The System Of Equation               Ax + By + (aα + B)z = 0                Bx + Cy + (bα + C)z = 0             (aα + B)x + (bα + C)y = 0 Has A Non – Zero Solution If A, B, C Are In

The number of distinct real roots of

The value of θ lying between θ = 0 and θ = π/2 and satisfying the equation

If pqr ≠ 0 and the system of equations

         (p + a)x + by + cz = 0

         ax + (q + b)y + cz = 0

          ax + by + (r + c)z = 0

has sc non – trivial solution, then value of

The system of equations

            ax + ay – z = 0

            bx – y + bz = 0

         – x + cy + cz = 0

(where a, b, c ≠ – 1 )has a non – trivial solution, then value of

The values of λ for which the system of equations

(λ + 5)x + (λ – 4)y + z = 0

(λ – 2)x + (λ + 3)y + z = 0

                 λx + λy + z = 0

has a non – trivial solution is (are)