If ` A^2B=BA` then `(AB)^20=A^lambda B^20` then find the value of `lambda`.

If x=a cos nt-b sin nt and (d^(2)x)/(dt^(2))=lambda x then find the value of lambda.

Let A=[[4, a ],[-1,b]] and B=[[1,-2],[1,4]] are two matrices satisfying the relation A^(3)+3A^(2)B+3AB^(2)+B^(3)=(A+B)^(3) .If (A+B)= lambda(A^(-1)+B^(-1)) ,then find the value of lambda

If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda ) are collinear then find the value of lambda .

If a,b and c are three consecutive positive integers such that 1/(a!)+1/(b!)=lambda/(c!) then find the value of root under lambda .

If a,b and c are three consecutive positive integers such that 1/(a!)+1/(b!)=lambda/(c!) then find the value of root under lambda .

If a,b and c are three consecutive positive integers such that 1/(a!)+1/(b!)=lambda/(c!) then find the value of root under lambda .

If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lambdaa^2b^2c^2, then find the value of lambda

If s in2A=lambda sin2B, then write the value of (lambda+1)/(lambda-1)