Find the value of m – n, if [9ⁿ × 3² × {(3)^(−n/2)}^(−2) − (27)ⁿ] / (3^(3m) × 2³) = 1/27 :यदि [9ⁿ × 3² × {(3)^(−n/2)}^(−2) − (27)ⁿ] / (3^(3m) × 2³) = 1/27, तो m – n का मान ज्ञात कीजिए :

1. A–2
2. B1
3. C–1
4. D2

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: B. 1

Explanation

9ⁿ = 3^(2n) and {3^(−n/2)}^(−2) = 3ⁿ, so the numerator = 3^(2n) × 3² × 3ⁿ − 3^(3n) = 3^(3n)(9 − 1) = 8 × 3^(3n). The whole fraction = 8 × 3^(3n) / (8 × 3^(3m)) = 3^(3n − 3m) = 1/27 = 3^(−3). So 3(n − m) = −3, n − m = −1, hence m − n = 1.9ⁿ = 3^(2n) और {3^(−n/2)}^(−2) = 3ⁿ, अतः अंश = 3^(2n) × 3² × 3ⁿ − 3^(3n) = 3^(3n)(9 − 1) = 8 × 3^(3n)। पूरा भिन्न = 8 × 3^(3n) / (8 × 3^(3m)) = 3^(3n − 3m) = 1/27 = 3^(−3)। अतः 3(n − m) = −3, n − m = −1, इसलिए m − n = 1।