If the two roots of the equation `(lambda-2)(x^2+x+1)^2-(lambda+2)(x^4+x^2+1)` are real and equal for `lambda=lambda_1,lambda_2` then `lambda_1+lambda_2=0` (b) `|lambda_1-lambda_2|=6` (c) `lambda_1+lambda_2=32` (d) all of these

If the two roots of the equation (lambda-1)(x^(2)+x+1)^(2)-(lambda+1)(x^(4)+x^(2)+1)=0 are real and distin then lambda lies in the interval

If the roots of the given equation 2x^(2)+3(lambda-2)x+lambda+4=0 be equal in a magnitude but opposite in sign then lambda

Two protons are having same kinetic energy. One proton enters a uniform magnetic field at right angles ot it. Second proton enters a uniform electric field in the direction of field. After some time their de Broglie wavelengths are lambda_1 and lambda_2 then (a) lambda_1 = lambda_2 (b) lambda_1 lt lambda_2 (c) lambda_1 gt lambda_2 (d) some more information is required

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

If alpha, beta are the roots of the equation lambda(x^(2)-x)+x+5=0 and if lambda_(1) and lambda_(2) are two values of lambda obtained from (alpha)/(beta)+(beta)/(alpha)=(4)/(5) , then (lambda_(1))/(lambda_(2)^(2))+(lambda_(2))/(lambda_(1)^(2)) equals

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

p(lambda)^4+q(lambda)^3+r(lambda)^2+s(lambda)+t = |((lambda^2 + 3lambda) , lambda -1 , lambda+3) , (lambda +1 , -2lambda , lambda-4 ) ,(lambda-3 , lambda+4 , 3lambda)| find t=?

If the points A(lambda, 2lambda), B(3lambda,3lambda) and C(3,1) are collinear, then lambda=

A=[[1,4, of matrix 1,8,8 lambda-6lambda,8,8 lambda-61+lambda^(2),8 lambda+4,2 lambda+21]]

If |[lambda^(2),-lambda,2 lambda-1],[lambda+2,1-lambda,lambda],[lambda+2,lambda+1,-lambda]|=a lambda^(4)+b lambda^(3)+c lambda^(2)+d lambda+e Then values of a, b, c, d and e are.