SarkariPYQ

SSC CHSL 2025 PYQ — Question 70

SSC CHSL - 14 Nov 2025 - Shift 1 • Quantitative Aptitude • Q70

Back to paper

Given that 343×(7)n=494343 \times (\sqrt{7})^{n} = 49^{4}, find n.

Show answer & explanation

Correct answer: B

Explanation

Given:

343 × (√7)ⁿ = 49⁴

By the formula:

343 = 7³

49 = 7²

√7 = 7¹ᐟ²

aᵐ × aⁿ = aᵐ⁺ⁿ

7³ × (7¹ᐟ²)ⁿ = (7²)⁴

7³ × 7ⁿᐟ² = 7⁸

7^(3 + n/2) = 7⁸

3 + n/2 = 8

n/2 = 5

n = 10