Level 29 • 50/50 questions • 35 seconds per question.
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What is the degree of the polynomial \(3x^4-5x^2+7x-1\)?
C. (4)
सबसे बड़ी घात (4) है। डिग्री निकालते समय सबसे बड़ी घात वाला पद देखें। / The highest power is (4). To find the degree, look at the term with the highest power.
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What is the degree of \(8x^5+0x^7-2x^3+6\)?
B. (5)
\(0x^7\) शून्य पद है इसलिए उसे नहीं गिनते। सबसे बड़ी अशून्य घात (5) है। / \(0x^7\) is a zero term, so it is not counted. The highest non-zero power is (5).
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After simplifying \(4x^3-4x^3+9x^2-5\), what will be the degree?
B. (2)
\(4x^3-4x^3=0\) होने से \(9x^2-5\) बचता है। इसकी डिग्री (2) है। / Since \(4x^3-4x^3=0\), \(9x^2-5\) remains. Its degree is (2).
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If (p(x)=(a-3)x-6+2x-2-1) and (a=3), what is the degree of (p(x))?
C. (2)
(a=3) रखने पर \(x^6\) का गुणांक (0) हो जाता है। बची हुई सबसे बड़ी घात (2) है। / Putting (a=3) makes the coefficient of \(x^6\) equal to (0). The remaining highest power is (2).
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For which value will the degree of ((k+5)x-4-7x+9) be (1)?
B. (k=-5)
डिग्री (1) के लिए \(x^4\) का गुणांक (0) होना चाहिए। (k+5=0) से (k=-5) मिलता है। / For degree (1), the coefficient of \(x^4\) must be (0). From (k+5=0), we get (k=-5).
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The degree of \(-2x^8+5x^6-x^2+4\) is decided by which term?
A. \(-2x^8\)
सबसे बड़ी घात (8) वाले पद से डिग्री तय होती है। ऋणात्मक गुणांक डिग्री को नहीं बदलता। / The degree is decided by the term with highest power (8). A negative coefficient does not change the degree.
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What is the degree of \(2x^2+x^9-6x^5+1\)?
D. (9)
पद घटते क्रम में नहीं हैं पर सबसे बड़ी घात (9) है। इसलिए डिग्री (9) है। / The terms are not in descending order, but the highest power is (9). Therefore the degree is (9).
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If (q(x)=0x-5+0x-3+11x-4), what is the degree of (q(x))?
C. (1)
शून्य गुणांक वाले पद हट जाते हैं। (11x-4) की सबसे बड़ी घात (1) है। / Terms with zero coefficients disappear. The highest power of (11x-4) is (1).
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What is the degree of \(x^0+6x^4-3x^2\)?
C. (4)
\(x^0=1\) होता है और सबसे बड़ी घात (4) है। इसलिए डिग्री (4) है। / \(x^0=1\), and the highest power is (4). Therefore the degree is (4).
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What is the degree of the polynomial (15)?
C. (0)
(15) अशून्य नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / (15) is a non-zero constant polynomial. The degree of a non-zero constant polynomial is (0).
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What is considered the degree of the zero polynomial (0)?
C. परिभाषित नहींNot defined
शून्य बहुपद की डिग्री परिभाषित नहीं होती। इसे अशून्य नियतांक बहुपद से अलग रखें। / The degree of the zero polynomial is not defined. Keep it separate from a non-zero constant polynomial.
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After simplifying \(3x^5+2x^5-4x^2+8\), what is the degree?
C. (5)
सरल रूप \(5x^5-4x^2+8\) है। इसमें सबसे बड़ी घात (5) है। / The simplified form is \(5x^5-4x^2+8\). Its highest power is (5).
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If \(r\neq0\), what will be the degree of \(rx^7+3x^2-10\)?
C. (7)
\(r\neq0\) होने से \(x^7\) पद मौजूद रहेगा। इसलिए सबसे बड़ी घात (7) है। / Since \(r\neq0\), the \(x^7\) term remains present. Therefore the highest power is (7).
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If (r=0), what will be the degree of \(rx^7+3x^2-10\)?
C. (2)
(r=0) होने पर \(x^7\) पद हट जाता है। बची हुई सबसे बड़ी घात (2) है। / When (r=0), the \(x^7\) term disappears. The remaining highest power is (2).
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What is the degree of the polynomial \(4y^5-3y^2+8\)?
C. (5)
चर (y) की सबसे बड़ी घात (5) है। इसलिए बहुपद की डिग्री (5) है। / The highest power of the variable (y) is (5). Therefore the degree of the polynomial is (5).
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With respect to (x), what is the degree of \(5y^2-3y+1\)?
C. (0)
(x) के संदर्भ में यह अशून्य नियतांक जैसा है। इसलिए इसकी डिग्री (0) है। / With respect to (x), it behaves like a non-zero constant. Therefore its degree is (0).
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If the degree of (p(x)=\(m^2-4\)x-5+6x-3+1) is (3), which can be a possible value of (m)?
B. (m=2)
डिग्री (3) के लिए \(x^5\) का गुणांक (0) होना चाहिए। \(m^2-4=0\) से \(m=\pm2\) मिलता है। / For degree (3), the coefficient of \(x^5\) must be (0). From \(m^2-4=0\), \(m=\pm2\).
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What will be the degree after expanding (2x-4\(3x^2-1\))?
C. (6)
फैलाने पर \(6x^6-2x^4\) मिलता है। सबसे बड़ी घात (6) है। / On expanding, we get \(6x^6-2x^4\). The highest power is (6).
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After simplifying (x-2\(x^3+1\)-x-5+4x), what is the degree?
C. (2)
(x-2\(x^3+1\)=x-5+x-2) और \(x^5\) कट जाता है। बचा \(x^2+4x\) है जिसकी डिग्री (2) है। / (x-2\(x^3+1\)=x-5+x-2), and \(x^5\) cancels. The remaining \(x^2+4x\) has degree (2).
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What is the degree of the polynomial (\(x^2+1\)\(x^3-2\))?
C. (5)
गुणन में सबसे बड़ी घात \(x^2\cdot x^3=x^5\) से आती है। इसलिए डिग्री (5) है। / In multiplication, the highest power comes from \(x^2\cdot x^3=x^5\). Therefore the degree is (5).
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What is the degree of the polynomial ((x-1)(x+1))?
B. (2)
गुणनफल \(x^2-1\) है। इसमें सबसे बड़ी घात (2) है। / The product is \(x^2-1\). Its highest power is (2).
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If a polynomial has degree (0), what type of non-zero polynomial can it be?
C. नियतांक बहुपदConstant polynomial
डिग्री (0) वाला अशून्य बहुपद नियतांक होता है। शून्य बहुपद की डिग्री परिभाषित नहीं होती। / A non-zero polynomial of degree (0) is constant. The degree of the zero polynomial is not defined.
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If (f(x)=x-4-2x-4+x-4+3x-5), what is the degree of (f(x))?
C. (1)
\(x^4-2x^4+x^4=0\) हो जाता है। बचा हुआ (3x-5) डिग्री (1) का है। / \(x^4-2x^4+x^4=0\). The remaining (3x-5) has degree (1).
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What is the total degree of the polynomial \(2x^3y^2+5xy-7\)?
C. (5)
पद \(2x^3y^2\) की कुल घात (3+2=5) है। यही सबसे बड़ी कुल घात है। / The total power of the term \(2x^3y^2\) is (3+2=5). This is the highest total power.
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What is the total degree of \(4x^2y^3-3xy^2+9\)?
B. (5)
पहले पद की कुल घात (2+3=5) है। इसलिए बहुपद की कुल डिग्री (5) है। / The total power of the first term is (2+3=5). Therefore the total degree of the polynomial is (5).
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With respect to (x), what is the degree of \(3x^2y^4+7xy-1\)?
B. (2)
(x) के संदर्भ में (y) को गुणांक जैसा माना जाता है। (x) की सबसे बड़ी घात (2) है। / With respect to (x), (y) is treated like a coefficient. The highest power of (x) is (2).
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With respect to (y), what is the degree of \(3x^2y^4+7xy-1\)?
C. (4)
(y) की सबसे बड़ी घात (4) है। इसलिए (y) के संदर्भ में डिग्री (4) है। / The highest power of (y) is (4). Therefore the degree with respect to (y) is (4).
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What is the degree of \(0x^8+0x^4+5\)?
C. (0)
शून्य गुणांक वाले पद हट जाते हैं और (5) बचता है। (5) अशून्य नियतांक बहुपद है जिसकी डिग्री (0) है। / Terms with zero coefficients disappear and (5) remains. (5) is a non-zero constant polynomial of degree (0).
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If the degree of ((t-1)x-3+(t+2)x-2+4) is (2), which value of (t) can be correct?
A. (t=1)
डिग्री (2) के लिए \(x^3\) पद हटना चाहिए और \(x^2\) पद बचना चाहिए। (t=1) पर दोनों शर्तें पूरी होती हैं। / For degree (2), the \(x^3\) term must vanish and the \(x^2\) term must remain. At (t=1), both conditions hold.
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If (u=-2), what is the degree of ((u+2)x-5+\(u^2-1\)x-4+x)?
B. (4)
(u=-2) पर \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक (3) होता है। इसलिए डिग्री (4) है। / At (u=-2), the coefficient of \(x^5\) is (0) and the coefficient of \(x^4\) is (3). Therefore the degree is (4).
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What is the degree of the polynomial (\(2x^2-1\)\(x^2+3\))?
C. (4)
सबसे बड़ी घात \(2x^2\cdot x^2=2x^4\) से आती है। इसलिए डिग्री (4) है। / The highest power comes from \(2x^2\cdot x^2=2x^4\). Therefore the degree is (4).
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What is the degree of the polynomial (x(x-2)(x+5))?
C. (3)
तीन रेखीय गुणनखंडों का गुणन उच्चतम घात \(x^3\) देता है। इसलिए डिग्री (3) है। / The product of three linear factors gives highest power \(x^3\). Therefore the degree is (3).
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If (g(x)=2x-6-2x-6+x-4-x-2), what is the degree of (g(x))?
B. (4)
\(2x^6-2x^6=0\) हो जाता है। बची हुई सबसे बड़ी घात (4) है। / \(2x^6-2x^6=0\). The remaining highest power is (4).
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Which polynomial does not have degree (0)?
C. (x+1)
(x+1) की सबसे बड़ी घात (1) है। बाकी अशून्य नियतांक बहुपद हैं जिनकी डिग्री (0) है। / The highest power of (x+1) is (1). The others are non-zero constant polynomials of degree (0).
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What is the degree of \(x^2+x^4+x^6+x^8\)?
D. (8)
सबसे बड़ी घात (8) है। इसलिए बहुपद की डिग्री (8) है। / The highest power is (8). Therefore the degree of the polynomial is (8).
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If (h(x)=\(x^2-1\)2), what is the degree of (h(x))?
C. (4)
वर्ग करने पर उच्चतम पद \(x^4\) बनेगा। इसलिए डिग्री (4) है। / On squaring, the highest term becomes \(x^4\). Therefore the degree is (4).
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What is the degree of \(3x^{10}+2x^7-5x^2+1\)?
B. (10)
सबसे बड़ी घात (10) है। गुणांक (3) डिग्री नहीं होता। / The highest power is (10). The coefficient (3) is not the degree.
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If the degree of \(2x^n+5x^3-1\) is (7) and (n>3), what is (n)?
C. (7)
डिग्री सबसे बड़ी घात होती है। (n>3) और डिग्री (7) होने से (n=7) होगा। / The degree is the highest power. Since (n>3) and the degree is (7), (n=7).
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If the degree of \(x^4+ax^2+7\) is (4), what is the correct statement about (a)?
A. (a) कोई भी वास्तविक संख्या हो सकता है(a) can be any real number
\(x^4\) का गुणांक (1) है जो शून्य नहीं है। इसलिए (a) का मान डिग्री (4) को नहीं बदलता। / The coefficient of \(x^4\) is (1), which is non-zero. So the value of (a) does not change degree (4).
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What is the degree of \(0x^9+0x^5+0x+13\)?
D. (0)
शून्य गुणांक वाले पद हट जाते हैं और (13) बचता है। यह डिग्री (0) का अशून्य नियतांक बहुपद है। / Terms with zero coefficients disappear and (13) remains. It is a non-zero constant polynomial of degree (0).
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Which option has a polynomial of degree (2) but coefficient of (x) is (0)?
A. \(5x^2-9\)
\(5x^2-9\) की डिग्री (2) है और (x) पद अनुपस्थित है। इसलिए (x) का गुणांक (0) है। / \(5x^2-9\) has degree (2), and the (x) term is absent. So the coefficient of (x) is (0).
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What is the degree of (x-3\(2x^2-5\)+4x-2)?
C. (5)
फैलाने पर \(2x^5-5x^3+4x^2\) मिलता है। सबसे बड़ी घात (5) है। / On expanding, we get \(2x^5-5x^3+4x^2\). The highest power is (5).
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If (s=1), what will be the degree of ((s-1)x-4+(s+3)x-3+2)?
B. (3)
(s=1) पर \(x^4\) का गुणांक (0) और \(x^3\) का गुणांक (4) है। इसलिए डिग्री (3) है। / At (s=1), the coefficient of \(x^4\) is (0) and the coefficient of \(x^3\) is (4). Therefore the degree is (3).
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What is the total degree of \(2x^2y+3xy^4+5\)?
C. (5)
\(3xy^4\) की कुल घात (1+4=5) है। यह सबसे बड़ी कुल घात है। / The total power of \(3xy^4\) is (1+4=5). This is the highest total power.
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Which option does not have degree (5)?
C. \(6x^4+7\)
\(6x^4+7\) की सबसे बड़ी घात (4) है। इसलिए इसकी डिग्री (5) नहीं है। / The highest power of \(6x^4+7\) is (4). Therefore its degree is not (5).
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If \(v\neq2\), what is the degree of ((v-2)x-6+x-4+1)?
C. (6)
\(v\neq2\) होने पर \(x^6\) का गुणांक शून्य नहीं है। इसलिए सबसे बड़ी घात (6) रहेगी। / When \(v\neq2\), the coefficient of \(x^6\) is not zero. Therefore the highest power remains (6).
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What is the degree of (\(x^3+2\)\(x^2-x+1\))?
C. (5)
उच्चतम पद \(x^3\cdot x^2=x^5\) है। इसलिए गुणनफल की डिग्री (5) होगी। / The highest term is \(x^3\cdot x^2=x^5\). Therefore the product has degree (5).
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If (w=3), what will be the degree of ((w-3)x-8+(w+1)x-5-2x+6)?
B. (5)
(w=3) रखने पर \(x^8\) का गुणांक (0) और \(x^5\) का गुणांक (4) होता है। इसलिए सबसे बड़ी घात (5) है। / Putting (w=3) makes the coefficient of \(x^8\) equal to (0) and the coefficient of \(x^5\) equal to (4). So the highest power is (5).
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What is the degree of the polynomial (\(x^2+2x+1\)\(x^4-3\))?
C. (6)
उच्चतम पद \(x^2\cdot x^4=x^6\) से मिलेगा। इसलिए गुणनफल की डिग्री (6) है। / The highest term comes from \(x^2\cdot x^4=x^6\). Therefore the degree of the product is (6).
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If the degree of \(2x^m+7x^4-5\) is (4) and (m<4), which value of (m) is possible?
D. (m=2)
\(x^4\) पद पहले से मौजूद है और (m<4) है। इसलिए (m=2) होने पर भी सबसे बड़ी घात (4) रहेगी। / The \(x^4\) term is already present and (m<4). So even when (m=2), the highest power remains (4).
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