[" If "^(25)C_(0)^(25)C_(2)+2.^(25)C_(1)^(25)C_(3)+3.^(25)C_(2)*^(25)C_(4)+....+24.^(25)C_(23)*^(25)C_(25)=k*^(49)C_(lambda)+],[2k-lambda-mu" is greater than (where "mu,lambda<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)

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 )

""^(25)C_(22)- ""^(24)C_(21)= …………

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

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)

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

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 "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 "

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