SSC Selection Post 2022 PYQ — Question 74

The correct answer is option 3 i.e. -32.

a + b = 23

Squaring both sides

⇒ (a + b)² = 2²

⇒ a² + b² + 2ab = 4

⇒ a² + b² = 4 - 8 = -4

Squaring both sides

⇒ (a² + b²)² = (-4)²

⇒ a⁴ + b⁴ + 2a²b² = 16

⇒ a⁴ + b⁴ = 16 - 32

⇒ a⁴ + b⁴ = -16

⇒ a⁴ + b⁴ + ab³ + ba³ = a⁴ + b⁴ + ab(b² + a²)

⇒ -16 + 4 × -4 = - 16 - 16 = -32