For what value of non-negative integer a will the system `x^2-y^2 = 0` `(x-a)^2+y^2=1` have exactly three real solution

For what value of k does 4x^2 + kx + 25 = 0 have exactly one real solution for x?

Find the number of non-negative integer solutions of equation x+y+z+2w=20.

The number of non trivial solutions of the system x-y+2=0,x+2y-z=0,2x+y+3z=0

lf the circle x^(2)+y^(2)=2 and x^(2)+y^(2)-4x-4y+lamda=0 have exactly three real common tangents then lamda=

If the cirles x^(2)+y^(2)=2 and x^(2)+y^(2)-4x-4y+lambda=0 have exactly three real common tangents then lambda=

Ilf the circle x^(2)+y^(2)=2 and x^(2)+y^(2)_4x-4y+lamda=0 have exactly three real common tangents then lamda=

The number of values of a for which the system of equations 2^(|x|)+|x|=y+x^(2)+a and x^(2)+y^(2)=1 has only one solution where a,x,y are real, is

The number of values of a for which the system of equations 2^(|x|)+|x|=y+x^(2)+a and x^(2)+y^(2)=1 has only one solution where a,x,y are real, is

The number of non-trivial solutions of the system x=y+z=0, x+2y-z=0, 2x+y+3z=0 , is