Question : If the expression px³ – 2x² – qx + 18  is completely divisible by  (x² – 9), then what is the ratio of p to q?

Option 1: 1 : 9

Option 2: 1 : 3

Option 3: 3 : 1

Option 4: 9 : 1

Question : What is the simplified form of the expression (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)?

Option 1: 1 – x⁴⁰

Option 2: 1 – x³²

Option 3: 1 – x¹⁶

Option 4: 1 – x⁴²

Question : If x + y = 36, then find (x – 27)³ + (y – 9)³.

Option 1: 1

Option 2: 81

Option 3: 2y

Option 4: 0

Question : If the expression px³ – qx² – 7x – 6 is completely divisible by x² – x – 6, then what are the values of p and q respectively?

Option 1: 0 and 1

Option 2: 1 and 0

Option 3: 2 and 1

Option 4: 1 and 2

Question : What is the value of (3x³ + 5x²y + 12xy² + 7y³), when x = – 4 and y = – 1?

Option 1: – 329

Option 2: – 359

Option 3: – 361

Option 4: – 327