Suppose the vectors x₁, x₂ and x₃ are the
solutions of the system of linear equations,
Ax = b when the vector b on the right side is equal to b₁, b₂ and b₃ respectively. if

$${x_1} = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } } \right]$$, $${x_2} = \left[ {\matrix{ 0 \cr 2 \cr 1 \cr } } \right]$$, $${x_3} = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]$$

$${b_1} = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]$$, $${b_2} = \left[ {\matrix{ 0 \cr 2 \cr 0 \cr } } \right]$$ and $${b_3} = \left[ {\matrix{ 0 \cr 0 \cr 2 \cr } } \right]$$,
then the determinant of A is equal to :

The distance of the point (1, –2, 3) from

the plane x – y + z = 5 measured parallel to

the line $${x \over 2} = {y \over 3} = {z \over { - 6}}$$ is :

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is: