निम्न में से कौन सा (x) में बहुपद है?
Which of the following is a polynomial in (x)?
#polynomial
#definition
#class9
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A \(\frac{1}{x}+2\)
B \(3x^2-5x+1\)
C \(\sqrt{x}+4\)
D \(x^{-2}+3\)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-5x+1\)
Step 1
Concept
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).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-5x+1\). 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).
Step 3
Exam Tip
बहुपद में चर की घात पूर्ण अशून्य या शून्य संख्या होनी चाहिए। \(3x^2-5x+1\) में घातें (2), (1), और (0) हैं।
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निम्न में से कौन सा (x) में बहुपद नहीं है?
Which of the following is not a polynomial in (x)?
#polynomial
#non_polynomial
#denominator
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A \(x^2+3x\)
B (7x-4)
C \(\frac{5}{x}+1\)
D (9)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5}{x}+1\)
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5}{x}+1\). 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.
Step 3
Exam Tip
\(\frac{5}{x}\) में चर हर में है, अर्थात घात (-1) है। ऋणात्मक घात वाला व्यंजक बहुपद नहीं होता।
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बहुपद में चर की घात कैसी होनी चाहिए?
What type of powers should the variable have in a polynomial?
#polynomial
#powers
#definition
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A ऋणात्मक पूर्णांक / Negative integers
B भिन्न संख्याएं / Fractional numbers
C पूर्ण अशून्य या शून्य पूर्णांक / Non-negative integers including zero
D केवल अभाज्य संख्याएं / Only prime numbers
Explanation opens after your attempt
Correct Answer
C. पूर्ण अशून्य या शून्य पूर्णांक / Non-negative integers including zero
Step 1
Concept
In a polynomial, powers can be like (0,1,2,3). Fractional or negative powers do not fit the definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is C. पूर्ण अशून्य या शून्य पूर्णांक / Non-negative integers including zero. In a polynomial, powers can be like (0,1,2,3). Fractional or negative powers do not fit the definition of a polynomial.
Step 3
Exam Tip
बहुपद में चर की घात (0,1,2,3) जैसी हो सकती है। भिन्न या ऋणात्मक घात बहुपद की परिभाषा में नहीं आती।
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व्यंजक \(4x^3-2x+8\) में सबसे बड़ी घात क्या है?
What is the highest power in the expression \(4x^3-2x+8\)?
#polynomial
#degree
#highest_power
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A (1)
B (2)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (3). The degree of a polynomial is identified by the highest power.
Step 2
Why this answer is correct
The correct answer is C. (3). The highest power is (3). The degree of a polynomial is identified by the highest power.
Step 3
Exam Tip
सबसे बड़ी घात (3) है। बहुपद की डिग्री सबसे बड़ी घात से पहचानी जाती है।
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व्यंजक (6x+11) किस प्रकार का बहुपद है?
What type of polynomial is (6x+11)?
#polynomial
#linear_polynomial
#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
The highest power of this polynomial 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. The highest power of this polynomial is (1). A polynomial of degree (1) is called a linear polynomial.
Step 3
Exam Tip
इस बहुपद की सबसे बड़ी घात (1) है। घात (1) वाला बहुपद रेखीय बहुपद कहलाता है।
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व्यंजक \(5x^2+2x-3\) किस प्रकार का बहुपद है?
What type of polynomial is \(5x^2+2x-3\)?
#polynomial
#quadratic_polynomial
#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
Its 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. Its highest power is (2). A polynomial of degree (2) is a quadratic polynomial.
Step 3
Exam Tip
इसमें सबसे बड़ी घात (2) है। घात (2) वाला बहुपद द्विघात बहुपद होता है।
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व्यंजक \(2x^3+x^2-7\) किस प्रकार का बहुपद है?
What type of polynomial is \(2x^3+x^2-7\)?
#polynomial
#cubic_polynomial
#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
C. त्रिघात बहुपद / Cubic polynomial
Step 1
Concept
The highest power of this polynomial is (3). A polynomial of degree (3) is called a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is C. त्रिघात बहुपद / Cubic polynomial. The highest power of this polynomial is (3). A polynomial of degree (3) is called a cubic polynomial.
Step 3
Exam Tip
इस बहुपद की सबसे बड़ी घात (3) है। घात (3) वाला बहुपद त्रिघात बहुपद कहलाता है।
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व्यंजक (12) को किस प्रकार माना जाएगा?
How will the expression (12) be considered?
#polynomial
#constant_polynomial
#degree_zero
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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
D. नियतांक बहुपद / Constant polynomial
Step 1
Concept
(12) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is D. नियतांक बहुपद / Constant polynomial. (12) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
(12) में कोई चर नहीं है, इसलिए यह नियतांक बहुपद है। अशून्य नियतांक बहुपद की डिग्री (0) होती है।
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क्या (0) एक बहुपद है?
Is (0) a polynomial?
#polynomial
#zero_polynomial
#definition
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A हां, यह शून्य बहुपद है / Yes, it is the zero polynomial
B नहीं, क्योंकि इसमें चर नहीं है / No, because it has no variable
C नहीं, क्योंकि इसका मान छोटा है / No, because its value is small
D हां, इसकी डिग्री हमेशा (1) है / Yes, its degree is always (1)
Explanation opens after your attempt
Correct Answer
A. हां, यह शून्य बहुपद है / Yes, it is the zero polynomial
Step 1
Concept
(0) is considered the zero polynomial. Its degree is not defined.
Step 2
Why this answer is correct
The correct answer is A. हां, यह शून्य बहुपद है / Yes, it is the zero polynomial. (0) is considered the zero polynomial. Its degree is not defined.
Step 3
Exam Tip
(0) को शून्य बहुपद माना जाता है। इसकी डिग्री परिभाषित नहीं होती।
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निम्न में से कौन सा नियतांक बहुपद है?
Which of the following is a constant polynomial?
#polynomial
#constant
#identification
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A (x+5)
B \(x^2\)
C (-8)
D \(3x^3\)
Explanation opens after your attempt
Step 1
Concept
A constant polynomial has no variable. (-8) is only a number, so it is a constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. (-8). A constant polynomial has no variable. (-8) is only a number, so it is a constant polynomial.
Step 3
Exam Tip
नियतांक बहुपद में चर नहीं होता। (-8) केवल एक संख्या है, इसलिए यह नियतांक बहुपद है।
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कौन सा व्यंजक बहुपद की परिभाषा को पूरा करता है?
Which expression satisfies the definition of a polynomial?
#polynomial
#definition
#identification
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A \(\sqrt{x}+1\)
B \(x^2+4x+4\)
C \(\frac{2}{x}\)
D \(x^{-1}+5\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+4x+4\)
Step 1
Concept
In \(x^2+4x+4\), the powers of the variable are non-negative integers. Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+4x+4\). In \(x^2+4x+4\), the powers of the variable are non-negative integers. Therefore it is a polynomial.
Step 3
Exam Tip
\(x^2+4x+4\) में चर की घातें अशून्य या शून्य पूर्णांक हैं। इसलिए यह बहुपद है।
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व्यंजक \(x^{\frac{1}{2}}+3\) बहुपद क्यों नहीं है?
Why is \(x^{\frac{1}{2}}+3\) not a polynomial?
#polynomial
#fractional_power
#non_polynomial
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A क्योंकि इसमें स्थिर पद है / Because it has a constant term
B क्योंकि इसमें घात भिन्न है / Because it has a fractional power
C क्योंकि इसमें (3) है / Because it has (3)
D क्योंकि इसमें जोड़ है / Because it has addition
Explanation opens after your attempt
Correct Answer
B. क्योंकि इसमें घात भिन्न है / Because it has a fractional power
Step 1
Concept
In a polynomial, the power of the variable cannot be fractional. The power of \(x^{\frac{1}{2}}\) is \(\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is B. क्योंकि इसमें घात भिन्न है / Because it has a fractional power. In a polynomial, the power of the variable cannot be fractional. The power of \(x^{\frac{1}{2}}\) is \(\frac{1}{2}\).
Step 3
Exam Tip
बहुपद में चर की घात भिन्न नहीं हो सकती। \(x^{\frac{1}{2}}\) की घात \(\frac{1}{2}\) है।
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व्यंजक \(x^{-3}+2\) बहुपद क्यों नहीं है?
Why is \(x^{-3}+2\) not a polynomial?
#polynomial
#negative_power
#non_polynomial
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A क्योंकि घात ऋणात्मक है / Because the power is negative
B क्योंकि इसमें (2) है / Because it has (2)
C क्योंकि इसमें (x) है / Because it has (x)
D क्योंकि इसमें दो पद हैं / Because it has two terms
Explanation opens after your attempt
Correct Answer
A. क्योंकि घात ऋणात्मक है / Because the power is negative
Step 1
Concept
In a polynomial, the power of the variable cannot be negative. Here the power of (x) is (-3).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि घात ऋणात्मक है / Because the power is negative. In a polynomial, the power of the variable cannot be negative. Here the power of (x) is (-3).
Step 3
Exam Tip
बहुपद में चर की घात ऋणात्मक नहीं हो सकती। यहां (x) की घात (-3) है।
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(x) में बहुपद \(7x^4-3x^2+1\) की डिग्री क्या है?
What is the degree of the polynomial \(7x^4-3x^2+1\) in (x)?
#polynomial
#degree
#highest_power
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The highest power is (4). Therefore the degree of the polynomial is (4).
Step 2
Why this answer is correct
The correct answer is D. (4). The highest power is (4). Therefore the degree of the polynomial is (4).
Step 3
Exam Tip
सबसे बड़ी घात (4) है। इसलिए बहुपद की डिग्री (4) होगी।
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किस व्यंजक में चर हर में होने के कारण बहुपद नहीं बनता?
Which expression is not a polynomial because the variable is in the denominator?
#polynomial
#denominator
#non_polynomial
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A \(x^2+1\)
B \(\frac{3}{x}+5\)
C (4x+7)
D \(9x^3\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{x}+5\)
Step 1
Concept
In \(\frac{3}{x}\), (x) is in the denominator, so it is like \(x^{-1}\). Negative powers are not accepted in polynomials.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{x}+5\). In \(\frac{3}{x}\), (x) is in the denominator, so it is like \(x^{-1}\). Negative powers are not accepted in polynomials.
Step 3
Exam Tip
\(\frac{3}{x}\) में (x) हर में है, इसलिए यह \(x^{-1}\) जैसा है। ऋणात्मक घात बहुपद में स्वीकार नहीं होती।
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बहुपद \(2x^5+x-6\) में कितने पद हैं?
How many terms are there in the polynomial \(2x^5+x-6\)?
#polynomial
#terms
#counting
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A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The terms are \(2x^5\), (x), and (-6). So there are (3) terms.
Step 2
Why this answer is correct
The correct answer is C. (3). The terms are \(2x^5\), (x), and (-6). So there are (3) terms.
Step 3
Exam Tip
पद \(2x^5\), (x), और (-6) हैं। इसलिए कुल (3) पद हैं।
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व्यंजक \(x^2+2x+1\) में सबसे बड़ी घात किस पद में है?
In \(x^2+2x+1\), which term has the highest power?
#polynomial
#highest_power
#degree
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A \(x^2\)
B (2x)
C (1)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(x^2\)
Step 1
Concept
The highest power is (2), which is in the term \(x^2\). While finding degree, look at the highest power.
Step 2
Why this answer is correct
The correct answer is A. \(x^2\). The highest power is (2), which is in the term \(x^2\). While finding degree, look at the highest power.
Step 3
Exam Tip
सबसे बड़ी घात (2) है, जो \(x^2\) पद में है। डिग्री खोजते समय सबसे बड़ी घात देखें।
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निम्न में से कौन सा रेखीय बहुपद है?
Which of the following is a linear polynomial?
#polynomial
#linear
#identification
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A \(x^2+1\)
B (5x-2)
C \(x^3+4\)
D (9)
Explanation opens after your attempt
Step 1
Concept
The highest power of (5x-2) is (1). Therefore it is a linear polynomial.
Step 2
Why this answer is correct
The correct answer is B. (5x-2). The highest power of (5x-2) is (1). Therefore it is a linear polynomial.
Step 3
Exam Tip
(5x-2) की सबसे बड़ी घात (1) है। इसलिए यह रेखीय बहुपद है।
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निम्न में से कौन सा द्विघात बहुपद है?
Which of the following is a quadratic polynomial?
#polynomial
#quadratic
#identification
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A \(4x^2-1\)
B (6x+1)
C \(x^3-2\)
D (10)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-1\)
Step 1
Concept
In \(4x^2-1\), the highest power is (2). Therefore it is a quadratic polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-1\). In \(4x^2-1\), the highest power is (2). Therefore it is a quadratic polynomial.
Step 3
Exam Tip
\(4x^2-1\) में सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है।
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निम्न में से कौन सा त्रिघात बहुपद है?
Which of the following is a cubic polynomial?
#polynomial
#cubic
#identification
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A (x+3)
B \(x^2+3\)
C \(x^3+3x-1\)
D (3)
Explanation opens after your attempt
Correct Answer
C. \(x^3+3x-1\)
Step 1
Concept
The highest power of \(x^3+3x-1\) is (3). Therefore it is a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(x^3+3x-1\). The highest power of \(x^3+3x-1\) is (3). Therefore it is a cubic polynomial.
Step 3
Exam Tip
\(x^3+3x-1\) की सबसे बड़ी घात (3) है। इसलिए यह त्रिघात बहुपद है।
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व्यंजक \(2x^2+\sqrt{3}x+5\) क्या है?
What is the expression \(2x^2+\sqrt{3}x+5\)?
#polynomial
#real_coefficient
#definition
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A बहुपद / Polynomial
B बहुपद नहीं / Not a polynomial
C चर रहित व्यंजक / Expression without variable
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
A. बहुपद / Polynomial
Step 1
Concept
\(\sqrt{3}\) is a real coefficient and the power of (x) is (1). So it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. बहुपद / Polynomial. \(\sqrt{3}\) is a real coefficient and the power of (x) is (1). So it is a polynomial.
Step 3
Exam Tip
\(\sqrt{3}\) एक वास्तविक गुणांक है और (x) की घात (1) है। इसलिए यह बहुपद है।
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व्यंजक \(\sqrt{x}+2x\) क्या है?
What is the expression \(\sqrt{x}+2x\)?
#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
\(\sqrt{x}=x^{\frac{1}{2}}\), which has a fractional power of the variable. Therefore it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. बहुपद नहीं / Not a polynomial. \(\sqrt{x}=x^{\frac{1}{2}}\), which has a fractional power of the variable. Therefore it is not a polynomial.
Step 3
Exam Tip
\(\sqrt{x}=x^{\frac{1}{2}}\) होता है, जिसमें चर की घात भिन्न है। इसलिए यह बहुपद नहीं है।
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बहुपद \(9x^2\) में नियतांक पद क्या है?
What is the constant term in the polynomial \(9x^2\)?
#polynomial
#constant_term
#zero
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A (9)
B (2)
C (0)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
In \(9x^2\), no term without a variable is written. So the constant term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). In \(9x^2\), no term without a variable is written. So the constant term is taken as (0).
Step 3
Exam Tip
\(9x^2\) में बिना चर वाला कोई पद नहीं लिखा है। इसलिए नियतांक पद (0) माना जाता है।
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बहुपद \(x^4+x^2+x\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in the polynomial \(x^4+x^2+x\)?
#polynomial
#missing_term
#coefficient
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A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
The term \(x^3\) is not present in this polynomial. So the coefficient of \(x^3\) is taken as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). The term \(x^3\) is not present in this polynomial. So the coefficient of \(x^3\) is taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) पद नहीं है। इसलिए \(x^3\) का गुणांक (0) माना जाता है।
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व्यंजक \(x^0+2x\) बहुपद है या नहीं?
Is the expression \(x^0+2x\) a polynomial or not?
#polynomial
#zero_power
#definition
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A हां, बहुपद है / Yes, it is a polynomial
B नहीं, क्योंकि \(x^0\) गलत है / No, because \(x^0\) is wrong
C नहीं, क्योंकि इसमें दो पद हैं / No, because it has two terms
D नहीं, क्योंकि इसमें (2x) है / No, because it has (2x)
Explanation opens after your attempt
Correct Answer
A. हां, बहुपद है / Yes, it is a polynomial
Step 1
Concept
\(x^0=1\), and (2x) has power (1). Both powers are valid for a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, बहुपद है / Yes, it is a polynomial. \(x^0=1\), and (2x) has power (1). Both powers are valid for a polynomial.
Step 3
Exam Tip
\(x^0=1\) और (2x) में घात (1) है। दोनों घातें बहुपद के लिए मान्य हैं।
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कौन सा व्यंजक एकपदी बहुपद है?
Which expression is a monomial polynomial?
#polynomial
#monomial
#terms
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A \(3x^2\)
B (x+2)
C \(x^2+x+1\)
D (x-4)
Explanation opens after your attempt
Correct Answer
A. \(3x^2\)
Step 1
Concept
A monomial polynomial has only one term. \(3x^2\) is a polynomial with one term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2\). A monomial polynomial has only one term. \(3x^2\) is a polynomial with one term.
Step 3
Exam Tip
एकपदी बहुपद में केवल एक पद होता है। \(3x^2\) एक पद वाला बहुपद है।
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कौन सा व्यंजक द्विपदी बहुपद है?
Which expression is a binomial polynomial?
#polynomial
#binomial
#terms
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A (5x)
B \(x^2-4\)
C \(x^2+x+4\)
D (7)
Explanation opens after your attempt
Correct Answer
B. \(x^2-4\)
Step 1
Concept
A binomial has two terms. \(x^2-4\) has the two terms \(x^2\) and (-4).
Step 2
Why this answer is correct
The correct answer is B. \(x^2-4\). A binomial has two terms. \(x^2-4\) has the two terms \(x^2\) and (-4).
Step 3
Exam Tip
द्विपदी में दो पद होते हैं। \(x^2-4\) में \(x^2\) और (-4) दो पद हैं।
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कौन सा व्यंजक त्रिपदी बहुपद है?
Which expression is a trinomial polynomial?
#polynomial
#trinomial
#terms
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A \(x^2+3x+2\)
B \(x^2-5\)
C (4x)
D (11)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+2\)
Step 1
Concept
A trinomial has three terms. \(x^2+3x+2\) has three terms and all powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+2\). A trinomial has three terms. \(x^2+3x+2\) has three terms and all powers are valid.
Step 3
Exam Tip
त्रिपदी में तीन पद होते हैं। \(x^2+3x+2\) में तीन पद हैं और सभी घातें मान्य हैं।
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क्या \(\frac{x}{2}+3\) (x) में बहुपद है?
Is \(\frac{x}{2}+3\) a polynomial in (x)?
#polynomial
#fraction_coefficient
#definition
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A नहीं, क्योंकि इसमें भिन्न है / No, because it has a fraction
B हां, क्योंकि चर की घात (1) है / Yes, because the power of the variable 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 चर की घात (1) है / Yes, because the power of the variable is (1)
Step 1
Concept
In \(\frac{x}{2}\), the power of (x) is (1) and the coefficient is \(\frac{1}{2}\). Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is B. हां, क्योंकि चर की घात (1) है / Yes, because the power of the variable is (1). In \(\frac{x}{2}\), the power of (x) is (1) and the coefficient is \(\frac{1}{2}\). Therefore it is a polynomial.
Step 3
Exam Tip
\(\frac{x}{2}\) में (x) की घात (1) है और गुणांक \(\frac{1}{2}\) है। इसलिए यह बहुपद है।
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क्या \(\frac{1}{2}x^2-7\) बहुपद है?
Is \(\frac{1}{2}x^2-7\) a polynomial?
#polynomial
#coefficient
#fraction
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A हां, क्योंकि गुणांक भिन्न हो सकता है / Yes, because the coefficient can be a fraction
B नहीं, क्योंकि गुणांक \(\frac{1}{2}\) है / No, because the coefficient is \(\frac{1}{2}\)
C नहीं, क्योंकि इसमें नियतांक है / No, because it has a constant
D नहीं, क्योंकि इसमें \(x^2\) है / No, because it has \(x^2\)
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि गुणांक भिन्न हो सकता है / Yes, because the coefficient can be a fraction
Step 1
Concept
Coefficients in a polynomial can be real numbers. Here the power of (x) is (2), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि गुणांक भिन्न हो सकता है / Yes, because the coefficient can be a fraction. Coefficients in a polynomial can be real numbers. Here the power of (x) is (2), so it is a polynomial.
Step 3
Exam Tip
बहुपद में गुणांक वास्तविक संख्या हो सकते हैं। यहां (x) की घात (2) है, इसलिए यह बहुपद है।
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किस व्यंजक में चर की घात \(\frac{3}{2}\) होने से वह बहुपद नहीं है?
Which expression is not a polynomial because the variable has power \(\frac{3}{2}\)?
#polynomial
#fractional_power
#non_polynomial
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A \(x^3+2\)
B \(x^{\frac{3}{2}}+1\)
C \(3x^2+x\)
D (4x+9)
Explanation opens after your attempt
Correct Answer
B. \(x^{\frac{3}{2}}+1\)
Step 1
Concept
\(\frac{3}{2}\) is a fractional power. In a polynomial, the variable power must be only a non-negative integer.
Step 2
Why this answer is correct
The correct answer is B. \(x^{\frac{3}{2}}+1\). \(\frac{3}{2}\) is a fractional power. In a polynomial, the variable power must be only a non-negative integer.
Step 3
Exam Tip
\(\frac{3}{2}\) भिन्न घात है। बहुपद में चर की घात केवल अशून्य या शून्य पूर्णांक होती है।
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बहुपद \(3x^2-5x+6\) की डिग्री क्या है?
What is the degree of the polynomial \(3x^2-5x+6\)?
#polynomial
#degree
#quadratic
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2). Therefore the degree of the 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 the polynomial is (2).
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए बहुपद की डिग्री (2) है।
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बहुपद (8x-13) की डिग्री क्या है?
What is the degree of the polynomial (8x-13)?
#polynomial
#degree
#linear
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A (0)
B (1)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (1). Therefore the degree of (8x-13) is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The highest power is (1). Therefore the degree of (8x-13) is (1).
Step 3
Exam Tip
सबसे बड़ी घात (1) है। इसलिए (8x-13) की डिग्री (1) है।
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अशून्य नियतांक बहुपद की डिग्री क्या होती है?
What is the degree of a non-zero constant polynomial?
#polynomial
#constant_degree
#degree_zero
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A (0)
B (1)
C (2)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). For example, (5) can be considered as \(5x^0\).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). For example, (5) can be considered as \(5x^0\).
Step 3
Exam Tip
अशून्य नियतांक बहुपद की डिग्री (0) होती है। उदाहरण के लिए \(5=5x^0\) माना जा सकता है।
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शून्य बहुपद की डिग्री के बारे में सही कथन कौन सा है?
Which statement is correct about the degree of the zero polynomial?
#polynomial
#zero_polynomial
#degree
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A इसकी डिग्री (0) है / Its degree is (0)
B इसकी डिग्री (1) है / Its degree is (1)
C इसकी डिग्री परिभाषित नहीं है / Its degree is not defined
D इसकी डिग्री (2) है / Its degree is (2)
Explanation opens after your attempt
Correct Answer
C. इसकी डिग्री परिभाषित नहीं है / Its degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. In exams, distinguish it from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. इसकी डिग्री परिभाषित नहीं है / Its degree is not defined. The degree of the zero polynomial is not defined. In exams, distinguish it from a non-zero constant polynomial.
Step 3
Exam Tip
शून्य बहुपद की डिग्री परिभाषित नहीं होती। परीक्षा में इसे अशून्य नियतांक बहुपद से अलग समझें।
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निम्न में से कौन सा (x) में बहुपद है लेकिन (y) शामिल नहीं करता?
Which of the following is a polynomial in (x) and does not include (y)?
#polynomial
#in_x
#identification
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A \(2x^2+3x-1\)
B \(2y^2+3\)
C (xy+1)
D \(\frac{1}{x}+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+3x-1\)
Step 1
Concept
\(2x^2+3x-1\) has only (x) and valid powers. Therefore it is a polynomial in (x).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+3x-1\). \(2x^2+3x-1\) has only (x) and valid powers. Therefore it is a polynomial in (x).
Step 3
Exam Tip
\(2x^2+3x-1\) में केवल (x) है और घातें मान्य हैं। इसलिए यह (x) में बहुपद है।
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किस विकल्प में बहुपद के सभी पदों में चर की घात मान्य है?
In which option do all terms have valid powers of the variable for a polynomial?
#polynomial
#valid_powers
#definition
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A \(x^2+x+1\)
B \(x^{-1}+x\)
C \(\sqrt{x}+x\)
D \(\frac{1}{x^2}+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x+1\)
Step 1
Concept
In \(x^2+x+1\), the powers are (2), (1), and (0). These are valid powers for a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x+1\). In \(x^2+x+1\), the powers are (2), (1), and (0). These are valid powers for a polynomial.
Step 3
Exam Tip
\(x^2+x+1\) में घातें (2), (1), और (0) हैं। ये बहुपद के लिए मान्य घातें हैं।
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बहुपद \(4x^3-9x^2+x-2\) में अग्रणी पद कौन सा है?
What is the leading term in the polynomial \(4x^3-9x^2+x-2\)?
#polynomial
#leading_term
#degree
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A \(4x^3\)
B \(-9x^2\)
C (x)
D (-2)
Explanation opens after your attempt
Correct Answer
A. \(4x^3\)
Step 1
Concept
The term with the highest power is the leading term. Here the highest power is (3), so the leading term is \(4x^3\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^3\). The term with the highest power is the leading term. Here the highest power is (3), so the leading term is \(4x^3\).
Step 3
Exam Tip
सबसे बड़ी घात वाला पद अग्रणी पद होता है। यहां सबसे बड़ी घात (3) है, इसलिए अग्रणी पद \(4x^3\) है।
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बहुपद \(5x^4+2x^2-1\) का अग्रणी गुणांक क्या है?
What is the leading coefficient of the polynomial \(5x^4+2x^2-1\)?
#polynomial
#leading_coefficient
#degree
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A (5)
B (4)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(5x^4\). Therefore the leading coefficient is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). The leading term is \(5x^4\). Therefore the leading coefficient is (5).
Step 3
Exam Tip
अग्रणी पद \(5x^4\) है। इसलिए अग्रणी गुणांक (5) है।
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व्यंजक \(2x^2+\frac{3}{x}\) बहुपद है या नहीं?
Is the expression \(2x^2+\frac{3}{x}\) a polynomial or not?
#polynomial
#denominator
#definition
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A हां, क्योंकि इसमें \(x^2\) है / Yes, because it has \(x^2\)
B नहीं, क्योंकि \(\frac{3}{x}\) में चर हर में है / No, because in \(\frac{3}{x}\) 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 \(\frac{3}{x}\) में चर हर में है / No, because in \(\frac{3}{x}\) the variable is in the denominator
Step 1
Concept
In \(\frac{3}{x}\), the power of (x) is (-1). Therefore the whole expression is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. नहीं, क्योंकि \(\frac{3}{x}\) में चर हर में है / No, because in \(\frac{3}{x}\) the variable is in the denominator. In \(\frac{3}{x}\), the power of (x) is (-1). Therefore the whole expression is not a polynomial.
Step 3
Exam Tip
\(\frac{3}{x}\) में (x) की घात (-1) है। इसलिए पूरा व्यंजक बहुपद नहीं है।
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कौन सा व्यंजक (x) में बहुपद नहीं है लेकिन केवल एक पद रखता है?
Which expression is not a polynomial in (x) but has only one term?
#polynomial
#monomial_non_polynomial
#negative_power
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A \(\frac{1}{x}\)
B (5x)
C \(x^2\)
D (7)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{x}\)
Step 1
Concept
\(\frac{1}{x}=x^{-1}\), so it is not a polynomial. Having one term is not enough; the power must also be valid.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{x}\). \(\frac{1}{x}=x^{-1}\), so it is not a polynomial. Having one term is not enough; the power must also be valid.
Step 3
Exam Tip
\(\frac{1}{x}=x^{-1}\) है, इसलिए यह बहुपद नहीं है। एक पद होना पर्याप्त नहीं है, घात भी मान्य होनी चाहिए।
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बहुपद \(x^2+0x+4\) को सरल रूप में कैसे लिखेंगे?
How will the polynomial \(x^2+0x+4\) be written in simplified form?
#polynomial
#zero_coefficient
#simplification
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A \(x^2+4\)
B \(x^2+x+4\)
C (0)
D \(4x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4\)
Step 1
Concept
(0x=0), so \(x^2+0x+4=x^2+4\). A term with zero coefficient can be removed.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4\). (0x=0), so \(x^2+0x+4=x^2+4\). A term with zero coefficient can be removed.
Step 3
Exam Tip
(0x=0), इसलिए \(x^2+0x+4=x^2+4\)। शून्य गुणांक वाला पद हटाया जा सकता है।
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किस बहुपद में \(x^2\) का गुणांक (0) है?
In which polynomial is the coefficient of \(x^2\) equal to (0)?
#polynomial
#missing_term
#coefficient_zero
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A \(x^2+5\)
B (3x+7)
C \(2x^2+x\)
D \(4x^2-1\)
Explanation opens after your attempt
Step 1
Concept
In (3x+7), the \(x^2\) term is absent. So the coefficient of \(x^2\) is taken as (0).
Step 2
Why this answer is correct
The correct answer is B. (3x+7). In (3x+7), the \(x^2\) term is absent. So the coefficient of \(x^2\) is taken as (0).
Step 3
Exam Tip
(3x+7) में \(x^2\) पद नहीं है। इसलिए \(x^2\) का गुणांक (0) माना जाता है।
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व्यंजक \(3x^2+2x^{-1}+1\) बहुपद क्यों नहीं है?
Why is \(3x^2+2x^{-1}+1\) not a polynomial?
#polynomial
#negative_power
#non_polynomial
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A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (1) है / Because it has (1)
C क्योंकि इसमें \(x^{-1}\) है / Because it has \(x^{-1}\)
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि इसमें \(x^{-1}\) है / Because it has \(x^{-1}\)
Step 1
Concept
In \(x^{-1}\), the power of the variable is negative. A polynomial cannot have a negative power.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि इसमें \(x^{-1}\) है / Because it has \(x^{-1}\). In \(x^{-1}\), the power of the variable is negative. A polynomial cannot have a negative power.
Step 3
Exam Tip
\(x^{-1}\) में चर की घात ऋणात्मक है। बहुपद में ऋणात्मक घात नहीं हो सकती।
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क्या \(3x^2+2x+1\) एक बहुपद है?
Is \(3x^2+2x+1\) a polynomial?
#polynomial
#definition
#yes_no
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A हां, क्योंकि घातें (2), (1), और (0) हैं / Yes, because the powers are (2), (1), and (0)
B नहीं, क्योंकि इसमें (3) पद हैं / No, because it has (3) terms
C नहीं, क्योंकि इसमें नियतांक है / No, because it has a constant
D नहीं, क्योंकि इसमें (x) है / No, because it has (x)
Explanation opens after your attempt
Correct Answer
A. हां, क्योंकि घातें (2), (1), और (0) हैं / Yes, because the powers are (2), (1), and (0)
Step 1
Concept
All powers are non-negative integers. Therefore \(3x^2+2x+1\) is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि घातें (2), (1), और (0) हैं / Yes, because the powers are (2), (1), and (0). All powers are non-negative integers. Therefore \(3x^2+2x+1\) is a polynomial.
Step 3
Exam Tip
सभी घातें अशून्य या शून्य पूर्णांक हैं। इसलिए \(3x^2+2x+1\) बहुपद है।
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किस विकल्प में बहुपद को मानक रूप में घटती घातों में लिखा गया है?
Which option writes a polynomial in standard form with descending powers?
#polynomial
#standard_form
#descending_powers
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A \(7+2x+x^2\)
B \(2x+x^3+1\)
C \(x^3+2x^2+x+5\)
D \(5+x^4+x\)
Explanation opens after your attempt
Correct Answer
C. \(x^3+2x^2+x+5\)
Step 1
Concept
In standard form, terms are written in descending powers. In \(x^3+2x^2+x+5\), powers are in the order (3), (2), (1), (0).
Step 2
Why this answer is correct
The correct answer is C. \(x^3+2x^2+x+5\). In standard form, terms are written in descending powers. In \(x^3+2x^2+x+5\), powers are in the order (3), (2), (1), (0).
Step 3
Exam Tip
मानक रूप में पदों को घटती घातों में लिखते हैं। \(x^3+2x^2+x+5\) में घातें (3), (2), (1), (0) क्रम में हैं।
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बहुपद \(2x^2-3x+5\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in the polynomial \(2x^2-3x+5\)?
#polynomial
#coefficient
#linear_term
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A (2)
B (-3)
C (5)
D (1)
Explanation opens after your attempt
Step 1
Concept
The term containing (x) is (-3x). Therefore the coefficient of (x) is (-3).
Step 2
Why this answer is correct
The correct answer is B. (-3). The term containing (x) is (-3x). Therefore the coefficient of (x) is (-3).
Step 3
Exam Tip
(x) वाला पद (-3x) है। इसलिए (x) का गुणांक (-3) है।
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किस विकल्प में बहुपद की सही परिभाषा दी गई है?
Which option gives the correct definition of a polynomial?
#polynomial
#definition
#basic
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A ऐसा व्यंजक जिसमें चर की घातें ऋणात्मक हों / An expression in which variable powers are negative
B ऐसा व्यंजक जिसमें चर हर में हो / An expression in which the variable is in the denominator
C ऐसा व्यंजक जिसमें चर की घातें अशून्य या शून्य पूर्णांक हों / An expression in which variable powers are non-negative integers
D ऐसा व्यंजक जिसमें केवल वर्गमूल हों / An expression that contains only square roots
Explanation opens after your attempt
Correct Answer
C. ऐसा व्यंजक जिसमें चर की घातें अशून्य या शून्य पूर्णांक हों / An expression in which variable powers are non-negative integers
Step 1
Concept
In a polynomial, variable powers are like (0,1,2,3). This is the basic definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is C. ऐसा व्यंजक जिसमें चर की घातें अशून्य या शून्य पूर्णांक हों / An expression in which variable powers are non-negative integers. In a polynomial, variable powers are like (0,1,2,3). This is the basic definition of a polynomial.
Step 3
Exam Tip
बहुपद में चर की घातें (0,1,2,3) जैसी होती हैं। यही बहुपद की मूल परिभाषा है।
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निम्न में से कौन सा व्यंजक केवल घात के कारण बहुपद नहीं है?
Which expression is not a polynomial only because of the power?
#polynomial
#fractional_exponent
#non_polynomial
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A \(x^2+5\)
B \(x^{\frac{2}{3}}+1\)
C (4x+9)
D \(6x^3-1\)
Explanation opens after your attempt
Correct Answer
B. \(x^{\frac{2}{3}}+1\)
Step 1
Concept
In \(x^{\frac{2}{3}}\), the power is fractional. Such a power is not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^{\frac{2}{3}}+1\). In \(x^{\frac{2}{3}}\), the power is fractional. Such a power is not allowed in a polynomial.
Step 3
Exam Tip
\(x^{\frac{2}{3}}\) में घात भिन्न है। बहुपद में ऐसी घात नहीं होती।
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बहुपद \(x^5-4x^3+x-2\) की डिग्री क्या है?
What is the degree of the polynomial \(x^5-4x^3+x-2\)?
#polynomial
#degree
#highest_power
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A (2)
B (3)
C (4)
D (5)
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Step 1
Concept
The highest power is (5). Therefore the degree of this polynomial is (5).
Step 2
Why this answer is correct
The correct answer is D. (5). The highest power is (5). Therefore the degree of this polynomial is (5).
Step 3
Exam Tip
सबसे बड़ी घात (5) है। इसलिए इस बहुपद की डिग्री (5) है।
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