Let `f(x) = ((x - gamma)(x - delta)) / ((x-alpha)(a-beta))` where, `gamma < alpha < delta < beta`, then which of the following is correct

If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of x^2+px+r=0, p+rphi0 ,then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta)) is equal to

lf, cos (x + alpha) cos (x + beta), cos (x + gamma) sin (x + alpha), sin (x + beta), sin (x + gamma) sin (beta + gamma), sin ( gamma-alpha), sin (alpha-beta) then (Given alpha! = beta! = gamma), sin (alpha-beta)

If f(x) = |(cos(x + alpha), cos(x+beta), cos(x + gamma)),(sin(x + alpha), sin(x+beta), sin(x + gamma)), (sin(beta - gamma), sin(gamma - alpha), sin(alpha - beta))| and f(2) = -2, then |sum_(r=1)^20 f(r)| equals

If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation x^3=1,t h e n|a b c b c a c a b| is equal to a. f(alpha)+f(beta)+f(gamma) b f(alpha)f(beta)+f(beta)f(gamma)+f(gamma)f(alpha) c. f(alpha)f(beta)f(gamma) d. -f(alpha)f(beta)f(gamma)

Let f(x)=alpha (x) beta (x) gamma (x) for all real x, where alpha (x), beta (X) and gamma (x) are differentiable functions of x. If f'(2)=18 f(2), alpha'(2)=3 alpha (2), beta' (2)=-4 beta (2) and gamma'(2)=k gamma (2) , then the value of k is