Class 9 Mathematics - Introduction to Polynomials - Definition of polynomial Easy Quiz

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निम्न में से कौन सा (x) में बहुपद है?

Which of the following is a polynomial in (x)?

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)?

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?

Explanation opens after your attempt
Correct Answer

C. पूर्ण अशून्य या शून्य पूर्णांकNon-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 \(4x^3-2x+8\)?

Explanation opens after your attempt
Correct Answer

C. (3)

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)?

Explanation opens after your attempt
Correct Answer

A. रेखीय बहुपदLinear 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 \(5x^2+2x-3\)?

Explanation opens after your attempt
Correct Answer

B. द्विघात बहुपदQuadratic 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 \(2x^3+x^2-7\)?

Explanation opens after your attempt
Correct Answer

C. त्रिघात बहुपदCubic 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?

Explanation opens after your attempt
Correct Answer

D. नियतांक बहुपदConstant 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?

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Correct Answer

A. हां, यह शून्य बहुपद हैYes, 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?

Explanation opens after your attempt
Correct Answer

C. (-8)

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?

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?

Explanation opens after your attempt
Correct Answer

B. क्योंकि इसमें घात भिन्न हैBecause 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?

Explanation opens after your attempt
Correct Answer

A. क्योंकि घात ऋणात्मक हैBecause 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)?

Explanation opens after your attempt
Correct Answer

D. (4)

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?

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 \(2x^5+x-6\)?

Explanation opens after your attempt
Correct Answer

C. (3)

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?

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?

Explanation opens after your attempt
Correct Answer

B. (5x-2)

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?

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?

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 \(2x^2+\sqrt{3}x+5\)?

Explanation opens after your attempt
Correct Answer

A. बहुपदPolynomial

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 \(\sqrt{x}+2x\)?

Explanation opens after your attempt
Correct Answer

C. बहुपद नहींNot 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 \(9x^2\)?

Explanation opens after your attempt
Correct Answer

C. (0)

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 \(x^4+x^2+x\)?

Explanation opens after your attempt
Correct Answer

D. (0)

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?

Explanation opens after your attempt
Correct Answer

A. हां, बहुपद हैYes, 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?

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?

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?

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)?

Explanation opens after your attempt
Correct Answer

B. हां, क्योंकि चर की घात (1) हैYes, 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?

Explanation opens after your attempt
Correct Answer

A. हां, क्योंकि गुणांक भिन्न हो सकता हैYes, 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 \(\frac{3}{2}\)?

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 \(3x^2-5x+6\)?

Explanation opens after your attempt
Correct Answer

C. (2)

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)?

Explanation opens after your attempt
Correct Answer

B. (1)

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?

Explanation opens after your attempt
Correct Answer

A. (0)

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?

Explanation opens after your attempt
Correct Answer

C. इसकी डिग्री परिभाषित नहीं हैIts 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)?

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?

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 \(4x^3-9x^2+x-2\)?

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 \(5x^4+2x^2-1\)?

Explanation opens after your attempt
Correct Answer

A. (5)

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?

Explanation opens after your attempt
Correct Answer

B. नहीं, क्योंकि \(\frac{3}{x}\) में चर हर में हैNo, 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?

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?

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)?

Explanation opens after your attempt
Correct Answer

B. (3x+7)

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?

Explanation opens after your attempt
Correct Answer

C. क्योंकि इसमें \(x^{-1}\) हैBecause 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?

Explanation opens after your attempt
Correct Answer

A. हां, क्योंकि घातें (2), (1), और (0) हैंYes, 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?

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 \(2x^2-3x+5\)?

Explanation opens after your attempt
Correct Answer

B. (-3)

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?

Explanation opens after your attempt
Correct Answer

C. ऐसा व्यंजक जिसमें चर की घातें अशून्य या शून्य पूर्णांक होंAn 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?

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 \(x^5-4x^3+x-2\)?

Explanation opens after your attempt
Correct Answer

D. (5)

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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FAQs

Class 9 Mathematics Quiz FAQs

How many questions are in this quiz?

This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.

Is there a timer in this quiz?

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Can I open each question separately?

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