यदि  जहाँ a ≠ c है, तो निम्नलिखित में से कौन-सा सत्य है?

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CDS 02/2022 Elementary Mathematics Official Paper (Held On 04 Sep 2022)
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  1. a + b = c + d
  2. a + c = b + d
  3. a - b - c + d = 0
  4. a + b + c + d = 0

Answer (Detailed Solution Below)

Option 4 : a + b + c + d = 0
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दिया गया है:

 a ≠ c

प्रयुक्त अवधारणा:

योगानुपात और अन्तरानुपात:

यदि a : b = c : d, तो

(a + b ) : (a – b) = (c + d) : (c – d) 

गणना:

उपरोक्त अवधारणा के अनुसार

⇒ 

⇒ 

⇒ 

⇒ a + 2b + c = -c - 2d - a

⇒ 2a + 2b + 2c + 2d = 0

⇒ a + b + c + d = 0

∴ अभीष्ट मान a + b + c + d = 0 है

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