" (a) "^(12)C_(1)+^(12)C_(2)+^(12)C_(3)+...+_(20)^(12)C_(12)

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_(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))| is equal to zero when m is

The value of .^(20)C_(0)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

The value of .^(20)C_(0)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

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 :

The value of .^(20)C_(10)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

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))| is equal to zero when m is

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))| is equal to zero when m is