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 |(a^2+lambda^2, a b+clambda, ca-blambda), (a b-clambda, b^2+lambda^2, b c+a), (ca+blambda, bc-alambda, c^2+lambda^2)| |(lambda, c, -b), (-c,lambda, a), (b,-a,lambda)|=(1+a^2+b^2+c^2)^3 , then he value of lambda is a. 8 b. 27 c. 1 d. -1

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

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 lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1,0)| .

If lambda = - 2 , determine the value of |{:(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1 ,0):}|

If the rank of the matrix [(lambda,-1,0),(0, lambda,-1),(-1,0,lambda)] is 2, then find lambda .

If A = [(lambda,1),(-1,-lambda)] , then for what value of lambda,A^(2)=0 ?

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

If f(x)=lambda|sinx|+lambda^2|cosx|+g(lambda) has a period = pi/2 then find the value of lambda

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}