बहुपद \(3x^4-5x^2+7x-1\) की डिग्री क्या है?
What is the degree of the polynomial \(3x^4-5x^2+7x-1\)?
#polynomial
#degree
#highest_power
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A (1)
B (2)
C (4)
D (7)
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Explanation
Simple Explanation
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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बहुपद \(8x^5+0x^7-2x^3+6\) की डिग्री क्या है?
What is the degree of \(8x^5+0x^7-2x^3+6\)?
#polynomial
#zero_coefficient
#degree
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A (7)
B (5)
C (3)
D (0)
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\(0x^7\) 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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सरल करने के बाद \(4x^3-4x^3+9x^2-5\) की डिग्री क्या होगी?
After simplifying \(4x^3-4x^3+9x^2-5\), what will be the degree?
#polynomial
#simplification
#degree
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A (3)
B (2)
C (1)
D (0)
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\(4x^3-4x^3=0\) 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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यदि (p(x)=(a-3)x-6 +2x-2 -1) और (a=3), तो (p(x)) की डिग्री क्या है?
If (p(x)=(a-3)x-6 +2x-2 -1) and (a=3), what is the degree of (p(x))?
#polynomial
#parameter
#degree
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A (6)
B (3)
C (2)
D (0)
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(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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किस मान पर ((k+5)x-4 -7x+9) की डिग्री (1) होगी?
For which value will the degree of ((k+5)x-4 -7x+9) be (1)?
#polynomial
#degree
#parameter_value
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A (k=5)
B (k=-5)
C (k=0)
D (k=1)
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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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बहुपद \(-2x^8+5x^6-x^2+4\) की डिग्री किस पद से तय होती है?
The degree of \(-2x^8+5x^6-x^2+4\) is decided by which term?
#polynomial
#leading_term
#degree
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A \(-2x^8\)
B \(5x^6\)
C \(-x^2\)
D (4)
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Correct Answer
A. \(-2x^8\)
Explanation
Simple Explanation
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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बहुपद \(2x^2+x^9-6x^5+1\) की डिग्री क्या है?
What is the degree of \(2x^2+x^9-6x^5+1\)?
#polynomial
#unordered_terms
#degree
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A (2)
B (5)
C (6)
D (9)
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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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यदि (q(x)=0x-5 +0x-3 +11x-4), तो (q(x)) की डिग्री क्या है?
If (q(x)=0x-5 +0x-3 +11x-4), what is the degree of (q(x))?
#polynomial
#zero_coefficient
#linear_degree
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A (5)
B (3)
C (1)
D (0)
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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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बहुपद \(x^0+6x^4-3x^2\) की डिग्री क्या है?
What is the degree of \(x^0+6x^4-3x^2\)?
#polynomial
#zero_power
#degree
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A (0)
B (2)
C (4)
D (6)
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\(x^0=1\) 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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बहुपद (15) की डिग्री क्या है?
What is the degree of the polynomial (15)?
#polynomial
#constant
#degree_zero
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A (15)
B (1)
C (0)
D परिभाषित नहीं / Not defined
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(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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शून्य बहुपद (0) की डिग्री क्या मानी जाती है?
What is considered the degree of the zero polynomial (0)?
#polynomial
#zero_polynomial
#degree
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A (0)
B (1)
C परिभाषित नहीं / Not defined
D अनंत / Infinite
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Correct Answer
C. परिभाषित नहीं / Not defined
Explanation
Simple Explanation
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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सरल करने के बाद \(3x^5+2x^5-4x^2+8\) की डिग्री क्या है?
After simplifying \(3x^5+2x^5-4x^2+8\), what is the degree?
#polynomial
#like_terms
#degree
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A (2)
B (3)
C (5)
D (8)
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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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यदि \(r\neq0\), तो \(rx^7+3x^2-10\) की डिग्री क्या होगी?
If \(r\neq0\), what will be the degree of \(rx^7+3x^2-10\)?
#polynomial
#nonzero_parameter
#degree
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A (0)
B (2)
C (7)
D (10)
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\(r\neq0\) 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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यदि (r=0), तो \(rx^7+3x^2-10\) की डिग्री क्या होगी?
If (r=0), what will be the degree of \(rx^7+3x^2-10\)?
#polynomial
#parameter_zero
#degree
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A (7)
B (3)
C (2)
D (0)
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(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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बहुपद \(4y^5-3y^2+8\) की डिग्री क्या है?
What is the degree of the polynomial \(4y^5-3y^2+8\)?
#polynomial
#degree
#in_y
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A (2)
B (3)
C (5)
D (8)
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Explanation
Simple Explanation
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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(x) के संदर्भ में \(5y^2-3y+1\) की डिग्री क्या है?
With respect to (x), what is the degree of \(5y^2-3y+1\)?
#polynomial
#degree_in_x
#constant
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A (2)
B (1)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
(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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यदि (p(x)=\(m^2-4\)x-5 +6x-3 +1) की डिग्री (3) है, तो (m) का संभावित मान कौन सा है?
If the degree of (p(x)=\(m^2-4\)x-5 +6x-3 +1) is (3), which can be a possible value of (m)?
#polynomial
#parameter_value
#degree
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A (m=0)
B (m=2)
C (m=3)
D (m=4)
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Explanation
Simple Explanation
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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बहुपद (2x-4 \(3x^2-1\)) को फैलाने पर डिग्री क्या होगी?
What will be the degree after expanding (2x-4 \(3x^2-1\))?
#polynomial
#expansion
#degree
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A (2)
B (4)
C (6)
D (8)
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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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सरल करने के बाद (x-2 \(x^3+1\)-x-5 +4x) की डिग्री क्या है?
After simplifying (x-2 \(x^3+1\)-x-5 +4x), what is the degree?
#polynomial
#simplification
#cancellation
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A (5)
B (3)
C (2)
D (1)
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Explanation
Simple Explanation
(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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बहुपद (\(x^2+1\)\(x^3-2\)) की डिग्री क्या है?
What is the degree of the polynomial (\(x^2+1\)\(x^3-2\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
Simple Explanation
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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बहुपद ((x-1)(x+1)) की डिग्री क्या है?
What is the degree of the polynomial ((x-1)(x+1))?
#polynomial
#product
#degree
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A (1)
B (2)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
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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यदि बहुपद की डिग्री (0) है, तो वह किस प्रकार का अशून्य बहुपद हो सकता है?
If a polynomial has degree (0), what type of non-zero polynomial can it be?
#polynomial
#degree_zero
#constant
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A रेखीय बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C नियतांक बहुपद / Constant polynomial
D शून्य बहुपद / Zero polynomial
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Correct Answer
C. नियतांक बहुपद / Constant polynomial
Explanation
Simple Explanation
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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यदि (f(x)=x-4 -2x-4 +x-4 +3x-5), तो (f(x)) की डिग्री क्या है?
If (f(x)=x-4 -2x-4 +x-4 +3x-5), what is the degree of (f(x))?
#polynomial
#cancellation
#degree
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A (4)
B (3)
C (1)
D (0)
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Explanation
Simple Explanation
\(x^4-2x^4+x^4=0\) 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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बहुपद \(2x^3y^2+5xy-7\) की कुल डिग्री क्या है?
What is the total degree of the polynomial \(2x^3y^2+5xy-7\)?
#polynomial
#total_degree
#two_variables
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A (2)
B (3)
C (5)
D (7)
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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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बहुपद \(4x^2y^3-3xy^2+9\) की कुल डिग्री क्या है?
What is the total degree of \(4x^2y^3-3xy^2+9\)?
#polynomial
#total_degree
#variables
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A (3)
B (5)
C (4)
D (2)
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Explanation
Simple Explanation
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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(x) के संदर्भ में \(3x^2y^4+7xy-1\) की डिग्री क्या है?
With respect to (x), what is the degree of \(3x^2y^4+7xy-1\)?
#polynomial
#degree_in_x
#two_variables
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A (1)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
(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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(y) के संदर्भ में \(3x^2y^4+7xy-1\) की डिग्री क्या है?
With respect to (y), what is the degree of \(3x^2y^4+7xy-1\)?
#polynomial
#degree_in_y
#two_variables
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A (1)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
(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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बहुपद \(0x^8+0x^4+5\) की डिग्री क्या है?
What is the degree of \(0x^8+0x^4+5\)?
#polynomial
#zero_coefficient
#constant_degree
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A (8)
B (4)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
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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यदि ((t-1)x-3 +(t+2)x-2 +4) की डिग्री (2) है, तो (t) का सही मान कौन सा हो सकता है?
If the degree of ((t-1)x-3 +(t+2)x-2 +4) is (2), which value of (t) can be correct?
#polynomial
#degree
#parameter_condition
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A (t=1)
B (t=-2)
C (t=0)
D (t=3)
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Explanation
Simple Explanation
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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यदि (u=-2), तो ((u+2)x-5 +\(u^2-1\)x-4 +x) की डिग्री क्या है?
If (u=-2), what is the degree of ((u+2)x-5 +\(u^2-1\)x-4 +x)?
#polynomial
#parameter_substitution
#degree
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A (5)
B (4)
C (1)
D (0)
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Explanation
Simple Explanation
(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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बहुपद (\(2x^2-1\)\(x^2+3\)) की डिग्री क्या है?
What is the degree of the polynomial (\(2x^2-1\)\(x^2+3\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
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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बहुपद (x(x-2)(x+5)) की डिग्री क्या है?
What is the degree of the polynomial (x(x-2)(x+5))?
#polynomial
#factors
#degree
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A (1)
B (2)
C (3)
D (5)
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Explanation
Simple Explanation
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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यदि (g(x)=2x-6 -2x-6 +x-4 -x-2 ), तो (g(x)) की डिग्री क्या है?
If (g(x)=2x-6 -2x-6 +x-4 -x-2 ), what is the degree of (g(x))?
#polynomial
#cancellation
#degree
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A (6)
B (4)
C (2)
D (0)
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Explanation
Simple Explanation
\(2x^6-2x^6=0\) 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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किस बहुपद की डिग्री (0) नहीं है?
Which polynomial does not have degree (0)?
#polynomial
#degree_zero
#identification
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A (8)
B \(-3\)
C (x+1)
D \(\sqrt{2}\)
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Explanation
Simple Explanation
(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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बहुपद \(x^2+x^4+x^6+x^8\) की डिग्री क्या है?
What is the degree of \(x^2+x^4+x^6+x^8\)?
#polynomial
#ascending_powers
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
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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यदि (h(x)=\(x^2-1\)2 ), तो (h(x)) की डिग्री क्या है?
If (h(x)=\(x^2-1\)2 ), what is the degree of (h(x))?
#polynomial
#power_of_polynomial
#degree
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A (2)
B (3)
C (4)
D (1)
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Explanation
Simple Explanation
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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बहुपद \(3x^{10}+2x^7-5x^2+1\) की डिग्री क्या है?
What is the degree of \(3x^{10}+2x^7-5x^2+1\)?
#polynomial
#higher_power
#degree
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A (7)
B (10)
C (12)
D (3)
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Explanation
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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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यदि \(2x^n+5x^3-1\) की डिग्री (7) है और (n>3), तो (n) क्या होगा?
If the degree of \(2x^n+5x^3-1\) is (7) and (n>3), what is (n)?
#polynomial
#unknown_power
#degree
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A (3)
B (5)
C (7)
D (10)
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Explanation
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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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यदि \(x^4+ax^2+7\) की डिग्री (4) है, तो (a) के लिए सही कथन क्या है?
If the degree of \(x^4+ax^2+7\) is (4), what is the correct statement about (a)?
#polynomial
#parameter
#degree
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A (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
B (a=0) ही होना चाहिए / (a) must be (0) only
C (a=4) ही होना चाहिए / (a) must be (4) only
D \(a\neq0\) होना चाहिए / \(a\neq0\) is required
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Correct Answer
A. (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
Explanation
Simple Explanation
\(x^4\) 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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बहुपद \(0x^9+0x^5+0x+13\) की डिग्री क्या है?
What is the degree of \(0x^9+0x^5+0x+13\)?
#polynomial
#constant_degree
#zero_coefficient
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A (9)
B (5)
C (1)
D (0)
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Explanation
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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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किस विकल्प में डिग्री (2) वाला बहुपद है लेकिन (x) का गुणांक (0) है?
Which option has a polynomial of degree (2) but coefficient of (x) is (0)?
#polynomial
#degree
#missing_term
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A \(5x^2-9\)
B \(5x^2+x-9\)
C (5x-9)
D \(x^3+5x^2-9\)
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Correct Answer
A. \(5x^2-9\)
Explanation
Simple Explanation
\(5x^2-9\) 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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बहुपद (x-3 \(2x^2-5\)+4x-2 ) की डिग्री क्या है?
What is the degree of (x-3 \(2x^2-5\)+4x-2 )?
#polynomial
#expansion
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
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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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यदि (s=1), तो ((s-1 )x-4 +(s+3)x-3 +2) की डिग्री क्या होगी?
If (s=1), what will be the degree of ((s-1 )x-4 +(s+3)x-3 +2)?
#polynomial
#parameter_substitution
#degree
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A (4)
B (3)
C (1)
D (0)
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Explanation
Simple Explanation
(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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बहुपद \(2x^2y+3xy^4+5\) की कुल डिग्री क्या है?
What is the total degree of \(2x^2y+3xy^4+5\)?
#polynomial
#total_degree
#two_variables
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A (3)
B (4)
C (5)
D (6)
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Explanation
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\(3xy^4\) 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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किस विकल्प में डिग्री (5) नहीं है?
Which option does not have degree (5)?
#polynomial
#degree
#identification
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A \(x^5+2\)
B \(3x^5-4x\)
C \(6x^4+7\)
D \(x^5+x^2+1\)
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Correct Answer
C. \(6x^4+7\)
Explanation
Simple Explanation
\(6x^4+7\) 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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यदि \(v\neq2\), तो ((v-2)x-6 +x-4 +1) की डिग्री क्या है?
If \(v\neq2\), what is the degree of ((v-2)x-6 +x-4 +1)?
#polynomial
#nonzero_parameter
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
\(v\neq2\) 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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बहुपद (\(x^3+2\)\(x^2-x+1\)) की डिग्री क्या है?
What is the degree of (\(x^3+2\)\(x^2-x+1\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
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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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यदि (w=3), तो ((w-3)x-8 +(w+1)x-5 -2x+6) की डिग्री क्या होगी?
If (w=3), what will be the degree of ((w-3)x-8 +(w+1)x-5 -2x+6)?
#polynomial
#parameter_substitution
#degree
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A (8)
B (5)
C (1)
D (0)
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Explanation
Simple Explanation
(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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बहुपद (\(x^2+2x+1\)\(x^4-3\)) की डिग्री क्या है?
What is the degree of the polynomial (\(x^2+2x+1\)\(x^4-3\))?
#polynomial
#product
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
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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यदि \(2x^m+7x^4-5\) की डिग्री (4) है और (m<4), तो (m) का कौन सा मान संभव है?
If the degree of \(2x^m+7x^4-5\) is (4) and (m<4), which value of (m) is possible?
#polynomial
#unknown_power
#degree
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A (m=6)
B (m=5)
C (m=4)
D (m=2)
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Explanation
Simple Explanation
\(x^4\) 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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बहुपद \(5x^6-3x^4+2x-9\) की डिग्री क्या है?
What is the degree of the polynomial \(5x^6-3x^4+2x-9\)?
#polynomial
#degree
#highest_power
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A (2)
B (4)
C (6)
D (9)
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Explanation
Simple Explanation
सबसे बड़ी घात (6) है। डिग्री हमेशा सबसे बड़ी अशून्य घात से तय करें। / The highest power is (6). Always decide the degree from the highest non-zero power.
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बहुपद \(0x^8+7x^5-4x^2+1\) की डिग्री क्या है?
What is the degree of \(0x^8+7x^5-4x^2+1\)?
#polynomial
#zero_coefficient
#degree
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A (8)
B (7)
C (5)
D (2)
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Explanation
Simple Explanation
\(0x^8\) शून्य पद है इसलिए उसे नहीं गिनते। सबसे बड़ी अशून्य घात (5) है। / \(0x^8\) is a zero term, so it is not counted. The highest non-zero power is (5).
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सरल करने के बाद \(6x^4-6x^4+3x^3-2\) की डिग्री क्या होगी?
After simplifying \(6x^4-6x^4+3x^3-2\), what will be the degree?
#polynomial
#simplification
#degree
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A (4)
B (3)
C (2)
D (0)
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Explanation
Simple Explanation
\(6x^4-6x^4=0\) होने से \(3x^3-2\) बचता है। इसकी डिग्री (3) है। / Since \(6x^4-6x^4=0\), \(3x^3-2\) remains. Its degree is (3).
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यदि (p(x)=(a+2)x-7 +4x-3 -5) और (a=-2), तो (p(x)) की डिग्री क्या है?
If (p(x)=(a+2)x-7 +4x-3 -5) and (a=-2), what is the degree of (p(x))?
#polynomial
#parameter
#degree
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A (7)
B (4)
C (3)
D (0)
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Explanation
Simple Explanation
(a=-2) रखने पर \(x^7\) का गुणांक (0) हो जाता है। बची हुई सबसे बड़ी घात (3) है। / Putting (a=-2) makes the coefficient of \(x^7\) equal to (0). The remaining highest power is (3).
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किस मान पर ((m-6 )x-5 +2x-2 +7) की डिग्री (2) होगी?
For which value will the degree of ((m-6 )x-5 +2x-2 +7) be (2)?
#polynomial
#degree
#parameter_value
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A (m=6)
B (m=-6)
C (m=2)
D (m=0)
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Explanation
Simple Explanation
डिग्री (2) के लिए \(x^5\) का गुणांक (0) होना चाहिए। (m-6 =0) से (m=6) मिलता है। / For degree (2), the coefficient of \(x^5\) must be (0). From (m-6 =0), we get (m=6).
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बहुपद \(-9x^7+4x^5-x+8\) की डिग्री किस पद से तय होती है?
The degree of \(-9x^7+4x^5-x+8\) is decided by which term?
#polynomial
#leading_term
#degree
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A \(-9x^7\)
B \(4x^5\)
C (-x)
D (8)
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Correct Answer
A. \(-9x^7\)
Explanation
Simple Explanation
सबसे बड़ी घात (7) वाले पद से डिग्री तय होती है। ऋणात्मक गुणांक डिग्री को नहीं बदलता। / The degree is decided by the term with highest power (7). A negative coefficient does not change the degree.
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बहुपद \(4x^2+x^{10}-6x^4+11\) की डिग्री क्या है?
What is the degree of \(4x^2+x^{10}-6x^4+11\)?
#polynomial
#unordered_terms
#degree
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A (2)
B (4)
C (6)
D (10)
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Explanation
Simple Explanation
पद घटते क्रम में नहीं हैं पर सबसे बड़ी घात (10) है। इसलिए डिग्री (10) है। / The terms are not in descending order, but the highest power is (10). Therefore the degree is (10).
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यदि (q(x)=0x-6 +0x-4 -13x+9), तो (q(x)) की डिग्री क्या है?
If (q(x)=0x-6 +0x-4 -13x+9), what is the degree of (q(x))?
#polynomial
#zero_coefficient
#linear_degree
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A (6)
B (4)
C (1)
D (0)
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं। (-13x+9) की सबसे बड़ी घात (1) है। / Terms with zero coefficients disappear. The highest power of (-13x+9) is (1).
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बहुपद \(2x^0+9x^5-4x^2\) की डिग्री क्या है?
What is the degree of \(2x^0+9x^5-4x^2\)?
#polynomial
#zero_power
#degree
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A (0)
B (2)
C (5)
D (9)
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Explanation
Simple Explanation
\(x^0=1\) 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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बहुपद (-24) की डिग्री क्या है?
What is the degree of the polynomial (-24)?
#polynomial
#constant
#degree_zero
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A (24)
B (1)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
(-24) अशून्य नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / (-24) is a non-zero constant polynomial. The degree of a non-zero constant polynomial is (0).
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शून्य बहुपद \(0x^5+0x^2+0\) की डिग्री क्या मानी जाती है?
What is considered the degree of the zero polynomial \(0x^5+0x^2+0\)?
#polynomial
#zero_polynomial
#degree
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A (5)
B (2)
C (0)
D परिभाषित नहीं / Not defined
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Correct Answer
D. परिभाषित नहीं / Not defined
Explanation
Simple Explanation
यह शून्य बहुपद है और इसकी डिग्री परिभाषित नहीं होती। परीक्षा में इसे नियतांक (0) से अलग पहचानें। / This is the zero polynomial and its degree is not defined. In exams, identify it separately from non-zero constants.
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किस बहुपद की डिग्री (4) है?
Which polynomial has degree (4)?
#polynomial
#degree
#option_based
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A \(3x^3+4x-1\)
B \(5x^4-2x+6\)
C \(7x^5+1\)
D (18)
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Correct Answer
B. \(5x^4-2x+6\)
Explanation
Simple Explanation
\(5x^4-2x+6\) में सबसे बड़ी घात (4) है। इसलिए इसकी डिग्री (4) है। / In \(5x^4-2x+6\), the highest power is (4). Therefore its degree is (4).
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सरल करने के बाद \(8x^6-3x^6+2x^3-7\) की डिग्री क्या है?
After simplifying \(8x^6-3x^6+2x^3-7\), what is the degree?
#polynomial
#like_terms
#degree
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A (3)
B (5)
C (6)
D (8)
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Explanation
Simple Explanation
सरल रूप \(5x^6+2x^3-7\) है। इसमें सबसे बड़ी घात (6) है। / The simplified form is \(5x^6+2x^3-7\). Its highest power is (6).
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यदि \(r\neq0\), तो \(rx^8-5x^3+2\) की डिग्री क्या होगी?
If \(r\neq0\), what will be the degree of \(rx^8-5x^3+2\)?
#polynomial
#nonzero_parameter
#degree
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A (0)
B (3)
C (8)
D (10)
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Explanation
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\(r\neq0\) होने से \(x^8\) पद मौजूद रहेगा। इसलिए सबसे बड़ी घात (8) है। / Since \(r\neq0\), the \(x^8\) term remains present. Therefore the highest power is (8).
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यदि (r=0), तो \(rx^8-5x^3+2\) की डिग्री क्या होगी?
If (r=0), what will be the degree of \(rx^8-5x^3+2\)?
#polynomial
#parameter_zero
#degree
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A (8)
B (5)
C (3)
D (0)
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(r=0) होने पर \(x^8\) पद हट जाता है। बची हुई सबसे बड़ी घात (3) है। / When (r=0), the \(x^8\) term disappears. The remaining highest power is (3).
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बहुपद \(6y^4-7y^2+12\) की डिग्री क्या है?
What is the degree of the polynomial \(6y^4-7y^2+12\)?
#polynomial
#degree
#in_y
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A (2)
B (4)
C (6)
D (12)
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Explanation
Simple Explanation
चर (y) की सबसे बड़ी घात (4) है। इसलिए बहुपद की डिग्री (4) है। / The highest power of the variable (y) is (4). Therefore the degree of the polynomial is (4).
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(x) के संदर्भ में \(7y^3-2y+5\) की डिग्री क्या है?
With respect to (x), what is the degree of \(7y^3-2y+5\)?
#polynomial
#degree_in_x
#constant
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A (3)
B (1)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
(x) के संदर्भ में इसमें (x) नहीं है इसलिए यह अशून्य नियतांक जैसा है। इसकी डिग्री (0) है। / With respect to (x), it has no (x), so it behaves like a non-zero constant. Its degree is (0).
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यदि (p(x)=\(m^2-9\)x-6 +5x-4 -1) की डिग्री (4) है, तो (m) का संभावित मान कौन सा है?
If the degree of (p(x)=\(m^2-9\)x-6 +5x-4 -1) is (4), which can be a possible value of (m)?
#polynomial
#parameter_value
#degree
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A (m=0)
B (m=2)
C (m=3)
D (m=4)
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Explanation
Simple Explanation
डिग्री (4) के लिए \(x^6\) का गुणांक (0) होना चाहिए। \(m^2-9=0\) से \(m=\pm3\) मिलता है। / For degree (4), the coefficient of \(x^6\) must be (0). From \(m^2-9=0\), \(m=\pm3\).
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बहुपद (3x-3 \(2x^2-5\)) को फैलाने पर डिग्री क्या होगी?
What will be the degree after expanding (3x-3 \(2x^2-5\))?
#polynomial
#expansion
#degree
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A (2)
B (3)
C (5)
D (6)
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फैलाने पर \(6x^5-15x^3\) मिलता है। सबसे बड़ी घात (5) है। / On expanding, we get \(6x^5-15x^3\). The highest power is (5).
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सरल करने के बाद (x-3 \(x^2+2\)-x-5 +7x-2 ) की डिग्री क्या है?
After simplifying (x-3 \(x^2+2\)-x-5 +7x-2 ), what is the degree?
#polynomial
#simplification
#cancellation
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A (5)
B (3)
C (2)
D (1)
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Explanation
Simple Explanation
(x-3 \(x^2+2\)=x-5 +2x-3 ) और \(x^5\) कट जाता है। बचा \(2x^3+7x^2\) है जिसकी डिग्री (3) है। / (x-3 \(x^2+2\)=x-5 +2x-3 ), and \(x^5\) cancels. The remaining \(2x^3+7x^2\) has degree (3).
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बहुपद (\(x^3+1\)\(x^2-4\)) की डिग्री क्या है?
What is the degree of the polynomial (\(x^3+1\)\(x^2-4\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
Simple Explanation
गुणन में सबसे बड़ी घात \(x^3\cdot x^2=x^5\) से आती है। इसलिए डिग्री (5) है। / In multiplication, the highest power comes from \(x^3\cdot x^2=x^5\). Therefore the degree is (5).
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बहुपद ((x-2)(x+3)) की डिग्री क्या है?
What is the degree of the polynomial ((x-2)(x+3))?
#polynomial
#product
#degree
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A (1)
B (2)
C (3)
D (0)
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Simple Explanation
गुणनफल \(x^2+x-6\) है। इसमें सबसे बड़ी घात (2) है। / The product is \(x^2+x-6\). Its highest power is (2).
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यदि बहुपद की डिग्री (1) है, तो वह किस प्रकार का बहुपद कहलाता है?
If a polynomial has degree (1), what type of polynomial is it called?
#polynomial
#linear
#degree
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A नियतांक बहुपद / Constant polynomial
B रेखीय बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D त्रिघात बहुपद / Cubic polynomial
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Correct Answer
B. रेखीय बहुपद / Linear polynomial
Explanation
Simple Explanation
डिग्री (1) वाला बहुपद रेखीय बहुपद कहलाता है। डिग्री देखकर बहुपद का प्रकार पहचानें। / A polynomial of degree (1) is called a linear polynomial. Identify the type by its degree.
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यदि (f(x)=2x-5 -5x-5 +3x-2 -8), तो (f(x)) की डिग्री क्या है?
If (f(x)=2x-5 -5x-5 +3x-2 -8), what is the degree of (f(x))?
#polynomial
#cancellation
#degree
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A (5)
B (3)
C (2)
D (0)
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Explanation
Simple Explanation
सरल करने पर \(-3x^5+3x^2-8\) मिलता है। सबसे बड़ी घात (5) है। / On simplifying, we get \(-3x^5+3x^2-8\). The highest power is (5).
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बहुपद \(5x^2y^3+4xy-6\) की कुल डिग्री क्या है?
What is the total degree of the polynomial \(5x^2y^3+4xy-6\)?
#polynomial
#total_degree
#two_variables
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A (2)
B (3)
C (5)
D (6)
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Explanation
Simple Explanation
पद \(5x^2y^3\) की कुल घात (2+3=5) है। यही सबसे बड़ी कुल घात है। / The total power of the term \(5x^2y^3\) is (2+3=5). This is the highest total power.
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बहुपद \(7x^3y^2-2xy^4+10\) की कुल डिग्री क्या है?
What is the total degree of \(7x^3y^2-2xy^4+10\)?
#polynomial
#total_degree
#variables
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A (3)
B (4)
C (5)
D (7)
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Explanation
Simple Explanation
पहले पद की कुल घात (3+2=5) और दूसरे पद की (1+4=5) है। इसलिए कुल डिग्री (5) है। / The total power of the first term is (3+2=5) and of the second term is (1+4=5). Therefore the total degree is (5).
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(x) के संदर्भ में \(4x^3y^2+6xy^5-2\) की डिग्री क्या है?
With respect to (x), what is the degree of \(4x^3y^2+6xy^5-2\)?
#polynomial
#degree_in_x
#two_variables
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A (1)
B (2)
C (3)
D (5)
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Explanation
Simple Explanation
(x) के संदर्भ में (y) को गुणांक जैसा मानते हैं। (x) की सबसे बड़ी घात (3) है। / With respect to (x), (y) is treated like a coefficient. The highest power of (x) is (3).
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(y) के संदर्भ में \(4x^3y^2+6xy^5-2\) की डिग्री क्या है?
With respect to (y), what is the degree of \(4x^3y^2+6xy^5-2\)?
#polynomial
#degree_in_y
#two_variables
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A (1)
B (2)
C (3)
D (5)
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Explanation
Simple Explanation
(y) की सबसे बड़ी घात (5) है। इसलिए (y) के संदर्भ में डिग्री (5) है। / The highest power of (y) is (5). Therefore the degree with respect to (y) is (5).
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बहुपद \(0x^9+0x^6-12\) की डिग्री क्या है?
What is the degree of \(0x^9+0x^6-12\)?
#polynomial
#zero_coefficient
#constant_degree
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A (9)
B (6)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं और (-12) बचता है। (-12) अशून्य नियतांक बहुपद है जिसकी डिग्री (0) है। / Terms with zero coefficients disappear and (-12) remains. (-12) is a non-zero constant polynomial of degree (0).
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यदि ((t+4)x-3 +(t-1)x-2 +5) की डिग्री (2) है, तो (t) का सही मान कौन सा हो सकता है?
If the degree of ((t+4)x-3 +(t-1)x-2 +5) is (2), which value of (t) can be correct?
#polynomial
#degree
#parameter_condition
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A (t=-4)
B (t=1)
C (t=0)
D (t=4)
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Explanation
Simple Explanation
डिग्री (2) के लिए \(x^3\) पद हटना चाहिए और \(x^2\) पद बचना चाहिए। (t=-4) पर दोनों शर्तें पूरी होती हैं। / For degree (2), the \(x^3\) term must vanish and the \(x^2\) term must remain. At (t=-4), both conditions hold.
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यदि (u=2), तो ((u-2)x-6 +\(u^2+1\)x-4 +x) की डिग्री क्या है?
If (u=2), what is the degree of ((u-2)x-6 +\(u^2+1\)x-4 +x)?
#polynomial
#parameter_substitution
#degree
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A (6)
B (4)
C (1)
D (0)
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Explanation
Simple Explanation
(u=2) पर \(x^6\) का गुणांक (0) और \(x^4\) का गुणांक (5) होता है। इसलिए डिग्री (4) है। / At (u=2), the coefficient of \(x^6\) is (0) and the coefficient of \(x^4\) is (5). Therefore the degree is (4).
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बहुपद (\(3x^2+1\)\(x^3-2\)) की डिग्री क्या है?
What is the degree of the polynomial (\(3x^2+1\)\(x^3-2\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
Simple Explanation
सबसे बड़ी घात \(3x^2\cdot x^3=3x^5\) से आती है। इसलिए डिग्री (5) है। / The highest power comes from \(3x^2\cdot x^3=3x^5\). Therefore the degree is (5).
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बहुपद (x(x+4)(x-5)) की डिग्री क्या है?
What is the degree of the polynomial (x(x+4)(x-5))?
#polynomial
#factors
#degree
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A (1)
B (2)
C (3)
D (5)
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Explanation
Simple Explanation
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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यदि (g(x)=5x-7 -5x-7 +x-5 -x-2 ), तो (g(x)) की डिग्री क्या है?
If (g(x)=5x-7 -5x-7 +x-5 -x-2 ), what is the degree of (g(x))?
#polynomial
#cancellation
#degree
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A (7)
B (5)
C (2)
D (0)
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Explanation
Simple Explanation
\(5x^7-5x^7=0\) हो जाता है। बची हुई सबसे बड़ी घात (5) है। / \(5x^7-5x^7=0\). The remaining highest power is (5).
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बहुपद \(x^3+x^5+x^7+x^9\) की डिग्री क्या है?
What is the degree of \(x^3+x^5+x^7+x^9\)?
#polynomial
#ascending_powers
#degree
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A (3)
B (5)
C (7)
D (9)
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Explanation
Simple Explanation
सबसे बड़ी घात (9) है। इसलिए बहुपद की डिग्री (9) है। / The highest power is (9). Therefore the degree of the polynomial is (9).
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यदि (h(x)=\(x^3-2\)2 ), तो (h(x)) की डिग्री क्या है?
If (h(x)=\(x^3-2\)2 ), what is the degree of (h(x))?
#polynomial
#power_of_polynomial
#degree
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A (3)
B (5)
C (6)
D (9)
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Explanation
Simple Explanation
वर्ग करने पर उच्चतम पद \(x^6\) बनेगा। इसलिए डिग्री (6) है। / On squaring, the highest term becomes \(x^6\). Therefore the degree is (6).
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बहुपद \(4x^{11}-3x^8+2x^4-1\) की डिग्री क्या है?
What is the degree of \(4x^{11}-3x^8+2x^4-1\)?
#polynomial
#higher_power
#degree
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A (8)
B (11)
C (15)
D (4)
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Explanation
Simple Explanation
सबसे बड़ी घात (11) है। गुणांक (4) डिग्री नहीं होता। / The highest power is (11). The coefficient (4) is not the degree.
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यदि \(3x^n+2x^4-7\) की डिग्री (9) है और (n>4), तो (n) क्या होगा?
If the degree of \(3x^n+2x^4-7\) is (9) and (n>4), what is (n)?
#polynomial
#unknown_power
#degree
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A (4)
B (6)
C (9)
D (12)
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Simple Explanation
डिग्री सबसे बड़ी घात होती है। (n>4) और डिग्री (9) होने से (n=9) होगा। / The degree is the highest power. Since (n>4) and the degree is (9), (n=9).
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यदि \(x^5+ax^3+4\) की डिग्री (5) है, तो (a) के लिए सही कथन क्या है?
If the degree of \(x^5+ax^3+4\) is (5), what is the correct statement about (a)?
#polynomial
#parameter
#degree
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A (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
B (a=0) ही होना चाहिए / (a) must be (0) only
C (a=5) ही होना चाहिए / (a) must be (5) only
D \(a\neq0\) होना चाहिए / \(a\neq0\) is required
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Correct Answer
A. (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
Explanation
Simple Explanation
\(x^5\) का गुणांक (1) है जो शून्य नहीं है। इसलिए (a) का मान डिग्री (5) को नहीं बदलता। / The coefficient of \(x^5\) is (1), which is non-zero. So the value of (a) does not change degree (5).
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बहुपद \(0x^{10}+0x^6+0x+19\) की डिग्री क्या है?
What is the degree of \(0x^{10}+0x^6+0x+19\)?
#polynomial
#constant_degree
#zero_coefficient
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A (10)
B (6)
C (1)
D (0)
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं और (19) बचता है। यह डिग्री (0) का अशून्य नियतांक बहुपद है। / Terms with zero coefficients disappear and (19) remains. It is a non-zero constant polynomial of degree (0).
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किस विकल्प में डिग्री (3) वाला बहुपद है लेकिन \(x^2\) का गुणांक (0) है?
Which option has a polynomial of degree (3) but coefficient of \(x^2\) is (0)?
#polynomial
#degree
#missing_term
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A \(4x^3-8x+1\)
B \(4x^3+x^2+1\)
C \(4x^2-8x+1\)
D \(x^4+4x^3-1\)
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Correct Answer
A. \(4x^3-8x+1\)
Explanation
Simple Explanation
\(4x^3-8x+1\) की डिग्री (3) है और \(x^2\) पद अनुपस्थित है। इसलिए \(x^2\) का गुणांक (0) है। / \(4x^3-8x+1\) has degree (3), and the \(x^2\) term is absent. So the coefficient of \(x^2\) is (0).
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बहुपद (x-4 \(3x^2-2\)+5x-3 ) की डिग्री क्या है?
What is the degree of (x-4 \(3x^2-2\)+5x-3 )?
#polynomial
#expansion
#degree
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A (3)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
फैलाने पर \(3x^6-2x^4+5x^3\) मिलता है। सबसे बड़ी घात (6) है। / On expanding, we get \(3x^6-2x^4+5x^3\). The highest power is (6).
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यदि (s=-1), तो ((s+1)x-5 +(s+4)x-2 +8) की डिग्री क्या होगी?
If (s=-1), what will be the degree of ((s+1)x-5 +(s+4)x-2 +8)?
#polynomial
#parameter_substitution
#degree
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A (5)
B (4)
C (2)
D (0)
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Explanation
Simple Explanation
(s=-1) पर \(x^5\) का गुणांक (0) और \(x^2\) का गुणांक (3) है। इसलिए डिग्री (2) है। / At (s=-1), the coefficient of \(x^5\) is (0) and the coefficient of \(x^2\) is (3). Therefore the degree is (2).
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बहुपद \(4x^3y+2xy^5+6\) की कुल डिग्री क्या है?
What is the total degree of \(4x^3y+2xy^5+6\)?
#polynomial
#total_degree
#two_variables
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
\(2xy^5\) की कुल घात (1+5=6) है। यह सबसे बड़ी कुल घात है। / The total power of \(2xy^5\) is (1+5=6). This is the highest total power.
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किस विकल्प में डिग्री (6) नहीं है?
Which option does not have degree (6)?
#polynomial
#degree
#identification
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A \(x^6+2\)
B \(3x^6-4x\)
C \(6x^5+7\)
D \(x^6+x^2+1\)
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Correct Answer
C. \(6x^5+7\)
Explanation
Simple Explanation
\(6x^5+7\) की सबसे बड़ी घात (5) है। इसलिए इसकी डिग्री (6) नहीं है। / The highest power of \(6x^5+7\) is (5). Therefore its degree is not (6).
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यदि \(v\neq-3\), तो ((v+3)x-7 +x-3 +1) की डिग्री क्या है?
If \(v\neq-3\), what is the degree of ((v+3)x-7 +x-3 +1)?
#polynomial
#nonzero_parameter
#degree
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A (3)
B (4)
C (7)
D (10)
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Explanation
Simple Explanation
\(v\neq-3\) होने पर \(x^7\) का गुणांक शून्य नहीं है। इसलिए सबसे बड़ी घात (7) रहेगी। / When \(v\neq-3\), the coefficient of \(x^7\) is not zero. Therefore the highest power remains (7).
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बहुपद (\(x^4+3\)\(x^2-x+2\)) की डिग्री क्या है?
What is the degree of (\(x^4+3\)\(x^2-x+2\))?
#polynomial
#product
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
उच्चतम पद \(x^4\cdot x^2=x^6\) है। इसलिए गुणनफल की डिग्री (6) होगी। / The highest term is \(x^4\cdot x^2=x^6\). Therefore the product has degree (6).
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यदि (z=4), तो ((z-4)x-9 +(z-1)x-6 +3x-2 -5) की डिग्री क्या होगी?
If (z=4), what will be the degree of ((z-4)x-9 +(z-1)x-6 +3x-2 -5)?
#polynomial
#parameter_substitution
#degree
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A (9)
B (6)
C (2)
D (0)
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Explanation
Simple Explanation
(z=4) रखने पर \(x^9\) का गुणांक (0) और \(x^6\) का गुणांक (3) होता है। इसलिए सबसे बड़ी घात (6) है। / Putting (z=4) makes the coefficient of \(x^9\) equal to (0) and the coefficient of \(x^6\) equal to (3). So the highest power is (6).
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बहुपद (\(2x^3-1\)\(x^3+4\)) की डिग्री क्या है?
What is the degree of the polynomial (\(2x^3-1\)\(x^3+4\))?
#polynomial
#product
#degree
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A (3)
B (4)
C (6)
D (9)
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Explanation
Simple Explanation
उच्चतम पद \(2x^3\cdot x^3=2x^6\) से मिलेगा। इसलिए गुणनफल की डिग्री (6) है। / The highest term comes from \(2x^3\cdot x^3=2x^6\). Therefore the product has degree (6).
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यदि \(4x^n+3x^5-2\) की डिग्री (5) है और (n<5), तो (n) का कौन सा मान संभव है?
If the degree of \(4x^n+3x^5-2\) is (5) and (n<5), which value of (n) is possible?
#polynomial
#unknown_power
#degree
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A (n=7)
B (n=6)
C (n=5)
D (n=3)
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Explanation
Simple Explanation
\(x^5\) पद पहले से मौजूद है और (n<5) है। इसलिए (n=3) पर भी सबसे बड़ी घात (5) रहेगी। / The \(x^5\) term is already present and (n<5). So even when (n=3), the highest power remains (5).
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बहुपद \(7x^5-4x^3+2x-8\) की डिग्री क्या है?
What is the degree of the polynomial \(7x^5-4x^3+2x-8\)?
#polynomial
#degree
#highest_power
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A (2)
B (3)
C (5)
D (7)
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Explanation
Simple Explanation
सबसे बड़ी घात (5) है। डिग्री सबसे बड़ी अशून्य घात से तय होती है। / The highest power is (5). The degree is decided by the highest non-zero power.
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बहुपद \(0x^9+6x^4-5x+3\) की डिग्री क्या है?
What is the degree of \(0x^9+6x^4-5x+3\)?
#polynomial
#zero_coefficient
#degree
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A (9)
B (6)
C (4)
D (1)
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Explanation
Simple Explanation
\(0x^9\) शून्य पद है इसलिए उसे नहीं गिनते। सबसे बड़ी अशून्य घात (4) है। / \(0x^9\) is a zero term so it is not counted. The highest non-zero power is (4).
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सरल करने के बाद \(5x^6-5x^6+8x^2-1\) की डिग्री क्या होगी?
After simplifying \(5x^6-5x^6+8x^2-1\), what will be the degree?
#polynomial
#simplification
#degree
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A (6)
B (5)
C (2)
D (0)
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Explanation
Simple Explanation
\(5x^6-5x^6=0\) होने से \(8x^2-1\) बचता है। इसकी डिग्री (2) है। / Since \(5x^6-5x^6=0\), \(8x^2-1\) remains. Its degree is (2).
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यदि (p(x)=(b-4)x-8 +3x-3 +2) और (b=4), तो (p(x)) की डिग्री क्या है?
If (p(x)=(b-4)x-8 +3x-3 +2) and (b=4), what is the degree of (p(x))?
#polynomial
#parameter
#degree
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A (8)
B (4)
C (3)
D (0)
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Explanation
Simple Explanation
(b=4) रखने पर \(x^8\) का गुणांक (0) हो जाता है। बची हुई सबसे बड़ी घात (3) है। / Putting (b=4) makes the coefficient of \(x^8\) equal to (0). The remaining highest power is (3).
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किस मान पर ((a+7)x-6 -4x-2 +9) की डिग्री (2) होगी?
For which value will the degree of ((a+7)x-6 -4x-2 +9) be (2)?
#polynomial
#degree
#parameter_value
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A (a=7)
B (a=-7)
C (a=2)
D (a=0)
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Explanation
Simple Explanation
डिग्री (2) के लिए \(x^6\) का गुणांक (0) होना चाहिए। (a+7=0) से (a=-7) मिलता है। / For degree (2), the coefficient of \(x^6\) must be (0). From (a+7=0), we get (a=-7).
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बहुपद \(-6x^9+2x^5-3x+11\) की डिग्री किस पद से तय होती है?
The degree of \(-6x^9+2x^5-3x+11\) is decided by which term?
#polynomial
#leading_term
#degree
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A \(-6x^9\)
B \(2x^5\)
C (-3x)
D (11)
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Correct Answer
A. \(-6x^9\)
Explanation
Simple Explanation
सबसे बड़ी घात (9) वाले पद से डिग्री तय होती है। ऋणात्मक गुणांक डिग्री को नहीं बदलता। / The degree is decided by the term with highest power (9). A negative coefficient does not change the degree.
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बहुपद \(5x^3+x^{11}-7x^6+4\) की डिग्री क्या है?
What is the degree of \(5x^3+x^{11}-7x^6+4\)?
#polynomial
#unordered_terms
#degree
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A (3)
B (6)
C (11)
D (15)
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Explanation
Simple Explanation
पद घटते क्रम में नहीं हैं पर सबसे बड़ी घात (11) है। इसलिए डिग्री (11) है। / The terms are not in descending order but the highest power is (11). Therefore the degree is (11).
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यदि (q(x)=0x-7 +0x-4 +15x-6), तो (q(x)) की डिग्री क्या है?
If (q(x)=0x-7 +0x-4 +15x-6), what is the degree of (q(x))?
#polynomial
#zero_coefficient
#linear_degree
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A (7)
B (4)
C (1)
D (0)
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं। (15x-6) की सबसे बड़ी घात (1) है। / Terms with zero coefficients disappear. The highest power of (15x-6) is (1).
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बहुपद \(3x^0+4x^6-9x^2\) की डिग्री क्या है?
What is the degree of \(3x^0+4x^6-9x^2\)?
#polynomial
#zero_power
#degree
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
\(x^0=1\) होता है और सबसे बड़ी घात (6) है। इसलिए डिग्री (6) है। / \(x^0=1\), and the highest power is (6). Therefore the degree is (6).
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बहुपद (23) की डिग्री क्या है?
What is the degree of the polynomial (23)?
#polynomial
#constant
#degree_zero
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A (23)
B (1)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
(23) अशून्य नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / (23) is a non-zero constant polynomial. The degree of a non-zero constant polynomial is (0).
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शून्य बहुपद \(0x^8+0x^3+0\) की डिग्री क्या मानी जाती है?
What is considered the degree of the zero polynomial \(0x^8+0x^3+0\)?
#polynomial
#zero_polynomial
#degree
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A (8)
B (3)
C (0)
D परिभाषित नहीं / Not defined
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Correct Answer
D. परिभाषित नहीं / Not defined
Explanation
Simple Explanation
यह शून्य बहुपद है और इसकी डिग्री परिभाषित नहीं होती। परीक्षा में इसे अशून्य नियतांक से अलग पहचानें। / This is the zero polynomial and its degree is not defined. In exams, identify it separately from non-zero constants.
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किस बहुपद की डिग्री (5) है?
Which polynomial has degree (5)?
#polynomial
#degree
#option_based
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A \(4x^4+3x-1\)
B \(6x^5-2x+7\)
C \(8x^6+1\)
D (19)
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Correct Answer
B. \(6x^5-2x+7\)
Explanation
Simple Explanation
\(6x^5-2x+7\) में सबसे बड़ी घात (5) है। इसलिए इसकी डिग्री (5) है। / In \(6x^5-2x+7\), the highest power is (5). Therefore its degree is (5).
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सरल करने के बाद \(9x^7-4x^7+5x^3-2\) की डिग्री क्या है?
After simplifying \(9x^7-4x^7+5x^3-2\), what is the degree?
#polynomial
#like_terms
#degree
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A (3)
B (5)
C (7)
D (9)
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Explanation
Simple Explanation
सरल रूप \(5x^7+5x^3-2\) है। इसमें सबसे बड़ी घात (7) है। / The simplified form is \(5x^7+5x^3-2\). Its highest power is (7).
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यदि \(r\neq0\), तो \(rx^9+2x^4-3\) की डिग्री क्या होगी?
If \(r\neq0\), what will be the degree of \(rx^9+2x^4-3\)?
#polynomial
#nonzero_parameter
#degree
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A (0)
B (4)
C (9)
D (12)
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Explanation
Simple Explanation
\(r\neq0\) होने से \(x^9\) पद मौजूद रहेगा। इसलिए सबसे बड़ी घात (9) है। / Since \(r\neq0\), the \(x^9\) term remains present. Therefore the highest power is (9).
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यदि (r=0), तो \(rx^9+2x^4-3\) की डिग्री क्या होगी?
If (r=0), what will be the degree of \(rx^9+2x^4-3\)?
#polynomial
#parameter_zero
#degree
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A (9)
B (4)
C (2)
D (0)
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Simple Explanation
(r=0) होने पर \(x^9\) पद हट जाता है। बची हुई सबसे बड़ी घात (4) है। / When (r=0), the \(x^9\) term disappears. The remaining highest power is (4).
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बहुपद \(8y^6-5y^3+14\) की डिग्री क्या है?
What is the degree of the polynomial \(8y^6-5y^3+14\)?
#polynomial
#degree
#in_y
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A (3)
B (5)
C (6)
D (14)
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Simple Explanation
चर (y) की सबसे बड़ी घात (6) है। इसलिए बहुपद की डिग्री (6) है। / The highest power of the variable (y) is (6). Therefore the degree of the polynomial is (6).
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(x) के संदर्भ में \(9y^4-3y^2+10\) की डिग्री क्या है?
With respect to (x), what is the degree of \(9y^4-3y^2+10\)?
#polynomial
#degree_in_x
#constant
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A (4)
B (2)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
(x) के संदर्भ में इसमें (x) नहीं है इसलिए यह अशून्य नियतांक जैसा है। इसकी डिग्री (0) है। / With respect to (x), it has no (x), so it behaves like a non-zero constant. Its degree is (0).
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यदि (p(x)=\(m^2-16\)x-7 +6x-2 +1) की डिग्री (2) है, तो (m) का संभावित मान कौन सा है?
If the degree of (p(x)=\(m^2-16\)x-7 +6x-2 +1) is (2), which can be a possible value of (m)?
#polynomial
#parameter_value
#degree
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A (m=0)
B (m=3)
C (m=4)
D (m=5)
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Explanation
Simple Explanation
डिग्री (2) के लिए \(x^7\) का गुणांक (0) होना चाहिए। \(m^2-16=0\) से \(m=\pm4\) मिलता है। / For degree (2), the coefficient of \(x^7\) must be (0). From \(m^2-16=0\), \(m=\pm4\).
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बहुपद (4x-4 \(3x^2-1\)) को फैलाने पर डिग्री क्या होगी?
What will be the degree after expanding (4x-4 \(3x^2-1\))?
#polynomial
#expansion
#degree
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A (2)
B (4)
C (6)
D (8)
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Simple Explanation
फैलाने पर \(12x^6-4x^4\) मिलता है। सबसे बड़ी घात (6) है। / On expanding, we get \(12x^6-4x^4\). The highest power is (6).
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सरल करने के बाद (x-4 \(x^2+3\)-x-6 +5x-3 ) की डिग्री क्या है?
After simplifying (x-4 \(x^2+3\)-x-6 +5x-3 ), what is the degree?
#polynomial
#simplification
#cancellation
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A (6)
B (4)
C (3)
D (1)
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Explanation
Simple Explanation
(x-4 \(x^2+3\)=x-6 +3x-4 ) और \(x^6\) कट जाता है। बचा \(3x^4+5x^3\) है जिसकी डिग्री (4) है। / (x-4 \(x^2+3\)=x-6 +3x-4 ), and \(x^6\) cancels. The remaining \(3x^4+5x^3\) has degree (4).
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बहुपद (\(x^4+1\)\(x^2-5\)) की डिग्री क्या है?
What is the degree of the polynomial (\(x^4+1\)\(x^2-5\))?
#polynomial
#product
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
गुणन में सबसे बड़ी घात \(x^4\cdot x^2=x^6\) से आती है। इसलिए डिग्री (6) है। / In multiplication, the highest power comes from \(x^4\cdot x^2=x^6\). Therefore the degree is (6).
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बहुपद ((x-4)(x+6)) की डिग्री क्या है?
What is the degree of the polynomial ((x-4)(x+6))?
#polynomial
#product
#degree
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A (1)
B (2)
C (3)
D (0)
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Simple Explanation
गुणनफल \(x^2+2x-24\) है। इसमें सबसे बड़ी घात (2) है। / The product is \(x^2+2x-24\). Its highest power is (2).
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किस विकल्प में बहुपद की डिग्री (8) है?
Which option has a polynomial of degree (8)?
#polynomial
#degree
#option_based
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A \(x^7+8\)
B \(8x^4+x\)
C \(2x^8-6x^3+5\)
D (16x-8)
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Correct Answer
C. \(2x^8-6x^3+5\)
Explanation
Simple Explanation
तीसरे विकल्प में सबसे बड़ी घात (8) है। इसलिए उसकी डिग्री (8) है। / In the third option, the highest power is (8). Therefore its degree is (8).
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यदि बहुपद की डिग्री (2) है, तो वह किस प्रकार का बहुपद कहलाता है?
If a polynomial has degree (2), what type of polynomial is it called?
#polynomial
#quadratic
#degree
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A रेखीय बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C त्रिघात बहुपद / Cubic polynomial
D नियतांक बहुपद / Constant polynomial
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Correct Answer
B. द्विघात बहुपद / Quadratic polynomial
Explanation
Simple Explanation
डिग्री (2) वाला बहुपद द्विघात बहुपद कहलाता है। बहुपद का प्रकार डिग्री से पहचानें। / A polynomial of degree (2) is called a quadratic polynomial. Identify the type by degree.
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यदि (f(x)=3x-6 -8x-6 +4x-2 -7), तो (f(x)) की डिग्री क्या है?
If (f(x)=3x-6 -8x-6 +4x-2 -7), what is the degree of (f(x))?
#polynomial
#cancellation
#degree
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A (6)
B (4)
C (2)
D (0)
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Explanation
Simple Explanation
सरल करने पर \(-5x^6+4x^2-7\) मिलता है। सबसे बड़ी घात (6) है। / On simplifying, we get \(-5x^6+4x^2-7\). The highest power is (6).
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बहुपद \(6x^3y^2+5xy-4\) की कुल डिग्री क्या है?
What is the total degree of the polynomial \(6x^3y^2+5xy-4\)?
#polynomial
#total_degree
#two_variables
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A (2)
B (3)
C (5)
D (6)
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पद \(6x^3y^2\) की कुल घात (3+2=5) है। यही सबसे बड़ी कुल घात है। / The total power of the term \(6x^3y^2\) is (3+2=5). This is the highest total power.
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बहुपद \(2x^4y-7xy^3+9\) की कुल डिग्री क्या है?
What is the total degree of \(2x^4y-7xy^3+9\)?
#polynomial
#total_degree
#variables
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A (3)
B (4)
C (5)
D (7)
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Simple Explanation
पहले पद की कुल घात (4+1=5) है। यह सबसे बड़ी कुल घात है। / The total power of the first term is (4+1=5). This is the highest total power.
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(x) के संदर्भ में \(5x^4y^3+2xy^6-8\) की डिग्री क्या है?
With respect to (x), what is the degree of \(5x^4y^3+2xy^6-8\)?
#polynomial
#degree_in_x
#two_variables
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A (1)
B (3)
C (4)
D (6)
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Explanation
Simple Explanation
(x) के संदर्भ में (y) को गुणांक जैसा मानते हैं। (x) की सबसे बड़ी घात (4) है। / With respect to (x), (y) is treated like a coefficient. The highest power of (x) is (4).
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(y) के संदर्भ में \(5x^4y^3+2xy^6-8\) की डिग्री क्या है?
With respect to (y), what is the degree of \(5x^4y^3+2xy^6-8\)?
#polynomial
#degree_in_y
#two_variables
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A (1)
B (3)
C (4)
D (6)
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Explanation
Simple Explanation
(y) की सबसे बड़ी घात (6) है। इसलिए (y) के संदर्भ में डिग्री (6) है। / The highest power of (y) is (6). Therefore the degree with respect to (y) is (6).
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बहुपद \(0x^{11}+0x^5+31\) की डिग्री क्या है?
What is the degree of \(0x^{11}+0x^5+31\)?
#polynomial
#zero_coefficient
#constant_degree
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A (11)
B (5)
C (0)
D परिभाषित नहीं / Not defined
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं और (31) बचता है। (31) अशून्य नियतांक बहुपद है जिसकी डिग्री (0) है। / Terms with zero coefficients disappear and (31) remains. (31) is a non-zero constant polynomial of degree (0).
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यदि ((t-5)x-4 +(t+2)x-3 +6) की डिग्री (3) है, तो (t) का सही मान कौन सा हो सकता है?
If the degree of ((t-5)x-4 +(t+2)x-3 +6) is (3), which value of (t) can be correct?
#polynomial
#degree
#parameter_condition
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A (t=5)
B (t=-2)
C (t=0)
D (t=4)
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Explanation
Simple Explanation
डिग्री (3) के लिए \(x^4\) पद हटना चाहिए और \(x^3\) पद बचना चाहिए। (t=5) पर दोनों शर्तें पूरी होती हैं। / For degree (3), the \(x^4\) term must vanish and the \(x^3\) term must remain. At (t=5), both conditions hold.
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यदि (u=-3), तो ((u+3)x-7 +\(u^2-2\)x-5 +x-2 ) की डिग्री क्या है?
If (u=-3), what is the degree of ((u+3)x-7 +\(u^2-2\)x-5 +x-2 )?
#polynomial
#parameter_substitution
#degree
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A (7)
B (5)
C (2)
D (0)
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Explanation
Simple Explanation
(u=-3) पर \(x^7\) का गुणांक (0) और \(x^5\) का गुणांक (7) होता है। इसलिए डिग्री (5) है। / At (u=-3), the coefficient of \(x^7\) is (0) and the coefficient of \(x^5\) is (7). Therefore the degree is (5).
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बहुपद (\(4x^3+1\)\(x^2-3\)) की डिग्री क्या है?
What is the degree of the polynomial (\(4x^3+1\)\(x^2-3\))?
#polynomial
#product
#degree
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A (2)
B (3)
C (5)
D (6)
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Explanation
Simple Explanation
सबसे बड़ी घात \(4x^3\cdot x^2=4x^5\) से आती है। इसलिए डिग्री (5) है। / The highest power comes from \(4x^3\cdot x^2=4x^5\). Therefore the degree is (5).
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बहुपद (x(x-6)(x+2)) की डिग्री क्या है?
What is the degree of the polynomial (x(x-6)(x+2))?
#polynomial
#factors
#degree
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A (1)
B (2)
C (3)
D (6)
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Explanation
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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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यदि (g(x)=4x-8 -4x-8 +x-6 -x-3 ), तो (g(x)) की डिग्री क्या है?
If (g(x)=4x-8 -4x-8 +x-6 -x-3 ), what is the degree of (g(x))?
#polynomial
#cancellation
#degree
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A (8)
B (6)
C (3)
D (0)
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Explanation
Simple Explanation
\(4x^8-4x^8=0\) हो जाता है। बची हुई सबसे बड़ी घात (6) है। / \(4x^8-4x^8=0\). The remaining highest power is (6).
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बहुपद \(x^4+x^6+x^8+x^{10}\) की डिग्री क्या है?
What is the degree of \(x^4+x^6+x^8+x^{10}\)?
#polynomial
#ascending_powers
#degree
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A (4)
B (6)
C (8)
D (10)
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Explanation
Simple Explanation
सबसे बड़ी घात (10) है। इसलिए बहुपद की डिग्री (10) है। / The highest power is (10). Therefore the degree of the polynomial is (10).
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यदि (h(x)=\(x^4-3\)2 ), तो (h(x)) की डिग्री क्या है?
If (h(x)=\(x^4-3\)2 ), what is the degree of (h(x))?
#polynomial
#power_of_polynomial
#degree
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A (4)
B (6)
C (8)
D (16)
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Explanation
Simple Explanation
वर्ग करने पर उच्चतम पद \(x^8\) बनेगा। इसलिए डिग्री (8) है। / On squaring, the highest term becomes \(x^8\). Therefore the degree is (8).
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बहुपद \(2x^{12}-5x^9+3x^4-6\) की डिग्री क्या है?
What is the degree of \(2x^{12}-5x^9+3x^4-6\)?
#polynomial
#higher_power
#degree
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A (9)
B (12)
C (16)
D (2)
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Explanation
Simple Explanation
सबसे बड़ी घात (12) है। गुणांक (2) डिग्री नहीं होता। / The highest power is (12). The coefficient (2) is not the degree.
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यदि \(5x^n+4x^6-2\) की डिग्री (11) है और (n>6), तो (n) क्या होगा?
If the degree of \(5x^n+4x^6-2\) is (11) and (n>6), what is (n)?
#polynomial
#unknown_power
#degree
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A (6)
B (8)
C (11)
D (14)
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Explanation
Simple Explanation
डिग्री सबसे बड़ी घात होती है। (n>6) और डिग्री (11) होने से (n=11) होगा। / The degree is the highest power. Since (n>6) and the degree is (11), (n=11).
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यदि \(x^6+ax^2+5\) की डिग्री (6) है, तो (a) के लिए सही कथन क्या है?
If the degree of \(x^6+ax^2+5\) is (6), what is the correct statement about (a)?
#polynomial
#parameter
#degree
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A (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
B (a=0) ही होना चाहिए / (a) must be (0) only
C (a=6) ही होना चाहिए / (a) must be (6) only
D \(a\neq0\) होना चाहिए / \(a\neq0\) is required
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Correct Answer
A. (a) कोई भी वास्तविक संख्या हो सकता है / (a) can be any real number
Explanation
Simple Explanation
\(x^6\) का गुणांक (1) है जो शून्य नहीं है। इसलिए (a) का मान डिग्री (6) को नहीं बदलता। / The coefficient of \(x^6\) is (1), which is non-zero. So the value of (a) does not change degree (6).
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बहुपद \(0x^{12}+0x^7+0x+37\) की डिग्री क्या है?
What is the degree of \(0x^{12}+0x^7+0x+37\)?
#polynomial
#constant_degree
#zero_coefficient
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A (12)
B (7)
C (1)
D (0)
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Explanation
Simple Explanation
शून्य गुणांक वाले पद हट जाते हैं और (37) बचता है। यह डिग्री (0) का अशून्य नियतांक बहुपद है। / Terms with zero coefficients disappear and (37) remains. It is a non-zero constant polynomial of degree (0).
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किस विकल्प में डिग्री (4) वाला बहुपद है लेकिन \(x^3\) का गुणांक (0) है?
Which option has a polynomial of degree (4) but coefficient of \(x^3\) is (0)?
#polynomial
#degree
#missing_term
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A \(3x^4-2x+1\)
B \(3x^4+x^3+1\)
C \(3x^3-2x+1\)
D \(x^5+3x^4-1\)
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Correct Answer
A. \(3x^4-2x+1\)
Explanation
Simple Explanation
\(3x^4-2x+1\) की डिग्री (4) है और \(x^3\) पद अनुपस्थित है। इसलिए \(x^3\) का गुणांक (0) है। / \(3x^4-2x+1\) has degree (4), and the \(x^3\) term is absent. So the coefficient of \(x^3\) is (0).
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बहुपद (x-5 \(2x^2-3\)+4x-4 ) की डिग्री क्या है?
What is the degree of (x-5 \(2x^2-3\)+4x-4 )?
#polynomial
#expansion
#degree
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A (4)
B (5)
C (7)
D (10)
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Explanation
Simple Explanation
फैलाने पर \(2x^7-3x^5+4x^4\) मिलता है। सबसे बड़ी घात (7) है। / On expanding, we get \(2x^7-3x^5+4x^4\). The highest power is (7).
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यदि (s=2), तो ((s-2 )x-6 +(s+5)x-3 +9) की डिग्री क्या होगी?
If (s=2), what will be the degree of ((s-2 )x-6 +(s+5)x-3 +9)?
#polynomial
#parameter_substitution
#degree
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A (6)
B (5)
C (3)
D (0)
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Explanation
Simple Explanation
(s=2) पर \(x^6\) का गुणांक (0) और \(x^3\) का गुणांक (7) है। इसलिए डिग्री (3) है। / At (s=2), the coefficient of \(x^6\) is (0) and the coefficient of \(x^3\) is (7). Therefore the degree is (3).
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बहुपद \(3x^4y+5xy^6+2\) की कुल डिग्री क्या है?
What is the total degree of \(3x^4y+5xy^6+2\)?
#polynomial
#total_degree
#two_variables
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A (5)
B (6)
C (7)
D (8)
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Explanation
Simple Explanation
\(5xy^6\) की कुल घात (1+6=7) है। यह सबसे बड़ी कुल घात है। / The total power of \(5xy^6\) is (1+6=7). This is the highest total power.
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किस विकल्प में डिग्री (7) नहीं है?
Which option does not have degree (7)?
#polynomial
#degree
#identification
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A \(x^7+2\)
B \(4x^7-3x\)
C \(7x^6+5\)
D \(x^7+x^2+1\)
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Correct Answer
C. \(7x^6+5\)
Explanation
Simple Explanation
\(7x^6+5\) की सबसे बड़ी घात (6) है। इसलिए इसकी डिग्री (7) नहीं है। / The highest power of \(7x^6+5\) is (6). Therefore its degree is not (7).
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यदि \(v\neq5\), तो ((v-5)x-8 +x-4 +1) की डिग्री क्या है?
If \(v\neq5\), what is the degree of ((v-5)x-8 +x-4 +1)?
#polynomial
#nonzero_parameter
#degree
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A (4)
B (5)
C (8)
D (12)
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Explanation
Simple Explanation
\(v\neq5\) होने पर \(x^8\) का गुणांक शून्य नहीं है। इसलिए सबसे बड़ी घात (8) रहेगी। / When \(v\neq5\), the coefficient of \(x^8\) is not zero. Therefore the highest power remains (8).
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बहुपद (\(x^5+2\)\(x^2-x+3\)) की डिग्री क्या है?
What is the degree of (\(x^5+2\)\(x^2-x+3\))?
#polynomial
#product
#degree
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A (2)
B (5)
C (7)
D (10)
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Explanation
Simple Explanation
उच्चतम पद \(x^5\cdot x^2=x^7\) है। इसलिए गुणनफल की डिग्री (7) होगी। / The highest term is \(x^5\cdot x^2=x^7\). Therefore the product has degree (7).
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यदि (c=0), तो (cx^{10}+(c+4)x-6 -3x+2) की डिग्री क्या होगी?
If (c=0), what will be the degree of (cx^{10}+(c+4)x-6 -3x+2)?
#polynomial
#parameter_zero
#degree
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A (10)
B (6)
C (1)
D (0)
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Explanation
Simple Explanation
(c=0) पर \(x^{10}\) पद हट जाता है और \(x^6\) का गुणांक (4) रहता है। इसलिए डिग्री (6) है। / When (c=0), the \(x^{10}\) term disappears and the coefficient of \(x^6\) remains (4). Therefore the degree is (6).
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बहुपद (\(2x^2-3\)\(x^4+x+1\)) की डिग्री क्या है?
What is the degree of the polynomial (\(2x^2-3\)\(x^4+x+1\))?
#polynomial
#product
#degree
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
उच्चतम पद \(2x^2\cdot x^4=2x^6\) से मिलेगा। इसलिए गुणनफल की डिग्री (6) है। / The highest term comes from \(2x^2\cdot x^4=2x^6\). Therefore the degree of the product is (6).
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