Let `p lambda^(4)+q lambda^(3)+r lambda^(2)+s lambda+t=|[lambda^(2)+3 lambda,lambda-1,lambda-3],[lambda-1,-2 lambda,lambda-4],[lambda-3,lambda+3,3 lambda]|` be an identity in lamda,whare p,q,r,s and t are constants .Then the value of t is

"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 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=

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

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

If x - lambda is a factor of x^(4)-lambda x^(3)+2x+6 . Then the value of lambda is

If veca satisfies vec axx( hat i+2 hat j+ hat k)= hat i- hat k , then vec a is equal to a. lambda hat i+(2lambda-1) hat j+lambda hat k ,lambda in R b. lambda hat i+(1-2lambda) hat j+lambda hat k ,lambda inR c. lambda hat i+(2lambda+1) hat j+lambda hat k ,lambda inR d. lambda hat i-(1+2lambda) hat j+lambda hat k ,lambda inR

Two particle are moving perpendicular to each with de-Broglie wave length lambda_(1) and lambda_(2) . If they collide and stick then the de-Broglie wave length of system after collision is : (A) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (B) lambda = (lambda_(1))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (C) lambda = (sqrt(lambda_(1)^(2) + lambda_(2)^(2)))/(lambda_(2)) (D) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1) + lambda_(2)))