SSC CGL 2021 PYQ — Question 52

The correct answer is option 2 i.e. 7

Given :

(16√2x² + 81√3y³) ÷ (2√2x + 3√3y) = Ax² +By² + Cxy

Formula used :

a³ + b³ = (a + b)(a² + b² - ab)          ----- (1)

Calculations :

⇒ Ax² +By² + Cxy = (16√2x² + 81√3y³) ÷ (2√2x + 3√3y)

Using equation (1)

⇒ Ax² +By² + Cxy = ($2\sqrt{2}x + 3\sqrt{3}y$)($8x^2 + 27y^3 - 6\sqrt{6}xy$) ÷ ($2\sqrt{2}x+ 3\sqrt{3}y$)

⇒ Ax² +By² + Cxy = ($8x^2 + 27y^3 - 6\sqrt{6}xy$)

Comparing both the sides, we get

A = 8, B = 27 and C = -6√6

Now put the value of A, B and C in the equation given below

⇒ 2A - 3B - 2√6C

⇒ 2(8) - 3(27) - 2√6(-6√6)

⇒ 16 - 81 + 72

⇒ 7