If `alpha < beta < gamma` and `sin gamma cos alpha=1,` where `alpha,gamma in[pi,2 pi],` then the least integral value of `f(x) = | x - alpha| + | x - beta| + |x - gamma|` is

If lim_(x to alpha) (alpha^x - x^alpha)/(x^alpha - alpha^alpha) = -1 then what is the value of alpha ?

If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then A(alpha)A(beta)=

If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then the matrix A^(2)(alpha) is

If A(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then A(alpha)A(beta)

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha):}| , then find the value of f(3^(1/3)) .

If f(alpha)=[[1,alpha,alpha^2],[alpha,alpha^2,1],[alpha^2,1,alpha]] then find the value of f(3^(1/3))

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

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .