SarkariPYQ

SSC Selection Post 2022 PYQ — Question 51

SSC Selection Post - Graduation Level 2022 - 14 March 2022 - Shift 3 • Quantitative Aptitude • Q51

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If (x + y)3 + 27(x - y)3 = (Ax - 2y)(Bx2 + Cxy + 13y2), then the value of (2A + B + C) is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. -1.

(x + y)3 + 27(x - y)3 = (Ax - 2y)(Bx2 + Cxy + 13y2)

⇒ 28x3 - 78x2y + 84xy2 - 26y3 = ABx3 + (AC - 2B)x2y + (13A - 2C)xy2 - 26y3

Compare coefficients: AB = 28

AC - 2B = -78

13A - 2C = 84

Try A = 4, then B = 7 (since 4 × 7 = 28)

Also, 13(4) - 2C = 84 ⇒ C = - 16

2A + B + C = 2(4) + 7 + (-16) = 8 + 7 - 16 = -1