Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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If (p(x)=(a-1)x-2+(a+3)x+2) has degree (0), what happens?
C. ऐसा कोई (a) नहीं हैNo such (a) exists
घात (0) के लिए (a-1=0) और (a+3=0) दोनों चाहिए। ये दोनों साथ-साथ संभव नहीं हैं। / For degree (0), both (a-1=0) and (a+3=0) are required. These cannot be true together.
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Which expression is not a polynomial in (x) because \(\sqrt{x^2+1}\) is present?
C. \(\sqrt{x^2+1}+x\)
\(\sqrt{x^2+1}\) में चर मूल के अंदर है। कक्षा (9) की परिभाषा में यह बहुपद पद नहीं माना जाता। / \(\sqrt{x^2+1}\) has the variable inside a root. In the class (9) definition, it is not treated as a polynomial term.
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If (p(x)=ax-5+bx-3+c) and \(a\neq0\), what is the degree of (p(x))?
B. (5)
\(a\neq0\) होने से \(x^5\) पद मौजूद रहता है। इसलिए सबसे बड़ी घात (5) है। / Since \(a\neq0\), the \(x^5\) term is present. Therefore, the highest power is (5).
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Which expression becomes a polynomial after simplification for \(x\neq0\)?
B. \(\frac{x^3+x}{x}\)
\(\frac{x^3+x}{x}=x^2+1\) है, जो बहुपद है। सरल करने से पहले और बाद की घातों को ध्यान से देखें। / \(\frac{x^3+x}{x}=x^2+1\), which is a polynomial. Check powers carefully before and after simplification.
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Which expression is a polynomial in (x) and has constant term (0)?
A. \(x^3-4x\)
\(x^3-4x\) में कोई अलग स्थिर पद नहीं है, इसलिए स्थिर पद (0) माना जाता है। इसकी घातें मान्य हैं। / In \(x^3-4x\), there is no separate constant term, so the constant term is considered (0). Its powers are valid.
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If (p(x)=0), which statement about its degree is correct?
C. घात परिभाषित नहीं हैDegree is not defined
(p(x)=0) शून्य बहुपद है। शून्य बहुपद की घात परिभाषित नहीं होती। / (p(x)=0) is the zero polynomial. The degree of the zero polynomial is not defined.
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In which expression are all powers integers, yet it is not a polynomial?
B. \(x^{-2}+x^3\)
(-2) पूर्णांक है लेकिन ऋणात्मक है। बहुपद में घातें शून्य या धनात्मक पूर्णांक होनी चाहिए। / (-2) is an integer but it is negative. In a polynomial, powers must be zero or positive integers.
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Given (p(x)=2x-2-3x+5) and (q(x)=x-3+p(x)), what is the degree of (q(x))?
B. (3)
(q(x)=x-3+2x-2-3x+5) है। सबसे बड़ी घात (3) है। / (q(x)=x-3+2x-2-3x+5). The highest power is (3).
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Which option gives the correct identification of \(x^2-4\)?
D. द्विघात द्विपदीQuadratic binomial
\(x^2-4\) की घात (2) है और इसमें दो पद हैं। इसलिए यह द्विघात द्विपदी है। / \(x^2-4\) has degree (2) and two terms. Therefore, it is a quadratic binomial.
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If (p(x)=(a-2)x-4+(a+1)x-3+6) is to be exactly a cubic polynomial, what is the value of (a)?
A. (2)
ठीक घन के लिए \(x^4\) का गुणांक शून्य होना चाहिए और \(x^3\) का गुणांक अशून्य रहना चाहिए। (a-2=0) से (a=2) मिलता है। / For exactly cubic, the coefficient of \(x^4\) must be zero and the coefficient of \(x^3\) must remain non-zero. From (a-2=0), (a=2).
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