If `plambda^4+qlambda^3+rlambda^2+slambda+t=lambda^2+3lambdalambda-1lambda+3lambda^2+1 2-lambdalambda-3lambda^2-3lambda+4 3lambdat h e np` is equal to `-5` b. `-4` c. `-3` d. `-2`

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

"Let "plambda^(4) + qlambda^(3) +rlambda^(2) + slambda +t =|{:(lambda^(2)+3lambda,lambda-1, lambda+3),(lambda+1, -2lambda, lambda-4),(lambda-3, lambda+4, 3lambda):}| be an identity in lambda , where p,q,r,s and t are constants. Then, the value of t is..... .

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

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. lambda_(1), lambda_(2) and lambda_(3) . Which one of the following equations correctly ralates lambda_(1), lambda_(2) and lambda_(3) ? lambda_(1)=lambda_(2)-lambda_(3) lambda_(1)=lambda_(3)-lambda_(2) (1)/(lambda_(1))=(1)/(lambda_(2))+(1)/(lambda_(3)) (1)/(lambda_(2))=(1)/(lambda_(3))+(1)/(lambda_(1))

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

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to :

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C , where A, B and C are matrices then find matrices B and C.

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 |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to : (A) 4 lambda abc (B) -4 lambda abc (C) 4 lambda^2 (D) -4 lambda^2