SSC CHSL 2024 PYQ — Question 5

SSC CHSL Tier II - 10 Jan 2024 - Shift 1 • Quantitative Aptitude • Q5

The simplified form of the expression (x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3)\frac{(x^2 - 9)\times (9x^2 - 1)}{\left(x- \frac{1}{3}\right) \times \left(1-\frac{x}{3}\right)} \times \frac{9}{\left(x+ \frac{1}{3}\right)\left(1 + \frac{x}{3}\right)} is _____.

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. -729.

Given that

⇒ (x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3)\frac{(x^2 - 9)\times (9x^2 - 1)}{\left(x- \frac{1}{3}\right) \times \left(1-\frac{x}{3}\right)} \times \frac{9}{\left(x+ \frac{1}{3}\right)\left(1 + \frac{x}{3}\right)}

⇒ 9(x+3)(x−3)×(3x+1)(3x−1)(3x−1)×(3−x)×81(3x+1)(3+x)\frac{9(x + 3)(x-3)\times (3x + 1)(3x-1)}{\left(3x-1\right) \times \left(3-x\right)} \times \frac{81}{\left(3x+1\right)\left(3 +x\right)}

⇒ -9 × 81

⇒ - 729