SSC Selection Post 2022 PYQ — Question 51

The correct answer is option 2 i.e. $\frac{13}{8}$.

⇒ 2x - y = 2

⇒ y = 2x - 2....(1)

⇒ xy = $\frac{3}{2}$ ....(2)

Put the value of y in equation 2

⇒ x(2x - 2) = $\frac{3}{2}$

⇒ 2x² - 2x = $\frac{3}{2}$

⇒ 4x² - 4x - 3 = 0

⇒ 4x² - 6x + 2 x - 3 = 0

⇒ 2x(2x - 3) + 1(2x - 3) = 0

⇒ (2x + 1)(2x - 3) = 0

⇒ x = 3/2

Then, y = 3 - 2 = 1

⇒ $\frac{1}{2}(x^3 - \frac{y^3}{8})$ = $\frac{1}{2}(({3\over2})^3 - \frac{(1)^3}{8})$

⇒ $\frac{1}{2}({27\over8} - \frac{1}{8})$

⇒ $\frac{1}{2}({26\over8})$ = $\frac{13}{8}$