3) : ""^(n)C_(3) = 12:1 (ii) ""^(2n)C_(3): ""^(n)C_(3)= 11:1

If ""^(12)C_((s+1))=""^(12)C_((2s-5)), then find s.