.^(20)C_(10)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_( 4)+.^(20)C_(12)+.^(20)C_(...

1.^(20)C_(1)-2.^(20)C_(2)+3.^(20)C_(3)-...-20.^(20)C_(20)

The value of r for which .^(20)C_(r ), .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

Evaluate the following : (i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20) (ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9) (iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25) (iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10)) is (A) 2^(21) - 2^(11) (B) 2^(21) - 2^(10) (C) 2^(20) - 2^(9) (D) 2^(20) - 2^(10)

If .^(20)C_(1)+(2^(2)) .^(20)C_(2) + (3^(2)).^(20)C_(3) +......+(20^(2)).^(20)C_(20)=A(2^(beta)) , then the ordered pair (A, beta) is equal to

The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

The value of 1^(1).^(20)C_(1)+2^(2).^(20)C_(2)+3^(2).^(20)C_(3)+….+(20)^(2).^(20)C_(20) is