1.

If [49n+1(7-n/2)-2 – 343n]/[(2 × 7m)3 × 6] = 1/117649, find the value of m – n.

Answer» Correct Answer - Option 3 : 2

Given

[49n+1(7n/2)-2 – 343n]/[(2 × 7m)3 × 6] = 1/117649

Calculation

[49n+1(7n/2)-2 – 343n]/[(2 × 7m)3 × 6] = 1/117649

⇒ [{(72)n + 1} × (7(-n/2) × (-2)) – (73)n]/[23 × 73m × 6] = 1/76

⇒ [72n.72.7n- 73n]/[23 × 73m × 6] = 1/76

⇒ [73n.72 – 73n]/[23 × 73m × 6] = 1/76

⇒ [73n (72 – 1)]/[48 × 73m] = 1/76

⇒ [73n × 48]/[48 × 73m] = 1/76

⇒ 73n - 3m = 7-6

⇒ 3n - 3m = -6

⇒ 3(n - m) = -6

⇒ (n - m) = -2

⇒ m - n = 2

The required value is 2.



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