Question
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निम्न दो (02) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए :
मान लीजिए f = {(1, 1), (2, 4), (3, 7), (4, 10)}
यदि f(x) = px + q है, तो (p + q) का मान क्या है?
Answer (Detailed Solution Below)
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दिया गया है,
फलन \(f = \{(1, 1), (2, 4), (3, 7), (4, 10)\} \) है, और हमें दिया गया है कि फलन \( f(x) = px + q \) है, जहाँ p और q अचर हैं।
बिंदुओं f(1) = 1 और f(2) = 4 का उपयोग करके, हम निम्नलिखित समीकरण निकाय बनाते हैं:
- f(1) = 1 से, हमारे पास \(p(1) + q = 1 \) है, इसलिए p + q = 1 .......(1).
- f(2) = 4 से, हमारे पास p(2) + q = 4 है, इसलिए 2p + q = 4 ..........(2).
समीकरण 1 को समीकरण 2 से घटाने पर:
\( (2p + q) - (p + q) = 4 - 1 \)
\( p = 3 \)
अब, समीकरण 1 में p = 3 प्रतिस्थापित करने पर:
\( 3 + q = 1 \)
\( q = -2 \)
\( p + q = 3 + (-2) = 1 \)
∴ p + q का मान 1 है।
सही उत्तर विकल्प (3) है।
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