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Which of the following is a polynomial in (x)?
B. \(3x^2-5x+1\)
बहुपद में चर की घात पूर्ण अशून्य या शून्य संख्या होनी चाहिए। \(3x^2-5x+1\) में घातें (2), (1), और (0) हैं। / In a polynomial, powers of the variable must be whole numbers including zero. In \(3x^2-5x+1\), the powers are (2), (1), and (0).
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Which of the following is not a polynomial in (x)?
C. \(\frac{5}{x}+1\)
\(\frac{5}{x}\) में चर हर में है, अर्थात घात (-1) है। ऋणात्मक घात वाला व्यंजक बहुपद नहीं होता। / In \(\frac{5}{x}\), the variable is in the denominator, meaning the power is (-1). An expression with a negative power is not a polynomial.
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What type of powers should the variable have in a polynomial?
C. पूर्ण अशून्य या शून्य पूर्णांकNon-negative integers including zero
बहुपद में चर की घात (0,1,2,3) जैसी हो सकती है। भिन्न या ऋणात्मक घात बहुपद की परिभाषा में नहीं आती। / In a polynomial, powers can be like (0,1,2,3). Fractional or negative powers do not fit the definition of a polynomial.
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What is the highest power in the expression \(4x^3-2x+8\)?
C. (3)
सबसे बड़ी घात (3) है। बहुपद की डिग्री सबसे बड़ी घात से पहचानी जाती है। / The highest power is (3). The degree of a polynomial is identified by the highest power.
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What type of polynomial is (6x+11)?
A. रेखीय बहुपदLinear polynomial
इस बहुपद की सबसे बड़ी घात (1) है। घात (1) वाला बहुपद रेखीय बहुपद कहलाता है। / The highest power of this polynomial is (1). A polynomial of degree (1) is called a linear polynomial.
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What type of polynomial is \(5x^2+2x-3\)?
B. द्विघात बहुपदQuadratic polynomial
इसमें सबसे बड़ी घात (2) है। घात (2) वाला बहुपद द्विघात बहुपद होता है। / Its highest power is (2). A polynomial of degree (2) is a quadratic polynomial.
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What type of polynomial is \(2x^3+x^2-7\)?
C. त्रिघात बहुपदCubic polynomial
इस बहुपद की सबसे बड़ी घात (3) है। घात (3) वाला बहुपद त्रिघात बहुपद कहलाता है। / The highest power of this polynomial is (3). A polynomial of degree (3) is called a cubic polynomial.
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How will the expression (12) be considered?
D. नियतांक बहुपदConstant polynomial
(12) में कोई चर नहीं है, इसलिए यह नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है। / (12) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
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A. हां, यह शून्य बहुपद हैYes, it is the zero polynomial
(0) को शून्य बहुपद माना जाता है। इसकी डिग्री परिभाषित नहीं होती। / (0) is considered the zero polynomial. Its degree is not defined.
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Which of the following is a constant polynomial?
C. (-8)
नियतांक बहुपद में चर नहीं होता। (-8) केवल एक संख्या है, इसलिए यह नियतांक बहुपद है। / A constant polynomial has no variable. (-8) is only a number, so it is a constant polynomial.
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