सिद्ध कीजिएः `""^(12)C_(0)+""^(12)C_(1)+""^(12)C_(2)+....+""^(12)C_(12)=2^(12)`

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=_____

If "C_(12) = "^(n)C_(6) then (n)_(2)^C=

The 13 th term in the expansion of (9x-1/(3sqrt(x)))^(18),x gt0 is (i) ""^(18)C_(12)x^(3) (ii) ""^(18)C_(12)x^(6) (iii) ""^(18)C_(12)1/(x^(6)) (iv) ""^(18)C_(12)