Mathematics — Standard (041) — CBSE Class 10 board question

Option (A) 0

$98 = 2 \times 7^2$, $28 = 2^2 \times 7$, so $m = \text{HCF} = 2 \times 7 = 14$ and $n = \text{LCM} = 2^2 \times 7^2 = 196$.
Therefore, $n - 7m = 196 - 7(14) = 196 - 98 = 98$...

Wait — recalculating: $n - 7m = 196 - 98 = 98$. → (C) 98

• $98 = 2 \times 7^2$; $28 = 2^2 \times 7$
• HCF = product of lowest powers of common primes = $2^1 \times 7^1 = 14 = m$
• LCM = product of highest powers = $2^2 \times 7^2 = 196 = n$
• $n - 7m = 196 - 98 = \mathbf{98}$

The correct answer is C. A common slip is miscalculating LCM or forgetting to multiply 7 by $m$ (not just subtract 7). Always verify using HCF × LCM = product of the two numbers: $14 \times 196 = 2744 = 98 \times 28$ ✓