" If "(1-i alpha)/(1+i alpha)=A+iB," then "A^(2)+B^(2)" equals to "

If (1-i alpha)/(1+i alpha)=A+iB then A^(2)+B^(2) is equal to

If tan A=(alpha^(2)-alpha)/(alpha^(2)-alpha+1) and tan B=(1)/(2 alpha^(2)-2 alpha+1) then (A+B) equals to

If (1+i)(1+2i).....(1+ix)=a+ib, then 2.5...(1+x^(2)) equals to

If f(alpha)=|{:(1,alpha,alpha^(2)),(alpha,alpha^(2),1),(alpha^(2),1,alpha):}| , then f(root(3)(3)) is equal to

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos 2 alpha + b cos 2 alpha =a II : If (sin alpha )/(a) =(cos alpha )/(b) then a sin 2 alpha + b cos 2 alpha = a

The real value of alpha for which the expression (1-i sin alpha)/(1+2 i sin alpha) is purely real is

If alpha, beta, gamma be the roots of the equation x(1+x^(2))+x^(2)(6+x)+2=0 then match the entries of column-I with those of column-II. {:("column-I" , " Column -II"),("(A) " alpha^(-1)+beta^(-1)+gamma^(-1) " is equal to " , "(p) 8"),("(B)" alpha^(2)+beta^(2)+gamma^(2)" equals" , "(q)" -1/2),("(C)"(alpha^(-1)+beta^(-1)+gamma^(-1))-(alpha+beta+gamma) " is equal to " , "(r) -1"),("(D)"[alpha^(-1)+beta^(-1)+gamma^(-1)] " equals where [.] denotes the greatest integer equal to " , "(t)" 5/2):}

If alpha, beta, gamma be the roots of the equation x(1+x^(2))+x^(2)(6+x)+2=0 then match the entries of column-I with those of column-II. {:("column-I" , " Column -II"),("(A) " alpha^(-1)+beta^(-1)+gamma^(-1) " is equal to " , "(p) 8"),("(B)" alpha^(2)+beta^(2)+gamma^(2)" equals" , "(q)" -1/2),("(C)"(alpha^(-1)+beta^(-1)+gamma^(-1))-(alpha+beta+gamma) " is equal to " , "(r) -1"),("(D)"[alpha^(-1)+beta^(-1)+gamma^(-1)] " equals where [.] denotes the greatest integer equal to " , "(t)" 5/2):}