Question : a³ + b³ + c³ = 3abc if _________.

Option 1: a = b = c

Option 2: a + b + c = 0

Option 3: a + b + c = 1

Option 4: a + b + c = –1

Question : If 847 × 385 × 675 × 3025 = 3^a × 5^b × 7^c × 11^d, then the value of ab – cd is:

Option 1: 4

Option 2: 5

Option 3: 1

Option 4: 7

Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a³ + b³ + c³ ?

Option 1: 67

Option 2: –53

Option 3: –51

Option 4: 27

Question : What is the value of a² + b² + c² – 2ab – 2bc + 2ca?

Option 1: (2a + b + c)²

Option 2: (a – b + c)²

Option 3: (a – b – 2c)²

Option 4: (a + 2b – c)²

Question : For what value of k will the expression x⁶ – 18x³ + k be a perfect square?

Option 1: –9

Option 2: –81

Option 3: 9

Option 4: 81