Comprehension

निम्न दो (02) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए :

x और y के सभी वास्तविक मानों के लिए एक फलन इस प्रकार है कि f(xy) = f(x + y) और f(5) = 10 है। 

. f(20) + f(- 20) किसके बराबर है?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 0
  2. 10
  3. 20
  4. 40

Answer (Detailed Solution Below)

Option 3 : 20
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Detailed Solution

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गणना:

दिया गया है,

फलन है, जहाँ x और y के सभी वास्तविक मान हैं, और f(5) = 10 है।

हमें ज्ञात करना है:

दिए गए फलन समीकरण का उपयोग करके, हमारे पास है:

के लिए, हमें मिलता है:

के लिए, हमें मिलता है:

के लिए, हमें मिलता है:

इस प्रकार,

इसलिए, सही उत्तर विकल्प 3 है।

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