Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Which polynomial is obtained by simplifying (x-3(x-2)-x-4+6x)?
B. \(-2x^3+6x\)
(x-3(x-2)=x-4-2x-3), फिर \(-x^4\) से \(x^4\) कट जाता है। सरल रूप \(-2x^3+6x\) है। / (x-3(x-2)=x-4-2x-3), then \(-x^4\) cancels \(x^4\). The simplified form is \(-2x^3+6x\).
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What is the degree of the simplified form \(-2x^3+6x\)?
C. (3)
सरल रूप में सबसे बड़ी घात (3) है। इसलिए डिग्री (3) है। / In the simplified form, the highest power is (3). Therefore the degree is (3).
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Which conclusion is correct for \(x^0+\pi x^3-\frac{2x}{7}\)?
B. यह बहुपद है और डिग्री (3) हैIt is a polynomial and degree is (3)
\(\pi\) और \(-\frac{2}{7}\) वास्तविक गुणांक हैं। (x) की घातें (0), (3), और (1) हैं, इसलिए डिग्री (3) है। / \(\pi\) and \(-\frac{2}{7}\) are real coefficients. The powers of (x) are (0), (3), and (1), so the degree is (3).
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If (c=0), what will be the degree of (cx-5+(c+1)x-4-3x+2)?
B. (4)
(c=0) होने पर \(x^5\) पद हट जाता है और \(x^4\) का गुणांक (1) रहता है। इसलिए डिग्री (4) है। / When (c=0), the \(x^5\) term disappears and the coefficient of \(x^4\) remains (1). Therefore the degree is (4).
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What is obtained by simplifying \(x^2+\frac{x^2-1}{x+1}\) for \(x\neq-1\)?
A. \(x^2+x-1\)
\(\frac{x^2-1}{x+1}=x-1\) जब \(x\neq-1\)। इसलिए सरल रूप \(x^2+x-1\) है। / \(\frac{x^2-1}{x+1}=x-1\) when \(x\neq-1\). So the simplified form is \(x^2+x-1\).
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What type of polynomial is the simplified form \(x^2+x-1\)?
B. द्विघात बहुपदQuadratic polynomial
\(x^2+x-1\) में सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है। / In \(x^2+x-1\), the highest power is (2). Therefore it is a quadratic polynomial.
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Which option contains a polynomial of degree (0)?
B. \(\sqrt{5}\)
\(\sqrt{5}\) अशून्य नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / \(\sqrt{5}\) is a non-zero constant polynomial. A non-zero constant polynomial has degree (0).
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What is the degree of \(x^5+x^3+x^0\)?
C. (5)
\(x^0=1\) होता है और सबसे बड़ी घात (5) है। इसलिए डिग्री (5) है। / \(x^0=1\), and the highest power is (5). Therefore the degree is (5).
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If \(a\neq0\), (b=0), what will be the degree of \(ax^2+bx^5-4\)?
B. (2)
(b=0) होने से \(x^5\) पद हट जाता है। \(a\neq0\) होने से \(x^2\) पद बचता है। / Since (b=0), the \(x^5\) term disappears. Since \(a\neq0\), the \(x^2\) term remains.
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How many non-zero terms are there in \(6x^4-2x^3+0x^2+5x-9\)?
B. (4)
\(0x^2\) शून्य पद है, इसलिए उसे नहीं गिनते। बाकी (4) पद अशून्य हैं। / \(0x^2\) is a zero term, so it is not counted. The remaining (4) terms are non-zero.
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