Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the degree of the non-zero constant polynomial (-31)?
A. (0)
अशून्य नियतांक बहुपद की डिग्री (0) होती है। (-31) को \(-31x^0\) माना जा सकता है। / A non-zero constant polynomial has degree (0). (-31) can be considered as \(-31x^0\).
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What is the correct difference between the zero polynomial and a non-zero constant polynomial?
C. शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती हैThe zero polynomial degree is not defined and a non-zero constant has degree (0)
शून्य बहुपद की डिग्री परिभाषित नहीं होती। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / The degree of the zero polynomial is not defined. The degree of a non-zero constant polynomial is (0).
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What is the leading term of \(-5x^6+3x^4-x+9\)?
A. \(-5x^6\)
सबसे बड़ी घात वाला पद अग्रणी पद होता है। यहां सबसे बड़ी घात (6) है। / The term with the highest power is the leading term. Here the highest power is (6).
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What is the leading coefficient of \(-11x^4+6x^2-3\)?
A. (-11)
अग्रणी पद \(-11x^4\) है। इसलिए अग्रणी गुणांक (-11) है। / The leading term is \(-11x^4\). Therefore the leading coefficient is (-11).
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Is \(6x^3+\frac{4}{x}\) a polynomial or not?
B. नहीं, क्योंकि \(\frac{4}{x}\) में चर हर में हैNo, because in \(\frac{4}{x}\) the variable is in the denominator
\(\frac{4}{x}\) में (x) की घात (-1) है। इसलिए यह व्यंजक बहुपद नहीं है। / In \(\frac{4}{x}\), the power of (x) is (-1). Therefore this expression is not a polynomial.
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Which is a monomial but not a polynomial in (x)?
A. \(\frac{7}{x^2}\)
\(\frac{7}{x^2}=7x^{-2}\) है, इसलिए घात ऋणात्मक है। एक पद होना बहुपद होने के लिए पर्याप्त नहीं है। / \(\frac{7}{x^2}=7x^{-2}\), so the power is negative. Having one term is not enough to be a polynomial.
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What is the simplified form of \(4x^3+0x^2+5\)?
A. \(4x^3+5\)
\(0x^2=0\), इसलिए वह पद हट जाता है। सरल रूप \(4x^3+5\) है। / \(0x^2=0\), so that term disappears. The simplified form is \(4x^3+5\).
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In which polynomial is the coefficient of \(x^5\) equal to (0)?
B. \(3x^2+2x-4\)
\(3x^2+2x-4\) में \(x^5\) पद नहीं है। इसलिए \(x^5\) का गुणांक (0) माना जाता है। / In \(3x^2+2x-4\), the \(x^5\) term is absent. So the coefficient of \(x^5\) is taken as (0).
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Why is \(7x^2+x^{-4}+3\) not a polynomial?
C. क्योंकि इसमें \(x^{-4}\) हैBecause it has \(x^{-4}\)
\(x^{-4}\) में चर की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार नहीं होती। / In \(x^{-4}\), the power of the variable is negative. Negative powers are not accepted in a polynomial.
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Is \(6x^4-3x^2+x-10\) a polynomial?
A. हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैंYes, because all powers are non-negative integers
घातें (4), (2), (1), और (0) हैं। ये सभी बहुपद की परिभाषा के अनुसार मान्य हैं। / The powers are (4), (2), (1), and (0). All are valid according to the definition of a polynomial.
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