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 "

If 25C_0 25C_2 +2. 25C_1 25C_3 +3. 25C_2 .25C_4+....+ 24. 25C_23.25C_25=k. 49C_lambda+50C_mu , then the value of 2k-lambda-mu is greater than (where mu,lambda lt 25 )

If ^25C_r= ^25C_(2r+1) ,the value of ^rC_5 is

(1+x)^25 = sum_(r = 0)^(25) C_r x^r then C_1 - C_3 + C_5 - C_7 + ……-C_25 =

(1+x)^25 = sum_(r = 0)^(25) C_r x^r then C_1 - C_3 + C_5 - C_7 + ……-C_25 =

25C_(0)25C_(2)+2.25C_(1)25C_(3)+3.25C_(2)*25C_(4)+....+24.25C_(23.25)C_(25)=k.49C_(lambda)+50C_(mu), then the value of 2k-lambda-mu is greater than (where mu,lambda<25)

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)