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Three positive numbers are in the ratio 2:3:4. If the sum of their squares is 2349, then the numbers respectively are

1. 14, 21 and 28
2. 18, 27 and 36
3. 16, 24 and 32
4. 12, 18 and 24

तीन धनात्मक संख्याएँ 2:3:4 के अनुपात में हैं। यदि उनके वर्गों का योग 2349 है, तो क्रमशः संख्याएँ हैं

1. 14, 21 और 28
2. 18, 27 और 36
3. 16, 24 और 32
4. 12, 18 और 24

This Question came in

UGC-NET-Commerce-03-September-2024-Shift-1-Q29

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Detailed Explanation & Answer

To find the three positive numbers in the ratio 2:3:4, let the numbers be represented as 2x, 3x, and 4x.

The sum of their squares:
(2x)^2 + (3x)^2 + (4x)^2
= 4x^2 + 9x^2 + 16x^2
= 29x^2.
= 2349.

Solve for x^2:
x^2 = 2349 / 29 = 81.
x = sqrt(81) = 9.

First number: 2x = 2 * 9 = 18.
Second number: 3x = 3 * 9 = 27.
Third number: 4x = 4 * 9 = 36.

2:3:4 के अनुपात में तीन धनात्मक संख्याएँ ज्ञात करने के लिए, मान लें कि संख्याओं को 2x, 3x और 4x के रूप में दर्शाया गया है।

उनके वर्गों का योग:
(2x)^2 + (3x)^2 + (4x)^2
= 4x^2 + 9x^2 + 16x^2
= 29x^2.
= 2349.

x^2 के लिए हल करें:
x^2 = 2349/29 = 81.
x = sqrt(81) = 9.

पहली संख्या: 2x = 2 * 9 = 18.
दूसरी संख्या: 3x = 3 * 9 = 27.
तीसरी संख्या: 4x = 4 * 9 = 36.

The Correct Answer is 2

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