Represent all possible functions defined from `{alpha, beta}` to `{1,2}`.

A={1,2} , B={3,4} Represent all possible functions from A to B(Arrow diagram may be used)

The number of into functions that can be defined from A={x, y, z, w, t} to B = {alpha,beta,gamma} is

If alpha and beta are such that the function f (x) defined by f (x) = {:{(alphax^(2) - beta",","for"|x|lt 1),((_1)/(|X|)",","for"|x|ge1):} is differentiable everywhere, then the ordered pair (alpha,beta) =

If the quadratic equation 4^(sec^(2)alpha)x^(2)+2x+(beta^(2)-beta+1/2)=0 have real roots, then find all the possible values of cos alpha+cos^(-1)beta .

A right angle is divided into three positive parts alpha,beta and gamma. Prove that for all possible divisions tan alpha+tan beta+tan gamma>1+tan alpha tan beta tan gamma

If alpha, beta, gamma in [0,2pi] , then the sum of all possible values of alpha, beta, gamma if sin alpha=-1/sqrt(2), cos beta=-1/sqrt(2), tan gamma =-sqrt(3) , is

If alpha, beta, gamma in [0,2pi] , then the sum of all possible values of alpha, beta, gamma if sin alpha=-1/sqrt(2), cos beta=-1/sqrt(2), tan gamma =-sqrt(3) , is

If the quadratic equation , 4^(sec^(2)alpha) x^(2) + 2x + (beta^(2)- beta + 1/2) = 0 have real roots, then find all the possible value of cos alpha + cos^(-1) beta .