Let `A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]`then prove that `A^(-1)` exists if `3x+lambda ne0, lambda=ne0`

Let f(x) = lambda + mu|x|+nu|x|^2 , where lambda,mu, nu in R , then f'(0) exists if

The values of lambda for which the function f(x)=lambdax^3-2lambdax^2+(lambda+1)x+3lambda is increasing through out number line (a) lambda in (-3,3) (b) lambda in (-3,0) (c) lambda in (0,3) (d) lambda in (1,3)

Let f(x)=(x^(4)-lambdax^(3)-3x^(2)+3lambdax)/(x-lambda). If range of f(x) is the set of entire real numbers, the true set in which lambda lies is

If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R , then lambda belongs to the interval :

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

If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a root common, then the irrational values of lambda and mu are (a) lambda=(-3)/4 b. lambda=0 c. mu=3/4 b. mu=0

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

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

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}

The value of the lambda if the lines (2x+3y+4)+lambda(6x-y+12)=0 are