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(0) 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. 1
  3. 5
  4. 10

Answer (Detailed Solution Below)

Option 4 : 10
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Detailed Solution

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गणना:

दिया गया है,

फलन इस प्रकार है कि: x और y के सभी वास्तविक मानों के लिए,  और  है। 

हमें का मान ज्ञात करना है।

दिए गए फलन समीकरण में और प्रतिस्थापित करने पर:

चूँकि , हम निष्कर्ष निकालते हैं:

इसलिए, सही उत्तर विकल्प 4 है।

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