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 :

The number of real solutions of the equation (x^(2))/(1-|x-5|)=1 is

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have a unique solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have no solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have infinitely many solutions?

Let t be a real number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. if the cubic has exactly two real and distinct solutions for x then exhaustive set of values of lamda be:

Let t be a real number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. If the above cubic has three real and distinct solutions for x then exhaustive set of value of lamda be :

Consider a equation x^(3)-3x=sqrt(x+2) such that x is a real number then sum of its positive roots is lamda where [(lamda)/2] is______

Consider a equation x^(3)-3x=sqrt(x+2) such that x is a real number then sum of its positive roots is lamda where [(lamda)/2] is______