बहुपद \(6x^5-2x^3+x-8\) की डिग्री क्या है?
What is the degree of the polynomial \(6x^5-2x^3+x-8\)?
#polynomial
#degree
#highest_power
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5). Therefore the degree of the polynomial is (5).
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5). Therefore the degree of the polynomial is (5).
Step 3
Exam Tip
सबसे बड़ी घात (5) है। इसलिए बहुपद की डिग्री (5) है।
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व्यंजक (8x-11) किस प्रकार का बहुपद है?
What type of polynomial is (8x-11)?
#polynomial
#linear
#degree
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A रेखीय बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C त्रिघात बहुपद / Cubic polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
A. रेखीय बहुपद / Linear polynomial
Step 1
Concept
Its highest power is (1). A polynomial of degree (1) is called a linear polynomial.
Step 2
Why this answer is correct
The correct answer is A. रेखीय बहुपद / Linear polynomial. Its highest power is (1). A polynomial of degree (1) is called a linear polynomial.
Step 3
Exam Tip
इसकी सबसे बड़ी घात (1) है। डिग्री (1) वाला बहुपद रेखीय बहुपद कहलाता है।
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व्यंजक \(7x^2+4x-9\) किस प्रकार का बहुपद है?
What type of polynomial is \(7x^2+4x-9\)?
#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
Explanation opens after your attempt
Correct Answer
B. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
The highest power is (2). A polynomial of degree (2) is a quadratic polynomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात बहुपद / Quadratic polynomial. The highest power is (2). A polynomial of degree (2) is a quadratic polynomial.
Step 3
Exam Tip
सबसे बड़ी घात (2) है। डिग्री (2) वाला बहुपद द्विघात बहुपद होता है।
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व्यंजक \(3x^3-5x+2\) किस प्रकार का बहुपद है?
What type of polynomial is \(3x^3-5x+2\)?
#polynomial
#cubic
#degree
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A द्विघात बहुपद / Quadratic polynomial
B रेखीय बहुपद / Linear polynomial
C त्रिघात बहुपद / Cubic polynomial
D नियतांक बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. त्रिघात बहुपद / Cubic polynomial
Step 1
Concept
Its highest power is (3). Therefore it is a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is C. त्रिघात बहुपद / Cubic polynomial. Its highest power is (3). Therefore it is a cubic polynomial.
Step 3
Exam Tip
इसमें सबसे बड़ी घात (3) है। इसलिए यह त्रिघात बहुपद है।
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व्यंजक (21) को किस रूप में माना जाएगा?
How will the expression (21) be considered?
#polynomial
#constant_polynomial
#identification
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A रेखीय बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C शून्य बहुपद / Zero polynomial
D नियतांक बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
D. नियतांक बहुपद / Constant polynomial
Step 1
Concept
(21) has no variable. Therefore it is a constant polynomial.
Step 2
Why this answer is correct
The correct answer is D. नियतांक बहुपद / Constant polynomial. (21) has no variable. Therefore it is a constant polynomial.
Step 3
Exam Tip
(21) में कोई चर नहीं है। इसलिए यह नियतांक बहुपद है।
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व्यंजक \(x^{\frac{7}{3}}+2\) बहुपद क्यों नहीं है?
Why is \(x^{\frac{7}{3}}+2\) not a polynomial?
#polynomial
#fractional_power
#non_polynomial
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A क्योंकि इसमें (2) है / Because it has (2)
B क्योंकि चर की घात भिन्न है / Because the variable has a fractional power
C क्योंकि इसमें जोड़ है / Because it has addition
D क्योंकि इसमें दो पद हैं / Because it has two terms
Explanation opens after your attempt
Correct Answer
B. क्योंकि चर की घात भिन्न है / Because the variable has a fractional power
Step 1
Concept
The power \(\frac{7}{3}\) is fractional. In a polynomial, the variable power must be a whole number.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि चर की घात भिन्न है / Because the variable has a fractional power. The power \(\frac{7}{3}\) is fractional. In a polynomial, the variable power must be a whole number.
Step 3
Exam Tip
घात \(\frac{7}{3}\) भिन्न है। बहुपद में चर की घात पूर्ण संख्या होनी चाहिए।
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व्यंजक \(x^{-5}+9x\) बहुपद क्यों नहीं है?
Why is \(x^{-5}+9x\) not a polynomial?
#polynomial
#negative_power
#non_polynomial
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A क्योंकि \(x^{-5}\) की घात ऋणात्मक है / Because \(x^{-5}\) has a negative power
B क्योंकि इसमें (9x) है / Because it has (9x)
C क्योंकि इसमें दो पद हैं / Because it has two terms
D क्योंकि इसमें जोड़ है / Because it has addition
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(x^{-5}\) की घात ऋणात्मक है / Because \(x^{-5}\) has a negative power
Step 1
Concept
A variable in a polynomial cannot have a negative power. Here (-5) is a negative power.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(x^{-5}\) की घात ऋणात्मक है / Because \(x^{-5}\) has a negative power. A variable in a polynomial cannot have a negative power. Here (-5) is a negative power.
Step 3
Exam Tip
बहुपद में चर की घात ऋणात्मक नहीं हो सकती। यहां (-5) ऋणात्मक घात है।
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बहुपद \(2x^7-3x^4+x^2-6\) की डिग्री क्या है?
What is the degree of \(2x^7-3x^4+x^2-6\)?
#polynomial
#degree
#highest_power
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A (2)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The highest power is (7). Therefore the degree of the polynomial is (7).
Step 2
Why this answer is correct
The correct answer is D. (7). The highest power is (7). Therefore the degree of the polynomial is (7).
Step 3
Exam Tip
सबसे बड़ी घात (7) है। इसलिए बहुपद की डिग्री (7) है।
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बहुपद \(5x^4-3x^2+x-12\) में कितने पद हैं?
How many terms are there in \(5x^4-3x^2+x-12\)?
#polynomial
#terms
#counting
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The terms are \(5x^4\), \(-3x^2\), (x), and (-12). So there are (4) terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The terms are \(5x^4\), \(-3x^2\), (x), and (-12). So there are (4) terms.
Step 3
Exam Tip
पद \(5x^4\), \(-3x^2\), (x), और (-12) हैं। इसलिए कुल (4) पद हैं।
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बहुपद \(9x^5+x^3-2\) में सबसे बड़ी घात किस पद में है?
In \(9x^5+x^3-2\), which term has the highest power?
#polynomial
#highest_power
#leading_term
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A \(9x^5\)
B \(x^3\)
C (-2)
D (9)
Explanation opens after your attempt
Correct Answer
A. \(9x^5\)
Step 1
Concept
The highest power is (5). It is in the term \(9x^5\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^5\). The highest power is (5). It is in the term \(9x^5\).
Step 3
Exam Tip
सबसे बड़ी घात (5) है। यह \(9x^5\) पद में है।
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व्यंजक \(3x^2-\sqrt{7}x+5\) क्या है?
What is the expression \(3x^2-\sqrt{7}x+5\)?
#polynomial
#real_coefficient
#definition
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A बहुपद / Polynomial
B बहुपद नहीं / Not a polynomial
C शून्य बहुपद / Zero polynomial
D चर रहित व्यंजक / Expression without variable
Explanation opens after your attempt
Correct Answer
A. बहुपद / Polynomial
Step 1
Concept
\(\sqrt{7}\) is a real coefficient and the power of (x) is (1). Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. बहुपद / Polynomial. \(\sqrt{7}\) is a real coefficient and the power of (x) is (1). Therefore it is a polynomial.
Step 3
Exam Tip
\(\sqrt{7}\) वास्तविक गुणांक है और (x) की घात (1) है। इसलिए यह बहुपद है।
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व्यंजक \(2x+\sqrt{x}\) क्या है?
What is the expression \(2x+\sqrt{x}\)?
#polynomial
#square_root
#non_polynomial
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A रेखीय बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C बहुपद नहीं / Not a polynomial
D नियतांक बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. बहुपद नहीं / Not a polynomial
Step 1
Concept
\(\sqrt{x}=x^{\frac{1}{2}}\). Due to the fractional power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. बहुपद नहीं / Not a polynomial. \(\sqrt{x}=x^{\frac{1}{2}}\). Due to the fractional power, it is not a polynomial.
Step 3
Exam Tip
\(\sqrt{x}=x^{\frac{1}{2}}\) होता है। भिन्न घात होने के कारण यह बहुपद नहीं है।
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बहुपद \(14x^2\) में नियतांक पद क्या है?
What is the constant term in the polynomial \(14x^2\)?
#polynomial
#constant_term
#zero
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A (14)
B (2)
C (0)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
This polynomial has no term without a variable. So the constant term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). This polynomial has no term without a variable. So the constant term is taken as (0).
Step 3
Exam Tip
इस बहुपद में बिना चर वाला पद नहीं है। इसलिए नियतांक पद (0) माना जाता है।
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बहुपद \(x^6+x^2+1\) में \(x^4\) का गुणांक क्या है?
What is the coefficient of \(x^4\) in \(x^6+x^2+1\)?
#polynomial
#missing_term
#coefficient
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A (1)
B (2)
C (4)
D (0)
Explanation opens after your attempt
Step 1
Concept
The \(x^4\) term is not present in this polynomial. So the coefficient of \(x^4\) is (0).
Step 2
Why this answer is correct
The correct answer is D. (0). The \(x^4\) term is not present in this polynomial. So the coefficient of \(x^4\) is (0).
Step 3
Exam Tip
इस बहुपद में \(x^4\) पद नहीं है। इसलिए \(x^4\) का गुणांक (0) है।
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क्या \(3x^0+5x\) बहुपद है?
Is \(3x^0+5x\) a polynomial?
#polynomial
#zero_power
#definition
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A हां, क्योंकि \(x^0=1\) और (x) की घात (1) है / Yes, because \(x^0=1\) and the power of (x) is (1)
B नहीं, क्योंकि \(x^0\) मान्य नहीं है / No, because \(x^0\) is not valid
C नहीं, क्योंकि इसमें दो पद हैं / No, because it has two terms
D नहीं, क्योंकि इसमें (5x) है / No, because it has (5x)
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि \(x^0=1\) और (x) की घात (1) है / Yes, because \(x^0=1\) and the power of (x) is (1)
Step 1
Concept
The power in \(x^0\) is (0), which is valid in a polynomial. Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि \(x^0=1\) और (x) की घात (1) है / Yes, because \(x^0=1\) and the power of (x) is (1). The power in \(x^0\) is (0), which is valid in a polynomial. Therefore it is a polynomial.
Step 3
Exam Tip
\(x^0\) की घात (0) है, जो बहुपद में मान्य है। इसलिए यह बहुपद है।
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क्या \(\frac{5x}{7}-3\) (x) में बहुपद है?
Is \(\frac{5x}{7}-3\) a polynomial in (x)?
#polynomial
#fraction_coefficient
#definition
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A नहीं, क्योंकि इसमें भिन्न गुणांक है / No, because it has a fractional coefficient
B हां, क्योंकि (x) की घात (1) है / Yes, because the power of (x) is (1)
C नहीं, क्योंकि इसमें (-3) है / No, because it has (-3)
D नहीं, क्योंकि यह द्विपदी है / No, because it is a binomial
Explanation opens after your attempt
Correct Answer
B. हां, क्योंकि (x) की घात (1) है / Yes, because the power of (x) is (1)
Step 1
Concept
In \(\frac{5x}{7}\), the coefficient is \(\frac{5}{7}\) and the power of (x) is (1). A fractional coefficient is valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. हां, क्योंकि (x) की घात (1) है / Yes, because the power of (x) is (1). In \(\frac{5x}{7}\), the coefficient is \(\frac{5}{7}\) and the power of (x) is (1). A fractional coefficient is valid in a polynomial.
Step 3
Exam Tip
\(\frac{5x}{7}\) में गुणांक \(\frac{5}{7}\) है और (x) की घात (1) है। भिन्न गुणांक बहुपद में मान्य है।
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क्या \(-\frac{4}{9}x^4+2x-1\) बहुपद है?
Is \(-\frac{4}{9}x^4+2x-1\) a polynomial?
#polynomial
#real_coefficient
#fraction
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A हां, क्योंकि गुणांक वास्तविक हो सकते हैं और घातें मान्य हैं / Yes, because coefficients can be real and powers are valid
B नहीं, क्योंकि गुणांक ऋणात्मक भिन्न है / No, because the coefficient is a negative fraction
C नहीं, क्योंकि इसमें \(x^4\) है / No, because it has \(x^4\)
D नहीं, क्योंकि इसमें तीन पद हैं / No, because it has three terms
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि गुणांक वास्तविक हो सकते हैं और घातें मान्य हैं / Yes, because coefficients can be real and powers are valid
Step 1
Concept
Coefficients can be negative or fractional. Here the variable powers are (4), (1), and (0), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि गुणांक वास्तविक हो सकते हैं और घातें मान्य हैं / Yes, because coefficients can be real and powers are valid. Coefficients can be negative or fractional. Here the variable powers are (4), (1), and (0), so it is a polynomial.
Step 3
Exam Tip
गुणांक ऋणात्मक या भिन्न हो सकते हैं। यहां चर की घातें (4), (1), और (0) हैं, इसलिए यह बहुपद है।
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किस व्यंजक में चर की घात \(\frac{5}{6}\) होने से वह बहुपद नहीं है?
Which expression is not a polynomial because the variable has power \(\frac{5}{6}\)?
#polynomial
#fractional_power
#non_polynomial
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A \(x^5+6\)
B \(x^{\frac{5}{6}}+4\)
C \(6x^2+1\)
D (5x+6)
Explanation opens after your attempt
Correct Answer
B. \(x^{\frac{5}{6}}+4\)
Step 1
Concept
\(\frac{5}{6}\) is a fractional power. In a polynomial, the variable power must be a whole number.
Step 2
Why this answer is correct
The correct answer is B. \(x^{\frac{5}{6}}+4\). \(\frac{5}{6}\) is a fractional power. In a polynomial, the variable power must be a whole number.
Step 3
Exam Tip
\(\frac{5}{6}\) भिन्न घात है। बहुपद में चर की घात पूर्ण संख्या होनी चाहिए।
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बहुपद \(8x^2-9x+16\) की डिग्री क्या है?
What is the degree of \(8x^2-9x+16\)?
#polynomial
#degree
#quadratic
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A (0)
B (1)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2). Therefore the degree of this polynomial is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). The highest power is (2). Therefore the degree of this polynomial is (2).
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए इस बहुपद की डिग्री (2) है।
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बहुपद (17x-5) की डिग्री क्या है?
What is the degree of (17x-5)?
#polynomial
#degree
#linear
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A (0)
B (1)
C (5)
D (17)
Explanation opens after your attempt
Step 1
Concept
The highest power is (1). Therefore the degree of (17x-5) is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The highest power is (1). Therefore the degree of (17x-5) is (1).
Step 3
Exam Tip
सबसे बड़ी घात (1) है। इसलिए (17x-5) की डिग्री (1) है।
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अशून्य नियतांक बहुपद (-31) की डिग्री क्या है?
What is the degree of the non-zero constant polynomial (-31)?
#polynomial
#constant_degree
#degree_zero
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A (0)
B (1)
C (31)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). (-31) can be considered as \(-31x^0\).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). (-31) can be considered as \(-31x^0\).
Step 3
Exam Tip
अशून्य नियतांक बहुपद की डिग्री (0) होती है। (-31) को \(-31x^0\) माना जा सकता है।
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शून्य बहुपद और अशून्य नियतांक बहुपद में सही अंतर क्या है?
What is the correct difference between the zero polynomial and a non-zero constant polynomial?
#polynomial
#zero_polynomial
#constant_degree
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A दोनों की डिग्री (0) होती है / Both have degree (0)
B शून्य बहुपद की डिग्री (1) होती है / The zero polynomial has degree (1)
C शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती है / The zero polynomial degree is not defined and a non-zero constant has degree (0)
D दोनों बहुपद नहीं होते / Both are not polynomials
Explanation opens after your attempt
Correct Answer
C. शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती है / The zero polynomial degree is not defined and a non-zero constant has degree (0)
Step 1
Concept
The degree of the zero polynomial is not defined. The degree of a non-zero constant polynomial is (0).
Step 2
Why this answer is correct
The correct answer is C. शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती है / The zero polynomial degree is not defined and a non-zero constant has degree (0). The degree of the zero polynomial is not defined. The degree of a non-zero constant polynomial is (0).
Step 3
Exam Tip
शून्य बहुपद की डिग्री परिभाषित नहीं होती। अशून्य नियतांक बहुपद की डिग्री (0) होती है।
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बहुपद \(-5x^6+3x^4-x+9\) में अग्रणी पद कौन सा है?
What is the leading term of \(-5x^6+3x^4-x+9\)?
#polynomial
#leading_term
#degree
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A \(-5x^6\)
B \(3x^4\)
C (-x)
D (9)
Explanation opens after your attempt
Correct Answer
A. \(-5x^6\)
Step 1
Concept
The term with the highest power is the leading term. Here the highest power is (6).
Step 2
Why this answer is correct
The correct answer is A. \(-5x^6\). The term with the highest power is the leading term. Here the highest power is (6).
Step 3
Exam Tip
सबसे बड़ी घात वाला पद अग्रणी पद होता है। यहां सबसे बड़ी घात (6) है।
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बहुपद \(-11x^4+6x^2-3\) का अग्रणी गुणांक क्या है?
What is the leading coefficient of \(-11x^4+6x^2-3\)?
#polynomial
#leading_coefficient
#degree
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A (-11)
B (4)
C (6)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(-11x^4\). Therefore the leading coefficient is (-11).
Step 2
Why this answer is correct
The correct answer is A. (-11). The leading term is \(-11x^4\). Therefore the leading coefficient is (-11).
Step 3
Exam Tip
अग्रणी पद \(-11x^4\) है। इसलिए अग्रणी गुणांक (-11) है।
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व्यंजक \(6x^3+\frac{4}{x}\) बहुपद है या नहीं?
Is \(6x^3+\frac{4}{x}\) a polynomial or not?
#polynomial
#denominator
#non_polynomial
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A हां, क्योंकि इसमें \(x^3\) है / Yes, because it has \(x^3\)
B नहीं, क्योंकि \(\frac{4}{x}\) में चर हर में है / No, because in \(\frac{4}{x}\) the variable is in the denominator
C हां, क्योंकि इसमें दो पद हैं / Yes, because it has two terms
D हां, क्योंकि गुणांक वास्तविक हैं / Yes, because coefficients are real
Explanation opens after your attempt
Correct Answer
B. नहीं, क्योंकि \(\frac{4}{x}\) में चर हर में है / No, because in \(\frac{4}{x}\) the variable is in the denominator
Step 1
Concept
In \(\frac{4}{x}\), the power of (x) is (-1). Therefore this expression is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. नहीं, क्योंकि \(\frac{4}{x}\) में चर हर में है / No, because in \(\frac{4}{x}\) the variable is in the denominator. In \(\frac{4}{x}\), the power of (x) is (-1). Therefore this expression is not a polynomial.
Step 3
Exam Tip
\(\frac{4}{x}\) में (x) की घात (-1) है। इसलिए यह व्यंजक बहुपद नहीं है।
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कौन सा एकपदी है लेकिन (x) में बहुपद नहीं है?
Which is a monomial but not a polynomial in (x)?
#polynomial
#monomial
#non_polynomial
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A \(\frac{7}{x^2}\)
B \(7x^2\)
C (x)
D (7)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{x^2}\)
Step 1
Concept
\(\frac{7}{x^2}=7x^{-2}\), so the power is negative. Having one term is not enough to be a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{x^2}\). \(\frac{7}{x^2}=7x^{-2}\), so the power is negative. Having one term is not enough to be a polynomial.
Step 3
Exam Tip
\(\frac{7}{x^2}=7x^{-2}\) है, इसलिए घात ऋणात्मक है। एक पद होना बहुपद होने के लिए पर्याप्त नहीं है।
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बहुपद \(4x^3+0x^2+5\) का सरल रूप क्या है?
What is the simplified form of \(4x^3+0x^2+5\)?
#polynomial
#zero_coefficient
#simplification
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A \(4x^3+5\)
B \(4x^3+x^2+5\)
C (0)
D \(9x^3\)
Explanation opens after your attempt
Correct Answer
A. \(4x^3+5\)
Step 1
Concept
\(0x^2=0\), so that term disappears. The simplified form is \(4x^3+5\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^3+5\). \(0x^2=0\), so that term disappears. The simplified form is \(4x^3+5\).
Step 3
Exam Tip
\(0x^2=0\), इसलिए वह पद हट जाता है। सरल रूप \(4x^3+5\) है।
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किस बहुपद में \(x^5\) का गुणांक (0) है?
In which polynomial is the coefficient of \(x^5\) equal to (0)?
#polynomial
#missing_term
#coefficient_zero
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A \(x^5+1\)
B \(3x^2+2x-4\)
C \(2x^5-x\)
D \(9x^5+7\)
Explanation opens after your attempt
Correct Answer
B. \(3x^2+2x-4\)
Step 1
Concept
In \(3x^2+2x-4\), the \(x^5\) term is absent. So the coefficient of \(x^5\) is taken as (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2+2x-4\). In \(3x^2+2x-4\), the \(x^5\) term is absent. So the coefficient of \(x^5\) is taken as (0).
Step 3
Exam Tip
\(3x^2+2x-4\) में \(x^5\) पद नहीं है। इसलिए \(x^5\) का गुणांक (0) माना जाता है।
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व्यंजक \(7x^2+x^{-4}+3\) बहुपद क्यों नहीं है?
Why is \(7x^2+x^{-4}+3\) not a polynomial?
#polynomial
#negative_power
#non_polynomial
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A क्योंकि इसमें \(7x^2\) है / Because it has \(7x^2\)
B क्योंकि इसमें (3) है / Because it has (3)
C क्योंकि इसमें \(x^{-4}\) है / Because it has \(x^{-4}\)
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि इसमें \(x^{-4}\) है / Because it has \(x^{-4}\)
Step 1
Concept
In \(x^{-4}\), the power of the variable is negative. Negative powers are not accepted in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि इसमें \(x^{-4}\) है / Because it has \(x^{-4}\). In \(x^{-4}\), the power of the variable is negative. Negative powers are not accepted in a polynomial.
Step 3
Exam Tip
\(x^{-4}\) में चर की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार नहीं होती।
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क्या \(6x^4-3x^2+x-10\) एक बहुपद है?
Is \(6x^4-3x^2+x-10\) a polynomial?
#polynomial
#definition
#yes_no
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A हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैं / Yes, because all powers are non-negative integers
B नहीं, क्योंकि इसमें चार पद हैं / No, because it has four terms
C नहीं, क्योंकि इसमें नियतांक है / No, because it has a constant
D नहीं, क्योंकि इसमें \(x^4\) है / No, because it has \(x^4\)
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैं / Yes, because all powers are non-negative integers
Step 1
Concept
The powers are (4), (2), (1), and (0). All are valid according to the definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैं / Yes, because all powers are non-negative integers. The powers are (4), (2), (1), and (0). All are valid according to the definition of a polynomial.
Step 3
Exam Tip
घातें (4), (2), (1), और (0) हैं। ये सभी बहुपद की परिभाषा के अनुसार मान्य हैं।
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बहुपद \(5x^2-8x+12\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(5x^2-8x+12\)?
#polynomial
#coefficient
#linear_term
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A (5)
B (-8)
C (12)
D (1)
Explanation opens after your attempt
Step 1
Concept
The term containing (x) is (-8x). Therefore the coefficient of (x) is (-8).
Step 2
Why this answer is correct
The correct answer is B. (-8). The term containing (x) is (-8x). Therefore the coefficient of (x) is (-8).
Step 3
Exam Tip
(x) वाला पद (-8x) है। इसलिए (x) का गुणांक (-8) है।
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बहुपद \(3x^8-4x^5+2x^2-1\) की डिग्री क्या है?
What is the degree of \(3x^8-4x^5+2x^2-1\)?
#polynomial
#degree
#highest_power
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (8). Therefore the degree of the polynomial is (8).
Step 2
Why this answer is correct
The correct answer is D. (8). The highest power is (8). Therefore the degree of the polynomial is (8).
Step 3
Exam Tip
सबसे बड़ी घात (8) है। इसलिए बहुपद की डिग्री (8) है।
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व्यंजक \(0.5x^2+3x-1\) (x) में बहुपद है या नहीं?
Is \(0.5x^2+3x-1\) a polynomial in (x)?
#polynomial
#decimal_coefficient
#definition
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A हां, क्योंकि दशमलव गुणांक भी वास्तविक संख्या है / Yes, because a decimal coefficient is also a real number
B नहीं, क्योंकि गुणांक (0.5) है / No, because the coefficient is (0.5)
C नहीं, क्योंकि इसमें तीन पद हैं / No, because it has three terms
D नहीं, क्योंकि इसमें \(x^2\) है / No, because it has \(x^2\)
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि दशमलव गुणांक भी वास्तविक संख्या है / Yes, because a decimal coefficient is also a real number
Step 1
Concept
Coefficients in a polynomial can be real numbers. Here the powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि दशमलव गुणांक भी वास्तविक संख्या है / Yes, because a decimal coefficient is also a real number. Coefficients in a polynomial can be real numbers. Here the powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
बहुपद में गुणांक वास्तविक संख्या हो सकते हैं। यहां (x) की घातें (2), (1), और (0) हैं।
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व्यंजक \(\frac{x+1}{x}\) बहुपद क्यों नहीं है?
Why is \(\frac{x+1}{x}\) not a polynomial?
#polynomial
#denominator
#non_polynomial
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A क्योंकि इसमें जोड़ है / Because it has addition
B क्योंकि सरल करने पर \(\frac{1}{x}\) वाला पद आता है / Because after simplifying, a \(\frac{1}{x}\) term appears
C क्योंकि इसमें (x+1) है / Because it has (x+1)
D क्योंकि इसमें दो पद हैं / Because it has two terms
Explanation opens after your attempt
Correct Answer
B. क्योंकि सरल करने पर \(\frac{1}{x}\) वाला पद आता है / Because after simplifying, a \(\frac{1}{x}\) term appears
Step 1
Concept
\(\frac{x+1}{x}=1+\frac{1}{x}\), which contains \(x^{-1}\). Negative powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि सरल करने पर \(\frac{1}{x}\) वाला पद आता है / Because after simplifying, a \(\frac{1}{x}\) term appears. \(\frac{x+1}{x}=1+\frac{1}{x}\), which contains \(x^{-1}\). Negative powers are not valid in a polynomial.
Step 3
Exam Tip
\(\frac{x+1}{x}=1+\frac{1}{x}\), जिसमें \(x^{-1}\) आता है। ऋणात्मक घात बहुपद में मान्य नहीं होती।
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बहुपद \(2x^3+0x^2+0x+9\) की डिग्री क्या है?
What is the degree of \(2x^3+0x^2+0x+9\)?
#polynomial
#degree
#zero_coefficient
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A (0)
B (2)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
Terms with zero coefficient do not change the degree. The highest non-zero power is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). Terms with zero coefficient do not change the degree. The highest non-zero power is (3).
Step 3
Exam Tip
शून्य गुणांक वाले पद डिग्री नहीं बदलते। सबसे बड़ी अशून्य घात (3) है।
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व्यंजक \(x^2+\sqrt[3]{x}\) बहुपद क्यों नहीं है?
Why is \(x^2+\sqrt[3]{x}\) not a polynomial?
#polynomial
#cube_root
#fractional_power
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A क्योंकि \(\sqrt[3]{x}=x^{\frac{1}{3}}\) है / Because \(\sqrt[3]{x}=x^{\frac{1}{3}}\)
B क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
C क्योंकि इसमें दो पद हैं / Because it has two terms
D क्योंकि इसमें जोड़ है / Because it has addition
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(\sqrt[3]{x}=x^{\frac{1}{3}}\) है / Because \(\sqrt[3]{x}=x^{\frac{1}{3}}\)
Step 1
Concept
The power of \(\sqrt[3]{x}\) is \(\frac{1}{3}\). An expression with a fractional power is not a polynomial.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(\sqrt[3]{x}=x^{\frac{1}{3}}\) है / Because \(\sqrt[3]{x}=x^{\frac{1}{3}}\). The power of \(\sqrt[3]{x}\) is \(\frac{1}{3}\). An expression with a fractional power is not a polynomial.
Step 3
Exam Tip
\(\sqrt[3]{x}\) की घात \(\frac{1}{3}\) है। भिन्न घात होने पर व्यंजक बहुपद नहीं होता।
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कौन सा व्यंजक (x) में बहुपद है?
Which expression is a polynomial in (x)?
#polynomial
#valid_powers
#identification
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A \(\frac{1}{x^2}+4\)
B \(x^{-\frac{1}{2}}+2\)
C \(3x^4+\frac{x}{5}-6\)
D \(\sqrt{x^3}+1\)
Explanation opens after your attempt
Correct Answer
C. \(3x^4+\frac{x}{5}-6\)
Step 1
Concept
In \(3x^4+\frac{x}{5}-6\), the powers of (x) are (4), (1), and (0). A fractional coefficient is valid.
Step 2
Why this answer is correct
The correct answer is C. \(3x^4+\frac{x}{5}-6\). In \(3x^4+\frac{x}{5}-6\), the powers of (x) are (4), (1), and (0). A fractional coefficient is valid.
Step 3
Exam Tip
\(3x^4+\frac{x}{5}-6\) में (x) की घातें (4), (1), और (0) हैं। भिन्न गुणांक मान्य होता है।
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बहुपद \(4x^2-7\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(4x^2-7\)?
#polynomial
#missing_linear_term
#coefficient
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A (4)
B (-7)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The term containing (x) is absent in this polynomial. So the coefficient of (x) is taken as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). The term containing (x) is absent in this polynomial. So the coefficient of (x) is taken as (0).
Step 3
Exam Tip
इस बहुपद में (x) वाला पद मौजूद नहीं है। इसलिए (x) का गुणांक (0) माना जाता है।
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किस विकल्प में अशून्य नियतांक बहुपद दिया गया है?
Which option gives a non-zero constant polynomial?
#polynomial
#nonzero_constant
#degree_zero
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A (0)
B (x+1)
C \(-\frac{5}{2}\)
D \(x^2\)
Explanation opens after your attempt
Correct Answer
C. \(-\frac{5}{2}\)
Step 1
Concept
\(-\frac{5}{2}\) has no variable and is not zero. Therefore it is a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(-\frac{5}{2}\). \(-\frac{5}{2}\) has no variable and is not zero. Therefore it is a non-zero constant polynomial.
Step 3
Exam Tip
\(-\frac{5}{2}\) में कोई चर नहीं है और यह शून्य नहीं है। इसलिए यह अशून्य नियतांक बहुपद है।
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बहुपद \(9-2x+5x^4\) को मानक रूप में कैसे लिखेंगे?
How will \(9-2x+5x^4\) be written in standard form?
#polynomial
#standard_form
#descending_powers
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A \(9-2x+5x^4\)
B \(5x^4-2x+9\)
C \(5x^4+9-2x\)
D \(-2x+5x^4+9\)
Explanation opens after your attempt
Correct Answer
B. \(5x^4-2x+9\)
Step 1
Concept
In standard form, terms are written in descending powers. Therefore \(5x^4-2x+9\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(5x^4-2x+9\). In standard form, terms are written in descending powers. Therefore \(5x^4-2x+9\) is correct.
Step 3
Exam Tip
मानक रूप में पद घटती घातों में लिखे जाते हैं। इसलिए \(5x^4-2x+9\) सही है।
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व्यंजक (\(\sqrt{3}\)x-3 -\pi x+2) के बारे में सही कथन कौन सा है?
Which statement is correct about (\(\sqrt{3}\)x-3 -\pi x+2)?
#polynomial
#real_coefficients
#pi
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A यह बहुपद नहीं है क्योंकि इसमें \(\pi\) है / It is not a polynomial because it has \(\pi\)
B यह बहुपद नहीं है क्योंकि इसमें \(\sqrt{3}\) है / It is not a polynomial because it has \(\sqrt{3}\)
C यह बहुपद है क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं / It is a polynomial because coefficients are real and powers are valid
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
C. यह बहुपद है क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं / It is a polynomial because coefficients are real and powers are valid
Step 1
Concept
\(\sqrt{3}\) and \(\pi\) are real coefficients. The powers of (x) are (3), (1), and (0).
Step 2
Why this answer is correct
The correct answer is C. यह बहुपद है क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं / It is a polynomial because coefficients are real and powers are valid. \(\sqrt{3}\) and \(\pi\) are real coefficients. The powers of (x) are (3), (1), and (0).
Step 3
Exam Tip
\(\sqrt{3}\) और \(\pi\) वास्तविक गुणांक हैं। (x) की घातें (3), (1), और (0) हैं।
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व्यंजक \(x^2+\frac{1}{x^3}\) बहुपद क्यों नहीं है?
Why is \(x^2+\frac{1}{x^3}\) not a polynomial?
#polynomial
#negative_power
#denominator
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A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\)
C क्योंकि इसमें दो पद हैं / Because it has two terms
D क्योंकि इसमें कोई नियतांक पद नहीं है / Because it has no constant term
Explanation opens after your attempt
Correct Answer
B. क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\)
Step 1
Concept
In \(\frac{1}{x^3}\), the variable has power (-3). Negative powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\). In \(\frac{1}{x^3}\), the variable has power (-3). Negative powers are not valid in a polynomial.
Step 3
Exam Tip
\(\frac{1}{x^3}\) में चर की घात (-3) है। बहुपद में ऋणात्मक घात मान्य नहीं होती।
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बहुपद \(x^{10}+2x^5+1\) की डिग्री क्या है?
What is the degree of \(x^{10}+2x^5+1\)?
#polynomial
#degree
#higher_power
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A (5)
B (10)
C (11)
D (1)
Explanation opens after your attempt
Step 1
Concept
The highest power is (10). Therefore the degree of the polynomial is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). The highest power is (10). Therefore the degree of the polynomial is (10).
Step 3
Exam Tip
सबसे बड़ी घात (10) है। इसलिए बहुपद की डिग्री (10) है।
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कौन सा व्यंजक रेखीय बहुपद नहीं है?
Which expression is not a linear polynomial?
#polynomial
#linear_polynomial
#degree
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A (3x+2)
B (-x+5)
C \(x^2+1\)
D \(\frac{x}{4}-6\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+1\)
Step 1
Concept
A linear polynomial has degree (1). The degree of \(x^2+1\) is (2).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+1\). A linear polynomial has degree (1). The degree of \(x^2+1\) is (2).
Step 3
Exam Tip
रेखीय बहुपद की डिग्री (1) होती है। \(x^2+1\) की डिग्री (2) है।
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कौन सा व्यंजक बहुपद है लेकिन द्विघात बहुपद नहीं है?
Which expression is a polynomial but not a quadratic polynomial?
#polynomial
#cubic_not_quadratic
#classification
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A \(x^2+3x+2\)
B \(4x^3+x-1\)
C \(\sqrt{x}+1\)
D \(\frac{1}{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3+x-1\)
Step 1
Concept
\(4x^3+x-1\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 2
Why this answer is correct
The correct answer is B. \(4x^3+x-1\). \(4x^3+x-1\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 3
Exam Tip
\(4x^3+x-1\) बहुपद है और इसकी डिग्री (3) है। इसलिए यह द्विघात नहीं है।
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बहुपद \(2x^6-4x^2+8\) में \(x^6\) का गुणांक क्या है?
What is the coefficient of \(x^6\) in \(2x^6-4x^2+8\)?
#polynomial
#coefficient
#power_six
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A (6)
B (2)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The term containing \(x^6\) is \(2x^6\). Therefore the coefficient of \(x^6\) is (2).
Step 2
Why this answer is correct
The correct answer is B. (2). The term containing \(x^6\) is \(2x^6\). Therefore the coefficient of \(x^6\) is (2).
Step 3
Exam Tip
\(x^6\) वाला पद \(2x^6\) है। इसलिए \(x^6\) का गुणांक (2) है।
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व्यंजक \(x^2+x^{-1}+x^0\) बहुपद है या नहीं?
Is \(x^2+x^{-1}+x^0\) a polynomial or not?
#polynomial
#negative_power
#zero_power
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A हां, क्योंकि \(x^0\) है / Yes, because it has \(x^0\)
B हां, क्योंकि इसमें तीन पद हैं / Yes, because it has three terms
C नहीं, क्योंकि \(x^{-1}\) की घात ऋणात्मक है / No, because \(x^{-1}\) has a negative power
D हां, क्योंकि इसमें \(x^2\) है / Yes, because it has \(x^2\)
Explanation opens after your attempt
Correct Answer
C. नहीं, क्योंकि \(x^{-1}\) की घात ऋणात्मक है / No, because \(x^{-1}\) has a negative power
Step 1
Concept
In \(x^{-1}\), the variable has a negative power. One invalid power makes the whole expression not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. नहीं, क्योंकि \(x^{-1}\) की घात ऋणात्मक है / No, because \(x^{-1}\) has a negative power. In \(x^{-1}\), the variable has a negative power. One invalid power makes the whole expression not a polynomial.
Step 3
Exam Tip
\(x^{-1}\) में चर की घात ऋणात्मक है। एक अमान्य घात होने से पूरा व्यंजक बहुपद नहीं रहता।
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व्यंजक \(\frac{x^2}{5}-\frac{3x}{2}+1\) (x) में बहुपद है या नहीं?
Is \(\frac{x^2}{5}-\frac{3x}{2}+1\) a polynomial in (x)?
#polynomial
#fraction_coefficients
#definition
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A नहीं, क्योंकि इसमें भिन्न हैं / No, because it has fractions
B हां, क्योंकि चर की घातें (2), (1), और (0) हैं / Yes, because the variable powers are (2), (1), and (0)
C नहीं, क्योंकि इसमें घटाव है / No, because it has subtraction
D नहीं, क्योंकि इसमें तीन पद हैं / No, because it has three terms
Explanation opens after your attempt
Correct Answer
B. हां, क्योंकि चर की घातें (2), (1), और (0) हैं / Yes, because the variable powers are (2), (1), and (0)
Step 1
Concept
Fractional coefficients are valid in a polynomial. Here all variable powers are non-negative integers.
Step 2
Why this answer is correct
The correct answer is B. हां, क्योंकि चर की घातें (2), (1), और (0) हैं / Yes, because the variable powers are (2), (1), and (0). Fractional coefficients are valid in a polynomial. Here all variable powers are non-negative integers.
Step 3
Exam Tip
भिन्न गुणांक बहुपद में मान्य होते हैं। यहां चर की सभी घातें अऋणात्मक पूर्णांक हैं।
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किस विकल्प में (x) में बहुपद नहीं है?
Which option is not a polynomial in (x)?
#polynomial
#denominator
#non_polynomial
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A \(2x^3+5x+1\)
B \(9x^2-4\)
C \(x^4+x^2+x\)
D \(\frac{x}{x+1}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{x}{x+1}\)
Step 1
Concept
In \(\frac{x}{x+1}\), the variable is in the denominator. Such an expression does not satisfy the definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{x}{x+1}\). In \(\frac{x}{x+1}\), the variable is in the denominator. Such an expression does not satisfy the definition of a polynomial.
Step 3
Exam Tip
\(\frac{x}{x+1}\) में चर हर में है। ऐसा व्यंजक बहुपद की परिभाषा को पूरा नहीं करता।
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व्यंजक \(2x^2+3\sqrt{x}+1\) (x) में बहुपद क्यों नहीं है?
Why is \(2x^2+3\sqrt{x}+1\) not a polynomial in (x)?
#polynomial
#square_root
#fractional_power
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A क्योंकि इसमें \(2x^2\) है / Because it has \(2x^2\)
B क्योंकि \(\sqrt{x}=x^{\frac{1}{2}}\) है / Because \(\sqrt{x}=x^{\frac{1}{2}}\)
C क्योंकि इसमें नियतांक (1) है / Because it has the constant (1)
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
B. क्योंकि \(\sqrt{x}=x^{\frac{1}{2}}\) है / Because \(\sqrt{x}=x^{\frac{1}{2}}\)
Step 1
Concept
In \(\sqrt{x}\), the power of the variable is \(\frac{1}{2}\). In a polynomial, the variable power must be a non-negative integer.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(\sqrt{x}=x^{\frac{1}{2}}\) है / Because \(\sqrt{x}=x^{\frac{1}{2}}\). In \(\sqrt{x}\), the power of the variable is \(\frac{1}{2}\). In a polynomial, the variable power must be a non-negative integer.
Step 3
Exam Tip
\(\sqrt{x}\) में चर की घात \(\frac{1}{2}\) है। बहुपद में चर की घात अऋणात्मक पूर्णांक होनी चाहिए।
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