Correct Answer: 1 and 0

Solution : Given: The expression px³ – qx² – 7x – 6 is completely divisible by x² – x – 6.
So, the roots of x² – x – 6 = 0 will also be the roots of px³ – qx² – 7x – 6 = 0
⇒ x² – x – 6 = 0
⇒ x² – 3x + 2x – 6 = 0
⇒ x(x – 3) + 2(x – 3) = 0
⇒ (x – 3)(x + 2) = 0
⇒ x = 3 or x  = –2
So, x = – 2 and 3 are the roots of px³ – qx² – 7x – 6 = 0
Putting x = – 2 and x = 3 in the expression, we should get the value equal to 0 because we know that if $\alpha$ is the root of the equation $f(x)=0$, then  $f(\alpha)=0$
⇒ p( – 2)³ – q( – 2)² – 7( – 2) – 6 = 0 and p(3)³ – q(3)² – 7(3) – 6 = 0
⇒ – 8p – 4q + 14 – 6 = 0 and 27p – 9q – 21 – 6 = 0
⇒ – 8p – 4q = – 8 and 27p – 9q = 27
Solving these equations, we get
⇒ p = 1 and q = 0
Hence, the correct answer is 1 and 0.