Evaluate the following: ` |[x+lamda, x, x],[x, x+lamda, x],[x, x, x+lamda]| `

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

Sum of the possible values of lamda for which the following threes line x+y=1,lamdax+2y=3,lamda^(2)x+4y+9=0 are concurrent is

If the following equations x+y-3z = 0, (1+lamda)x + (2+lamda) y - 8z = 0, x-(1+lamda)y + (2+lamda)z = 0 are consistent then the value of lamda is

The sum of all intergral values of lamda for which (lamda^(2) + lamda -2) x ^(2) + (lamda +2) x lt 1 AA x in R, is:

Find the locus of the point of intersection of the lines x+y=3+lamda and 5x-y=7+3lamda , where lamda is a variable.

Consider the equation is real number x and a real parameter lamda, |x-1| -|x-2| + |x-4| =lamda Then for lamda ge 1, the number of solutions, the equation can have is/are :

Consider the equation is real number x and a real parameter lamda, |x-1| -|x-2| + |x-4| =lamda Then for lamda ge 1, the number of solutions, the equation can have is/are :

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :