" Q20.If "^(25)C_(0)+5^(25)C_(1)+9^(25)C_(2).........+101^(25)C_(25)=2^(25)k" find "k=?

" If "C_(r)=^(25)C_(r)" and "C_(0)+5.C_(1)+9.C_(2)+....+(101)*C_(25)=2^(25)k," then "k" is equal to "

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 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 coefficient of x^(24) in ((25C_(1))/(25C_(0))-x)(x-2^(2)(25C_(2))/(25C_(1))(x-3^(2)(25C_(3))/(25C_(2)))(x-4^(2)(25C_(4))/(25C_(3)))......,(x-25^(2)(25C_(25))/(25C_(24))) is equal to 2925

if sum_(r=0)^(25).^(50)C_(r)(.^(50-r)C_(25-r))=k(.^(50)C_25) , then k equals:

The sum of the series (1)/(1xx2)""^(25)C_(0)+(1)/(2xx3)""^(25)C_(1)+(1)/(3xx4)""^(25)C_(2)+…+(1)/(26xx27)""^(25)C_(25) is

Evaluate .^(20)C_(5)+sum_(r=2)^(5).^(25-r)C_(4)

(1)/(1xx2)""^(25)C_(0)+(1)/(2xx3)""^(25)C_(1)+(1)/(3xx4)""^(25)C_(2)+…+(1)/(26xx27)""^(25)C_(25) is -