Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
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How many terms and what degree does (p(x)=x-4-2x-3+3x-2-4x+5) have?
B. (5) पद, घात (4)(5) terms, degree (4)
इसमें पाँच पद हैं और सबसे बड़ी घात (4) है। पदों को चिन्ह सहित गिनें। / It has five terms and the highest power is (4). Count terms with their signs.
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Which expression is a quadratic polynomial in (x) but not a trinomial?
C. \(5x^2-11\)
\(5x^2-11\) की घात (2) है और इसमें दो पद हैं। इसलिए यह द्विघात द्विपदी है, त्रिपदी नहीं। / \(5x^2-11\) has degree (2) and two terms. So it is a quadratic binomial, not a trinomial.
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If (p(x)=2x-3+(h-4)x-2+7) has degree (3), what is correct about (h)?
B. कोई भी वास्तविक (h)Any real (h)
\(x^3\) का गुणांक (2) है जो कभी शून्य नहीं होता। इसलिए घात (3) हर (h) के लिए रहेगी। / The coefficient of \(x^3\) is (2), which is never zero. So the degree remains (3) for every (h).
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Which expression is a polynomial in (x), but not a constant polynomial in (x)?
C. \(3x^2+1\)
\(3x^2+1\) में चर (x) मौजूद है और घात (2) है। इसलिए यह स्थिर बहुपद नहीं है। / \(3x^2+1\) contains the variable (x) and has degree (2). Therefore, it is not a constant polynomial.
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Why will \(\frac{x^4-1}{x^2}\) not remain a polynomial after simplification?
A. क्योंकि यह \(x^2-\frac{1}{x^2}\) बनता हैBecause it becomes \(x^2-\frac{1}{x^2}\)
सरल रूप \(x^2-\frac{1}{x^2}\) है। \(\frac{1}{x^2}=x^{-2}\) के कारण यह बहुपद नहीं है। / The simplified form is \(x^2-\frac{1}{x^2}\). Because \(\frac{1}{x^2}=x^{-2}\), it is not a polynomial.
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Which polynomial in (x) has degree (0)?
C. (25)
शून्य से अलग स्थिर बहुपद की घात (0) होती है। (25) में कोई चर पद नहीं है। / A non-zero constant polynomial has degree (0). (25) has no variable term.
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If (p(x)=x-2+ax+a-2), when will its degree in (x) be (2)?
C. सभी वास्तविक (a) के लिएFor all real (a)
\(x^2\) का गुणांक (1) है, जो शून्य नहीं है। इसलिए घात हर (a) के लिए (2) है। / The coefficient of \(x^2\) is (1), which is non-zero. Therefore, the degree is (2) for every (a).
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Which expression is not a polynomial because the power of (x) depends on a variable?
A. \(x^n+1\), जहाँ (n) बदलता चर है\(x^n+1\), where (n) is a changing variable
बहुपद में घातें निश्चित शून्य या धनात्मक पूर्णांक होनी चाहिए। बदलते चर वाली घात परिभाषा में मान्य नहीं है। / In a polynomial, powers must be fixed non-negative integers. A power depending on a changing variable is not valid in the definition.
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Which option correctly identifies the polynomial \(x^3-5x^2+2\)?
B. घन त्रिपदीCubic trinomial
इसकी घात (3) है और इसमें (3) पद हैं। इसलिए यह घन त्रिपदी है। / It has degree (3) and (3) terms. Therefore, it is a cubic trinomial.
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Which expression is a polynomial with only odd powers and a constant term?
A. \(x^5-2x^3+x-9\)
पहले विकल्प में घातें (5), (3), (1) और (0) हैं। सभी घातें बहुपद के लिए मान्य हैं। / In the first option, the powers are (5), (3), (1), and (0). All powers are valid for a polynomial.
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