Multiple choice

Find two mean proportionals between 2 & 54. 2 और 54 के बीच दो माध्य समानुपातिक ज्ञात कीजिये।

  1. 6 & 18

  2. 6 & 12

  3. 12 & 18

  4. 6 & 9
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A Correct answer
Explanation

For two mean proportionals between 2 and 54, we need to find x and y such that 2:x = x:y = y:54. This means x² = 2y and y² = 54x. From the geometric progression 2, x, y, 54, the common ratio r satisfies 2×r³ = 54, so r³ = 27 and r = 3. Therefore x = 2×3 = 6 and y = 6×3 = 18. The two mean proportionals are 6 and 18.

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