If the polynomial `P(x)=24x^(4)+lambda_(1)x^(3)+lambda_(2)x^(2)+lambda_(3)x+1,` where `lambda_(1),lambda_(2),lambda_(3)in R` has four positive real roots `alpha,beta,gamma,delta` such that `alpha+2 beta+3 gamma+4 delta=4,` then

If lambda_(alpha), lambda_(beta) and lambda_(gamma) are respectively the wavelength of k_(alpha), k_(beta) and k_(gamma) lines of tungsten then

" Consider "P(x)=x^(2)-2 lambda x+2 lambda^(2)-4 lambda,lambda in R" then minimum value of "P(x)" is "

If alpha=tan^(-1)((sqrt(3)x)/(2 lambda-x)),beta=tan^(-1)((2x-lambda)/(lambda sqrt(3))) then one of the value of alpha-beta is

The equation (x^(2)-6x+8)+lambda (x^(2)-4x+3)=0, lambda in R has

If the equation (lambda^(2)-5 lambda+6)x^(2)+(lambda^(2)-3 lambda+2)x+(lambda^(2)-4)=0 is satisfied by more then two values of x then lambda=

Let lambda_(alpha'), lambda_(beta),and lambda'_(alpha) denote the wavelength of the X-ray of the K_(alpha), K_(beta), and L_(alpha) lines in the characteristic X-rays for a metal. Then.

If the matrix A = [[lambda_(1)^(2), lambda_(1)lambda_(2), lambda_(1) lambda_(3)],[lambda_(2)lambda_(1),lambda_(2)^(2),lambda_(2)lambda_(3)],[lambda_(3)lambda_(1),lambda_(3)lambda_(2),lambda_(3)^(2)]] is idempotent, the value of lambda_(1)^(2) + lambda_(2)^(2) + lambda _(3)^(2) is