Show that:` .^20C_13+^20C_14-^20C_6-^20C_7=0`

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 a. 2^(19)-(( "^(20)C_10 + "^(20)C_9))/2 b. 2^(19)-((^(20)C 10+2xx^(20)C9))/2 c. 2^(19)-(^(20)C 10)/2 d. none of these

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

Evaluate: .^(20)C_(5)+^(20)C_(4)+^(21)C_(4)+^(22)C_(4)

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

Value of r for which expression 20C_(r)^(20)C_(0)+20C_(r-2)^(20)C_(1)+20C_(r-2)^(20)C_(2)+.......+20C_(0)^(20)C_(r) is maximum is equal to (A) 10 (B) 20 (C) 15 (D) 11

The sum of the series ""^20C_0+""^20C_1+""^20C_2+...+""^20C_9 is

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