Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the degree of (\(x^7+4x^3\)\(x^8-x^4\)-x^{15})?
B. (11)
गुणन से \(x^{15}+3x^{11}-4x^7\) मिलता है और \(x^{15}\) कटता है। बची सबसे बड़ी घात (11) है। / Multiplication gives \(x^{15}+3x^{11}-4x^7\), and \(x^{15}\) cancels. The remaining highest power is (11).
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If the degree of ((c-8)x^{10}+\(c^2-64\)x-7+47) is (0), what is the value of (c)?
C. (c=8)
डिग्री (0) के लिए \(x^{10}\) और \(x^7\) दोनों पद हटने चाहिए। (c=8) पर दोनों गुणांक (0) हो जाते हैं। / For degree (0), both \(x^{10}\) and \(x^7\) terms must vanish. At (c=8), both coefficients become (0).
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For which value will the degree of ((d+9)x-9+(d-4)x-6+19) be (6)?
B. (d=-9)
डिग्री (6) के लिए \(x^9\) पद हटना चाहिए और \(x^6\) पद बचना चाहिए। (d=-9) पर यह शर्त पूरी होती है। / For degree (6), the \(x^9\) term must vanish and the \(x^6\) term must remain. This condition holds at (d=-9).
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What is the total degree of \(x^7y^4z^3+5x^3y^2z^{10}-14\)?
B. (15)
पहले पद की कुल घात (7+4+3=14) है और दूसरे पद की (3+2+10=15) है। इसलिए कुल डिग्री (15) है। / The total power of the first term is (7+4+3=14) and of the second term is (3+2+10=15). Therefore the total degree is (15).
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With respect to (z), what is the degree of \(9x^6z^{10}-8x^2z^7+5x^3-6\)?
C. (10)
(z) की सबसे बड़ी घात (10) है। अन्य चर (z) के संदर्भ में गुणांक जैसे माने जाते हैं। / The highest power of (z) is (10). Other variables are treated like coefficients with respect to (z).
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If (h(x)=\(x^7+x^4\)2-x^{14}-2x^{11}), what is the degree of (h(x))?
C. (8)
(\(x^7+x^4\)2=x^{14}+2x^{11}+x-8) है। घटाने पर \(x^8\) बचता है जिसकी डिग्री (8) है। / (\(x^7+x^4\)2=x^{14}+2x^{11}+x-8). After subtraction, \(x^8\) remains, whose degree is (8).
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What is the degree of (\(x^8-1\)\(x^8+1\))?
B. (16)
गुणनफल \(x^{16}-1\) है। इसमें सबसे बड़ी घात (16) है। / The product is \(x^{16}-1\). Its highest power is (16).
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C. \(n\le4\)
डिग्री (11) के लिए \(n+7\le11\) होना चाहिए। इसलिए \(n\le4\) सही शर्त है। / For degree (11), \(n+7\le11\) must hold. Therefore \(n\le4\) is the correct condition.
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If (p(x)=\(x^9-7x^6+5\)-\(x^9-3x^6\)), what is the degree of (p(x))?
B. (6)
सरल करने पर \(-4x^6+5\) मिलता है। इसकी सबसे बड़ी घात (6) है। / On simplifying, we get \(-4x^6+5\). Its highest power is (6).
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What is the degree of (x-9\(x^2+1\)-x-2\(x^9-8\))?
B. (9)
सरल रूप \(x^{11}+x^9-x^{11}+8x^2=x^9+8x^2\) है। इसकी डिग्री (9) है। / The simplified form is \(x^{11}+x^9-x^{11}+8x^2=x^9+8x^2\). Its degree is (9).
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