Which of the following are correct in respect of the system of equations $$x + y + z = 8$$, $$x - y + 2z = 6$$ and $$3x - y + 5z = k$$ ?

I. They have no solution, if k = 15.

II. They have infinitely many solutions, if k = 20.

III. They have unique solution, if k = 25.

Select the correct answer using the code given below.

Which of the following determinants have value 'zero'?

1. $$\left| {\matrix{ {41} & 1 & 5 \cr {79} & 7 & 9 \cr {29} & 5 & 3 \cr } } \right|$$

2. $$\left| {\matrix{ 1 & a & {b + c} \cr 1 & b & {c + a} \cr 1 & c & {a + b} \cr } } \right|$$

3. $$\left| {\matrix{ 0 & c & b \cr { - c} & 0 & a \cr { - b} & { - a} & 0 \cr } } \right|$$

Select the correct answer using the code given below.

The system of linear equations $$kx + y + z = 1$$, $$x + ky + z = 1$$ and $$x + y + kz = 1$$ has a unique solution under which one of the following conditions?

The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k² has no solution if k equals.