`.^(25)C_(1) + .^(25)C_(2) +.^(25)C_(3) + .......+ .^(25)C_(25)` का मान है :

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)

If .^25 C_0 + 5 .^25 C_1 + 9 .^25 C_2 .... 101 .^25 C_25 = 2^(25) k find k = ?

If .^25 C_0 + 5 .^25 C_1 + 9 .^25 C_2 .... 101 .^25 C_25 = 2^(25) k find k = ?

""^(25)C_(22)- ""^(24)C_(21)= …………

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: (a) 2^(25) (b) 2^(25)-1 (c) 2^(24) (d) 25^(2)

if sum_(r=0)^(25).^(50)C_(r)(.^(50-r)C_(25-r))=k(.^(50)C_25) , then k equals: (a) 2^(25) (b) 2^(25)-1 (c) 2^(24) (d) 25^(2)

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