कौन-सा व्यंजक (y) में बहुपद नहीं है?
Which expression is not a polynomial in (y)?
#definition-polynomial
#denominator
#not-polynomial
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A \(\frac{5}{y}+2\)
B \(y^4-y+6\)
C \(9y^2+1\)
D (7)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{y}+2\)
Step 1
Concept
In \(\frac{5}{y}\), the power of (y) is (-1). Due to the negative power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{y}+2\). In \(\frac{5}{y}\), the power of (y) is (-1). Due to the negative power, it is not a polynomial.
Step 3
Exam Tip
\(\frac{5}{y}\) में (y) की घात (-1) होती है। ऋणात्मक घात के कारण यह बहुपद नहीं है।
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व्यंजक \(8x^6-3x^4+x-10\) की घात क्या है?
What is the degree of \(8x^6-3x^4+x-10\)?
#definition-polynomial
#degree
#highest-power
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A (4)
B (8)
C (10)
D (6)
Explanation opens after your attempt
Step 1
Concept
The degree of a polynomial is given by the highest power of the variable. Here the highest power is (6).
Step 2
Why this answer is correct
The correct answer is D. (6). The degree of a polynomial is given by the highest power of the variable. Here the highest power is (6).
Step 3
Exam Tip
बहुपद की घात सबसे बड़ी चर-घात से मिलती है। यहाँ सबसे बड़ी घात (6) है।
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(p(x)=0) के लिए सही कथन कौन-सा है?
Which statement is correct for (p(x)=0)?
#definition-polynomial
#zero-polynomial
#degree
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A यह रैखिक बहुपद है / It is a linear polynomial
B यह स्थिर बहुपद (1) है / It is constant polynomial (1)
C यह शून्य बहुपद है और इसकी घात परिभाषित नहीं होती / It is the zero polynomial and its degree is not defined
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. यह शून्य बहुपद है और इसकी घात परिभाषित नहीं होती / It is the zero polynomial and its degree is not defined
Step 1
Concept
(p(x)=0) is called the zero polynomial. Its degree is not defined.
Step 2
Why this answer is correct
The correct answer is C. यह शून्य बहुपद है और इसकी घात परिभाषित नहीं होती / It is the zero polynomial and its degree is not defined. (p(x)=0) is called the zero polynomial. Its degree is not defined.
Step 3
Exam Tip
(p(x)=0) को शून्य बहुपद कहते हैं। इसकी घात परिभाषित नहीं होती।
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किस व्यंजक में गुणांक अपरिमेय है लेकिन व्यंजक फिर भी बहुपद है?
In which expression is the coefficient irrational but the expression is still a polynomial?
#definition-polynomial
#irrational-coefficient
#real-coefficients
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A (x^{1 / 2}+3)
B \(\sqrt{3}x^2-2x+5\)
C \(\frac{1}{x}+\sqrt{3}\)
D \(x^{-1}+\sqrt{5}x\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}x^2-2x+5\)
Step 1
Concept
\(\sqrt{3}\) is a real coefficient and is allowed. The powers of the variable are (2), (1), and (0), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{3}x^2-2x+5\). \(\sqrt{3}\) is a real coefficient and is allowed. The powers of the variable are (2), (1), and (0), so it is a polynomial.
Step 3
Exam Tip
\(\sqrt{3}\) वास्तविक गुणांक है और स्वीकार्य है। चर की घातें (2), (1) और (0) हैं इसलिए यह बहुपद है।
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कौन-सा व्यंजक (x) में द्विघात बहुपद है?
Which expression is a quadratic polynomial in (x)?
#definition-polynomial
#quadratic-polynomial
#degree-two
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A \(5x^2-4x+9\)
B \(x^3+x+1\)
C (7x-2)
D \(x^{-2}+5\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-4x+9\)
Step 1
Concept
A quadratic polynomial has degree (2). The highest power in \(5x^2-4x+9\) is (2).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-4x+9\). A quadratic polynomial has degree (2). The highest power in \(5x^2-4x+9\) is (2).
Step 3
Exam Tip
द्विघात बहुपद की घात (2) होती है। \(5x^2-4x+9\) की सबसे बड़ी घात (2) है।
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\(3x^5+0x^7-2x+4\) की घात क्या होगी?
What will be the degree of \(3x^5+0x^7-2x+4\)?
#definition-polynomial
#zero-coefficient
#degree
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A (7)
B (2)
C (5)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(0x^7\) is a zero term and does not determine the degree. The highest non-zero power is (5).
Step 2
Why this answer is correct
The correct answer is C. (5). \(0x^7\) is a zero term and does not determine the degree. The highest non-zero power is (5).
Step 3
Exam Tip
\(0x^7\) शून्य पद है और घात तय नहीं करता। सबसे बड़ी अशून्य घात (5) है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर की घात भिन्न है?
Which expression is not a polynomial because the variable has a fractional power?
#definition-polynomial
#fractional-exponent
#not-polynomial
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A \(x^4+2x\)
B \(5x^0-1\)
C \(7x^3+x\)
D (x^{2 / 3}+4)
Explanation opens after your attempt
Correct Answer
D. (x^{2 / 3}+4)
Step 1
Concept
In \(x^{2/3}\), the power is \(\frac{2}{3}\), which is not an integer. Polynomial powers must be non-negative integers.
Step 2
Why this answer is correct
The correct answer is D. \(x^{2 / 3}+4\). In \(x^{2/3}\), the power is \(\frac{2}{3}\), which is not an integer. Polynomial powers must be non-negative integers.
Step 3
Exam Tip
\(x^{2/3}\) में घात \(\frac{2}{3}\) है जो पूर्णांक नहीं है। बहुपद में घातें शून्य या धनात्मक पूर्णांक होनी चाहिए।
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कौन-सा बहुपद घन बहुपद है?
Which polynomial is a cubic polynomial?
#definition-polynomial
#cubic-polynomial
#classification
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A \(4x^3-6x+1\)
B \(x^2+8\)
C (9x-5)
D (11)
Explanation opens after your attempt
Correct Answer
A. \(4x^3-6x+1\)
Step 1
Concept
A cubic polynomial has degree (3). The highest power in \(4x^3-6x+1\) is (3).
Step 2
Why this answer is correct
The correct answer is A. \(4x^3-6x+1\). A cubic polynomial has degree (3). The highest power in \(4x^3-6x+1\) is (3).
Step 3
Exam Tip
घन बहुपद की घात (3) होती है। \(4x^3-6x+1\) में सबसे बड़ी घात (3) है।
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(12) को किस प्रकार का बहुपद माना जाता है?
What type of polynomial is (12) considered?
#definition-polynomial
#constant-polynomial
#degree-zero
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A शून्य बहुपद / Zero polynomial
B रैखिक बहुपद / Linear polynomial
C स्थिर बहुपद / Constant polynomial
D घन बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
C. स्थिर 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 C. स्थिर 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 स्थिर बहुपद है। शून्य से अलग स्थिर बहुपद की घात (0) होती है।
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किस व्यंजक में (x) हर में होने के कारण बहुपद नहीं है?
Which expression is not a polynomial because (x) is in the denominator?
#definition-polynomial
#denominator
#negative-power
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A \(x^2-3x+2\)
B \(\frac{x+5}{x}\)
C \(5x^4+1\)
D \(x^0+x\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{x+5}{x}\)
Step 1
Concept
\(\frac{x+5}{x}=1+\frac{5}{x}\) contains \(\frac{5}{x}\), whose power is (-1). So it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{x+5}{x}\). \(\frac{x+5}{x}=1+\frac{5}{x}\) contains \(\frac{5}{x}\), whose power is (-1). So it is not a polynomial.
Step 3
Exam Tip
\(\frac{x+5}{x}=1+\frac{5}{x}\) में \(\frac{5}{x}\) की घात (-1) है। इसलिए यह बहुपद नहीं है।
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(p(t)=2t-4 -7t-2 +3) में कौन-सा पद घात तय करता है?
In (p(t)=2t-4 -7t-2 +3), which term determines the degree?
#definition-polynomial
#degree-determining-term
#highest-power
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A (3)
B \(7t^2\)
C \(2t^4\)
D \(2t^4-7t^2\)
Explanation opens after your attempt
Correct Answer
C. \(2t^4\)
Step 1
Concept
The degree is determined by the non-zero term with the highest power. Here \(2t^4\) has the highest power (4).
Step 2
Why this answer is correct
The correct answer is C. \(2t^4\). The degree is determined by the non-zero term with the highest power. Here \(2t^4\) has the highest power (4).
Step 3
Exam Tip
घात सबसे बड़ी चर-घात वाले अशून्य पद से तय होती है। यहाँ \(2t^4\) में सबसे बड़ी घात (4) है।
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कौन-सा व्यंजक (z) में बहुपद है?
Which expression is a polynomial in (z)?
#definition-polynomial
#polynomial-in-z
#valid-polynomial
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A \(z^{-1}+2\)
B \(\sqrt{z}+5\)
C \(3z^4-z^2+8\)
D \(\frac{6}{z}+1\)
Explanation opens after your attempt
Correct Answer
C. \(3z^4-z^2+8\)
Step 1
Concept
In \(3z^4-z^2+8\), the powers of (z) are (4), (2), and (0). All powers are valid.
Step 2
Why this answer is correct
The correct answer is C. \(3z^4-z^2+8\). In \(3z^4-z^2+8\), the powers of (z) are (4), (2), and (0). All powers are valid.
Step 3
Exam Tip
\(3z^4-z^2+8\) में (z) की घातें (4), (2) और (0) हैं। सभी घातें मान्य हैं।
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बहुपद \(5x^3-2x^2+7x-1\) में कितने पद हैं?
How many terms are there in the polynomial \(5x^3-2x^2+7x-1\)?
#definition-polynomial
#terms
#counting
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
It has four terms: \(5x^3\), \(-2x^2\), (7x), and (-1). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (4). It has four terms: \(5x^3\), \(-2x^2\), (7x), and (-1). Count terms with their signs.
Step 3
Exam Tip
इसमें \(5x^3\), \(-2x^2\), (7x) और (-1) चार पद हैं। पदों को चिन्ह सहित गिनें।
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यदि किसी बहुपद की सबसे बड़ी घात (4) है, तो उसकी घात क्या होगी?
If the highest power of a polynomial is (4), what will be its degree?
#definition-polynomial
#degree
#concept
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A (0)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The degree of a polynomial is its highest variable power. Therefore, the degree will be (4).
Step 2
Why this answer is correct
The correct answer is C. (4). The degree of a polynomial is its highest variable power. Therefore, the degree will be (4).
Step 3
Exam Tip
बहुपद की घात उसकी सबसे बड़ी चर-घात ही होती है। इसलिए घात (4) होगी।
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कौन-सा व्यंजक \(\sqrt{x}\) के कारण बहुपद नहीं है?
Which expression is not a polynomial because of \(\sqrt{x}\)?
#definition-polynomial
#radical
#not-polynomial
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A \(x^2+\sqrt{2}\)
B \(3x+\sqrt{5}\)
C \(\sqrt{x}+2x\)
D \(7x^3-1\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x}+2x\)
Step 1
Concept
\(\sqrt{x}=x^{1/2}\), and \(\frac{1}{2}\) is not an integer power. Hence it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{x}+2x\). \(\sqrt{x}=x^{1/2}\), and \(\frac{1}{2}\) is not an integer power. Hence it is not a polynomial.
Step 3
Exam Tip
\(\sqrt{x}=x^{1/2}\) होता है और \(\frac{1}{2}\) पूर्णांक घात नहीं है। इसलिए यह बहुपद नहीं है।
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कौन-सा बहुपद रैखिक है?
Which polynomial is linear?
#definition-polynomial
#linear-polynomial
#degree-one
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A \(2x^2+x\)
B (6x-11)
C \(x^3+1\)
D (15)
Explanation opens after your attempt
Correct Answer
B. (6x-11)
Step 1
Concept
A linear polynomial has degree (1). In (6x-11), the highest power is (1).
Step 2
Why this answer is correct
The correct answer is B. (6x-11). A linear polynomial has degree (1). In (6x-11), the highest power is (1).
Step 3
Exam Tip
रैखिक बहुपद की घात (1) होती है। (6x-11) में सबसे बड़ी घात (1) है।
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\(x^2+3x^{1/3}+4\) बहुपद क्यों नहीं है?
Why is \(x^2+3x^{1/3}+4\) not a polynomial?
#definition-polynomial
#fractional-power
#reason
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A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (4) है / Because it has (4)
C क्योंकि (x^{1 / 3}) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 3}\) is not an integer
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि (x^{1 / 3}) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 3}\) is not an integer
Step 1
Concept
In a polynomial, powers of the variable must be integers. The power in \(x^{1/3}\) is not an integer.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(x^{1 / 3}\) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 3}\) is not an integer. In a polynomial, powers of the variable must be integers. The power in \(x^{1/3}\) is not an integer.
Step 3
Exam Tip
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{1/3}\) की घात पूर्णांक नहीं है।
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किस विकल्प में घात (0) का बहुपद है?
Which option is a polynomial of degree (0)?
#definition-polynomial
#degree-zero
#constant
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A (0)
B (x+5)
C (13)
D \(x^2+1\)
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). (13) is such a constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. (13). A non-zero constant polynomial has degree (0). (13) is such a constant polynomial.
Step 3
Exam Tip
शून्य से अलग स्थिर बहुपद की घात (0) होती है। (13) ऐसा स्थिर बहुपद है।
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कौन-सा व्यंजक (x) में बहुपद है यदि (a) को स्थिर माना जाए?
Which expression is a polynomial in (x) if (a) is treated as a constant?
#definition-polynomial
#parameter
#polynomial-in-x
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A \(ax^2+3x-1\)
B \(\frac{a}{x}+1\)
C \(x^{-1}+a\)
D \(\sqrt{x}+a\)
Explanation opens after your attempt
Correct Answer
A. \(ax^2+3x-1\)
Step 1
Concept
Treating (a) as a constant, \(ax^2\) has (x)-power (2). All powers of (x) are non-negative integers.
Step 2
Why this answer is correct
The correct answer is A. \(ax^2+3x-1\). Treating (a) as a constant, \(ax^2\) has (x)-power (2). All powers of (x) are non-negative integers.
Step 3
Exam Tip
(a) को स्थिर मानने पर \(ax^2\) में (x) की घात (2) है। सभी (x) घातें शून्य या धनात्मक पूर्णांक हैं।
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\(4x^2+\frac{3}{7}x-6\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(4x^2+\frac{3}{7}x-6\)?
#definition-polynomial
#fractional-coefficient
#valid-polynomial
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A यह बहुपद नहीं है क्योंकि गुणांक भिन्न है / It is not a polynomial because a coefficient is fractional
B यह बहुपद है क्योंकि चर की घातें मान्य हैं / It is a polynomial because the variable powers are valid
C यह बहुपद नहीं है क्योंकि स्थिर पद ऋणात्मक है / It is not a polynomial because the constant term is negative
D यह केवल शून्य बहुपद है / It is only the zero polynomial
Explanation opens after your attempt
Correct Answer
B. यह बहुपद है क्योंकि चर की घातें मान्य हैं / It is a polynomial because the variable powers are valid
Step 1
Concept
Fractional coefficients are allowed. Here the powers of the variable are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is B. यह बहुपद है क्योंकि चर की घातें मान्य हैं / It is a polynomial because the variable powers are valid. Fractional coefficients are allowed. Here the powers of the variable are (2), (1), and (0).
Step 3
Exam Tip
भिन्न गुणांक स्वीकार्य होते हैं। यहाँ चर की घातें (2), (1) और (0) हैं।
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कौन-सा व्यंजक (x) में बहुपद नहीं है लेकिन (x) के बिना स्थिर पद भी रखता है?
Which expression is not a polynomial in (x) but also has a constant term?
#definition-polynomial
#negative-exponent
#constant-term
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A \(x^2+5\)
B (3x+9)
C \(x^{-2}+7\)
D \(4x^3-1\)
Explanation opens after your attempt
Correct Answer
C. \(x^{-2}+7\)
Step 1
Concept
The power in \(x^{-2}\) is negative, so it is not a polynomial. (7) is only a constant term, and the issue is the negative power.
Step 2
Why this answer is correct
The correct answer is C. \(x^{-2}+7\). The power in \(x^{-2}\) is negative, so it is not a polynomial. (7) is only a constant term, and the issue is the negative power.
Step 3
Exam Tip
\(x^{-2}\) की घात ऋणात्मक है इसलिए यह बहुपद नहीं है। (7) केवल स्थिर पद है और समस्या ऋणात्मक घात से है।
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\(9x^0-4x+2x^2\) को बहुपद मानने का मुख्य कारण क्या है?
What is the main reason \(9x^0-4x+2x^2\) is considered a polynomial?
#definition-polynomial
#zero-power
#valid-polynomial
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A क्योंकि \(x^0=0\) है / Because \(x^0=0\)
B क्योंकि सभी (x)-घातें (0), (1), (2) हैं / Because all (x)-powers are (0), (1), (2)
C क्योंकि इसमें कोई स्थिर पद नहीं है / Because it has no constant term
D क्योंकि यह शून्य बहुपद है / Because it is the zero polynomial
Explanation opens after your attempt
Correct Answer
B. क्योंकि सभी (x)-घातें (0), (1), (2) हैं / Because all (x)-powers are (0), (1), (2)
Step 1
Concept
The power in \(x^0\) is (0), and \(x^0=1\) is considered. All powers are non-negative integers.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि सभी (x)-घातें (0), (1), (2) हैं / Because all (x)-powers are (0), (1), (2). The power in \(x^0\) is (0), and \(x^0=1\) is considered. All powers are non-negative integers.
Step 3
Exam Tip
\(x^0\) की घात (0) है और \(x^0=1\) माना जाता है। सभी घातें शून्य या धनात्मक पूर्णांक हैं।
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किस बहुपद की घात (2) नहीं है?
Which polynomial does not have degree (2)?
#definition-polynomial
#degree-three
#comparison
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A \(x^2+x+1\)
B \(4x^2-7\)
C \(6x^3-x+5\)
D \(9x^2\)
Explanation opens after your attempt
Correct Answer
C. \(6x^3-x+5\)
Step 1
Concept
The highest power in \(6x^3-x+5\) is (3). Therefore, its degree is not (2).
Step 2
Why this answer is correct
The correct answer is C. \(6x^3-x+5\). The highest power in \(6x^3-x+5\) is (3). Therefore, its degree is not (2).
Step 3
Exam Tip
\(6x^3-x+5\) की सबसे बड़ी घात (3) है। इसलिए इसकी घात (2) नहीं है।
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कौन-सा व्यंजक बहुपद है जिसमें \(x^2\) का पद गायब है?
Which expression is a polynomial in which the \(x^2\) term is missing?
#definition-polynomial
#missing-term
#valid-polynomial
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A \(x^3+5x-2\)
B \(x^{-3}+5x\)
C \(\sqrt{x}+5x\)
D \(\frac{1}{x^2}+x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3+5x-2\)
Step 1
Concept
A polynomial need not contain every power. \(x^3+5x-2\) has powers (3), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(x^3+5x-2\). A polynomial need not contain every power. \(x^3+5x-2\) has powers (3), (1), and (0).
Step 3
Exam Tip
बहुपद में हर घात का पद होना जरूरी नहीं है। \(x^3+5x-2\) में घातें (3), (1) और (0) हैं।
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यदि (p(x)=3x-2 -5), तो यह किस प्रकार का बहुपद है?
If (p(x)=3x-2 -5), what type of polynomial is it?
#definition-polynomial
#quadratic-binomial
#classification
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A रैखिक द्विपदी / Linear binomial
B द्विघात द्विपदी / Quadratic binomial
C घन त्रिपदी / Cubic trinomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात द्विपदी / Quadratic binomial
Step 1
Concept
Its degree is (2) and it has two terms. Therefore, it is a quadratic binomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात द्विपदी / Quadratic binomial. Its degree is (2) and it has two terms. Therefore, it is a quadratic binomial.
Step 3
Exam Tip
इसकी घात (2) है और इसमें दो पद हैं। इसलिए यह द्विघात द्विपदी है।
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कौन-सा कथन बहुपद की परिभाषा के अनुसार गलत है?
Which statement is wrong according to the definition of a polynomial?
#definition-polynomial
#condition
#false-statement
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A चर की घातें शून्य हो सकती हैं / Powers of the variable can be zero
B चर की घातें धनात्मक पूर्णांक हो सकती हैं / Powers of the variable can be positive integers
C चर की घातें ऋणात्मक हो सकती हैं / Powers of the variable can be negative
D गुणांक वास्तविक हो सकते हैं / Coefficients can be real
Explanation opens after your attempt
Correct Answer
C. चर की घातें ऋणात्मक हो सकती हैं / Powers of the variable can be negative
Step 1
Concept
Negative powers are not allowed in a polynomial. Powers must be zero or positive integers.
Step 2
Why this answer is correct
The correct answer is C. चर की घातें ऋणात्मक हो सकती हैं / Powers of the variable can be negative. Negative powers are not allowed in a polynomial. Powers must be zero or positive integers.
Step 3
Exam Tip
बहुपद में ऋणात्मक घातें स्वीकार्य नहीं होतीं। घातें शून्य या धनात्मक पूर्णांक होनी चाहिए।
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\(2x^4+5x^2+1\) में कौन-सी घातें उपस्थित हैं?
Which powers are present in \(2x^4+5x^2+1\)?
#definition-polynomial
#powers
#missing-powers
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A (4), (2), (0)
B (4), (5), (1)
C (2), (1), (-1)
D (4), \(\frac{1}{2}\), (0)
Explanation opens after your attempt
Correct Answer
A. (4), (2), (0)
Step 1
Concept
The power of \(2x^4\) is (4), the power of \(5x^2\) is (2), and the constant (1) is treated as degree (0).
Step 2
Why this answer is correct
The correct answer is A. (4), (2), (0). The power of \(2x^4\) is (4), the power of \(5x^2\) is (2), and the constant (1) is treated as degree (0).
Step 3
Exam Tip
\(2x^4\) की घात (4), \(5x^2\) की घात (2), और (1) स्थिर पद की घात (0) मानी जाती है।
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कौन-सा व्यंजक बहुपद है लेकिन स्थिर बहुपद नहीं है?
Which expression is a polynomial but not a constant polynomial?
#definition-polynomial
#constant-vs-linear
#classification
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A (5)
B (0)
C (7x+3)
D (-11)
Explanation opens after your attempt
Step 1
Concept
(7x+3) contains the variable (x), so it is not a constant polynomial. Still, it is a polynomial because the power is (1).
Step 2
Why this answer is correct
The correct answer is C. (7x+3). (7x+3) contains the variable (x), so it is not a constant polynomial. Still, it is a polynomial because the power is (1).
Step 3
Exam Tip
(7x+3) में चर (x) है इसलिए यह स्थिर बहुपद नहीं है। फिर भी घात (1) होने से यह बहुपद है।
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कौन-सा विकल्प (x) में बहुपद नहीं है क्योंकि चर मूल के नीचे है?
Which option is not a polynomial in (x) because the variable is under a root?
#definition-polynomial
#radical-variable
#not-polynomial
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A \(x^2+\sqrt{7}x\)
B \(5x+\sqrt{11}\)
C \(\sqrt{x^2}+3\)
D \(\sqrt{3}x^3+1\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x^2}+3\)
Step 1
Concept
\(\sqrt{x^2}\) is not treated as a polynomial term in the usual class (9) definition. If the variable is under a root, it is not considered a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{x^2}+3\). \(\sqrt{x^2}\) is not treated as a polynomial term in the usual class (9) definition. If the variable is under a root, it is not considered a polynomial.
Step 3
Exam Tip
\(\sqrt{x^2}\) को सामान्य रूप से बहुपद पद की तरह नहीं लिया जाता। कक्षा (9) में चर मूल के अंदर हो तो उसे बहुपद नहीं मानते।
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(p(x)=7x-4) की घात और प्रकार क्या है?
What are the degree and type of (p(x)=7x-4)?
#definition-polynomial
#degree-type
#linear
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A घात (0), स्थिर / Degree (0), constant
B घात (1), रैखिक / Degree (1), linear
C घात (2), द्विघात / Degree (2), quadratic
D घात (3), घन / Degree (3), cubic
Explanation opens after your attempt
Correct Answer
B. घात (1), रैखिक / Degree (1), linear
Step 1
Concept
The highest power in (7x-4) is (1). Therefore, it is a linear polynomial.
Step 2
Why this answer is correct
The correct answer is B. घात (1), रैखिक / Degree (1), linear. The highest power in (7x-4) is (1). Therefore, it is a linear polynomial.
Step 3
Exam Tip
(7x-4) में सबसे बड़ी घात (1) है। इसलिए यह रैखिक बहुपद है।
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कौन-सा व्यंजक (x) में बहुपद है और (x) की सबसे बड़ी घात (5) है?
Which expression is a polynomial in (x) and has highest power (5)?
#definition-polynomial
#degree-five
#valid-polynomial
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A \(x^5-2x^2+6\)
B (x^{5 / 2}+1)
C \(x^{-5}+2\)
D \(\frac{1}{x^5}+3\)
Explanation opens after your attempt
Correct Answer
A. \(x^5-2x^2+6\)
Step 1
Concept
In \(x^5-2x^2+6\), all powers are valid and the highest power is (5). So it is a polynomial of degree (5).
Step 2
Why this answer is correct
The correct answer is A. \(x^5-2x^2+6\). In \(x^5-2x^2+6\), all powers are valid and the highest power is (5). So it is a polynomial of degree (5).
Step 3
Exam Tip
\(x^5-2x^2+6\) में सभी घातें मान्य हैं और सबसे बड़ी घात (5) है। इसलिए यह घात (5) का बहुपद है।
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कौन-सा बहुपद केवल एक पद वाला है?
Which polynomial has only one term?
#definition-polynomial
#monomial
#one-term
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A \(x^2+x\)
B \(4x^7\)
C \(x^3-1\)
D \(2x^2+3x+5\)
Explanation opens after your attempt
Correct Answer
B. \(4x^7\)
Step 1
Concept
A polynomial with only one term is called a monomial. \(4x^7\) has only one term.
Step 2
Why this answer is correct
The correct answer is B. \(4x^7\). A polynomial with only one term is called a monomial. \(4x^7\) has only one term.
Step 3
Exam Tip
केवल एक पद वाले बहुपद को एकपदी कहते हैं। \(4x^7\) में केवल एक पद है।
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\(x^2-9\) की सही पहचान कौन-सी है?
Which is the correct identification of \(x^2-9\)?
#definition-polynomial
#quadratic-binomial
#classification
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A रैखिक एकपदी / Linear monomial
B द्विघात द्विपदी / Quadratic binomial
C घन त्रिपदी / Cubic trinomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात द्विपदी / Quadratic binomial
Step 1
Concept
\(x^2-9\) has degree (2) and two terms. Therefore, it is a quadratic binomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात द्विपदी / Quadratic binomial. \(x^2-9\) has degree (2) and two terms. Therefore, it is a quadratic binomial.
Step 3
Exam Tip
\(x^2-9\) की घात (2) है और इसमें दो पद हैं। इसलिए यह द्विघात द्विपदी है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि इसमें \(x^{-4}\) है?
Which expression is not a polynomial because it contains \(x^{-4}\)?
#definition-polynomial
#negative-exponent
#not-polynomial
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A \(x^4-4x+1\)
B \(5x^{-4}+2x\)
C \(x^0+4x\)
D \(8x^3+7\)
Explanation opens after your attempt
Correct Answer
B. \(5x^{-4}+2x\)
Step 1
Concept
The power in \(x^{-4}\) is negative. Negative powers are not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(5x^{-4}+2x\). The power in \(x^{-4}\) is negative. Negative powers are not allowed in a polynomial.
Step 3
Exam Tip
\(x^{-4}\) की घात ऋणात्मक है। बहुपद में ऋणात्मक घातें स्वीकार्य नहीं होतीं।
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किस विकल्प में (x) में बहुपद और उसकी घात दोनों सही हैं?
Which option correctly gives a polynomial in (x) and its degree?
#definition-polynomial
#degree-check
#valid-polynomial
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A \(x^3+2x\), घात (3) / \(x^3+2x\), degree (3)
B \(x^{-2}+1\), घात (2) / \(x^{-2}+1\), degree (2)
C \(\sqrt{x}+1\), घात (1) / \(\sqrt{x}+1\), degree (1)
D \(\frac{1}{x}+3\), घात (0) / \(\frac{1}{x}+3\), degree (0)
Explanation opens after your attempt
Correct Answer
A. \(x^3+2x\), घात (3) / \(x^3+2x\), degree (3)
Step 1
Concept
In \(x^3+2x\), the powers are (3) and (1). So it is a polynomial and its degree is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3+2x\), घात (3) / \(x^3+2x\), degree (3). In \(x^3+2x\), the powers are (3) and (1). So it is a polynomial and its degree is (3).
Step 3
Exam Tip
\(x^3+2x\) में घातें (3) और (1) हैं। इसलिए यह बहुपद है और इसकी घात (3) है।
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कौन-सा बहुपद चार पदों वाला है?
Which polynomial has four terms?
#definition-polynomial
#term-count
#four-terms
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A \(x^4+x^2+1\)
B \(2x^3-x^2+x-6\)
C \(7x^2-5\)
D (9x)
Explanation opens after your attempt
Correct Answer
B. \(2x^3-x^2+x-6\)
Step 1
Concept
\(2x^3-x^2+x-6\) has four terms. Separate terms by plus or minus signs.
Step 2
Why this answer is correct
The correct answer is B. \(2x^3-x^2+x-6\). \(2x^3-x^2+x-6\) has four terms. Separate terms by plus or minus signs.
Step 3
Exam Tip
\(2x^3-x^2+x-6\) में चार पद हैं। पदों को जोड़ या घटाव के चिन्ह से अलग करें।
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\(6x^2-5x+0\) की घात क्या है?
What is the degree of \(6x^2-5x+0\)?
#definition-polynomial
#degree
#zero-term
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A (0)
B (1)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The zero constant term does not affect the degree. The highest power is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). The zero constant term does not affect the degree. The highest power is (2).
Step 3
Exam Tip
शून्य स्थिर पद घात को प्रभावित नहीं करता। सबसे बड़ी घात (2) है।
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कौन-सा व्यंजक (x) में बहुपद है हालांकि उसमें \(x^3\) का पद नहीं है?
Which expression is a polynomial in (x) although it has no \(x^3\) term?
#definition-polynomial
#missing-term
#valid-polynomial
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A \(x^4+x^2+1\)
B \(x^{-4}+x^2\)
C \(\frac{1}{x^3}+x\)
D (x^{3 / 2}+x)
Explanation opens after your attempt
Correct Answer
A. \(x^4+x^2+1\)
Step 1
Concept
A missing power does not stop an expression from being a polynomial. In \(x^4+x^2+1\), all present powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^4+x^2+1\). A missing power does not stop an expression from being a polynomial. In \(x^4+x^2+1\), all present powers are valid.
Step 3
Exam Tip
किसी घात का पद गायब होना बहुपद बनने से नहीं रोकता। \(x^4+x^2+1\) में सभी उपस्थित घातें मान्य हैं।
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बहुपद की परिभाषा में चर की घात कैसी होनी चाहिए?
According to the definition of a polynomial, how should the power of the variable be?
#definition-polynomial
#condition
#concept
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A ऋणात्मक पूर्णांक / Negative integer
B शून्य या धनात्मक पूर्णांक / Zero or positive integer
C हमेशा भिन्न / Always fraction
D हमेशा (1) / Always (1)
Explanation opens after your attempt
Correct Answer
B. शून्य या धनात्मक पूर्णांक / Zero or positive integer
Step 1
Concept
In a polynomial, the powers of the variable are zero or positive integers. This is the most important condition.
Step 2
Why this answer is correct
The correct answer is B. शून्य या धनात्मक पूर्णांक / Zero or positive integer. In a polynomial, the powers of the variable are zero or positive integers. This is the most important condition.
Step 3
Exam Tip
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होती हैं। यही सबसे जरूरी शर्त है।
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कौन-सा व्यंजक बहुपद है जिसमें स्थिर पद ऋणात्मक है?
Which expression is a polynomial with a negative constant term?
#definition-polynomial
#negative-constant
#valid-polynomial
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A \(x^2+3x-8\)
B \(x^{-2}-8\)
C \(\sqrt{x}-8\)
D \(\frac{1}{x}-8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-8\)
Step 1
Concept
A negative constant term does not prevent an expression from being a polynomial. All powers in \(x^2+3x-8\) are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-8\). A negative constant term does not prevent an expression from being a polynomial. All powers in \(x^2+3x-8\) are valid.
Step 3
Exam Tip
ऋणात्मक स्थिर पद होना बहुपद बनने में बाधा नहीं है। \(x^2+3x-8\) की सभी घातें मान्य हैं।
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(p(x)=2x-3 +5x-2 -x+4) की सही पहचान कौन-सी है?
Which is the correct identification of (p(x)=2x-3 +5x-2 -x+4)?
#definition-polynomial
#cubic
#term-count
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A द्विघात त्रिपदी / Quadratic trinomial
B घन चार-पदी बहुपद / Cubic four-term polynomial
C रैखिक द्विपदी / Linear binomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. घन चार-पदी बहुपद / Cubic four-term polynomial
Step 1
Concept
Its degree is (3) and it has four terms. Therefore, it is a cubic four-term polynomial.
Step 2
Why this answer is correct
The correct answer is B. घन चार-पदी बहुपद / Cubic four-term polynomial. Its degree is (3) and it has four terms. Therefore, it is a cubic four-term polynomial.
Step 3
Exam Tip
इसकी घात (3) है और इसमें चार पद हैं। इसलिए यह घन चार-पदी बहुपद है।
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किस व्यंजक में (x) की घातें (5), (3) और (0) हैं?
In which expression are the powers of (x) (5), (3), and (0)?
#definition-polynomial
#powers
#constant-term
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A \(x^5+2x^3-7\)
B \(x^5+2x^{-3}-7\)
C (x^{5 / 3}+2x-3 -7)
D \(x^5+\frac{2}{x^3}-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^5+2x^3-7\)
Step 1
Concept
In \(x^5+2x^3-7\), the powers of (x) are (5), (3), and (0) for the constant term.
Step 2
Why this answer is correct
The correct answer is A. \(x^5+2x^3-7\). In \(x^5+2x^3-7\), the powers of (x) are (5), (3), and (0) for the constant term.
Step 3
Exam Tip
\(x^5+2x^3-7\) में (x) की घातें (5), (3) और स्थिर पद के लिए (0) हैं।
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कौन-सा व्यंजक वास्तविक गुणांक वाला बहुपद है?
Which expression is a polynomial with real coefficients?
#definition-polynomial
#real-coefficients
#decimal-coefficient
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A \(2.5x^2-3x+1\)
B \(x^{-1}+2.5\)
C \(\sqrt{x}+2.5\)
D \(\frac{x+1}{x}\)
Explanation opens after your attempt
Correct Answer
A. \(2.5x^2-3x+1\)
Step 1
Concept
The decimal (2.5) is also a real coefficient. All powers of the variable are non-negative integers.
Step 2
Why this answer is correct
The correct answer is A. \(2.5x^2-3x+1\). The decimal (2.5) is also a real coefficient. All powers of the variable are non-negative integers.
Step 3
Exam Tip
दशमलव (2.5) भी वास्तविक गुणांक है। चर की सभी घातें शून्य या धनात्मक पूर्णांक हैं।
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\(x^2+\frac{1}{x}+4\) बहुपद क्यों नहीं है?
Why is \(x^2+\frac{1}{x}+4\) not a polynomial?
#definition-polynomial
#negative-power
#reason
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A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें \(\frac{1}{x}\) है जिसकी घात (-1) है / Because it has \(\frac{1}{x}\), whose power is (-1)
C क्योंकि इसमें (4) है / Because it has (4)
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
B. क्योंकि इसमें \(\frac{1}{x}\) है जिसकी घात (-1) है / Because it has \(\frac{1}{x}\), whose power is (-1)
Step 1
Concept
\(\frac{1}{x}=x^{-1}\). An expression with a negative power is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि इसमें \(\frac{1}{x}\) है जिसकी घात (-1) है / Because it has \(\frac{1}{x}\), whose power is (-1). \(\frac{1}{x}=x^{-1}\). An expression with a negative power is not a polynomial.
Step 3
Exam Tip
\(\frac{1}{x}=x^{-1}\) होता है। ऋणात्मक घात वाला व्यंजक बहुपद नहीं होता।
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कौन-सा विकल्प बहुपद की सही उदाहरण-व्याख्या देता है?
Which option gives a correct example-explanation of a polynomial?
#definition-polynomial
#example-explanation
#valid-powers
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A \(x^2+1\) क्योंकि घातें (2) और (0) हैं / \(x^2+1\) because powers are (2) and (0)
B \(x^{-2}+1\) क्योंकि घात (-2) है / \(x^{-2}+1\) because power is (-2)
C \(\sqrt{x}+1\) क्योंकि मूल चिन्ह है / \(\sqrt{x}+1\) because there is a radical sign
D \(\frac{1}{x}+1\) क्योंकि हर में (x) है / \(\frac{1}{x}+1\) because (x) is in denominator
Explanation opens after your attempt
Correct Answer
A. \(x^2+1\) क्योंकि घातें (2) और (0) हैं / \(x^2+1\) because powers are (2) and (0)
Step 1
Concept
In \(x^2+1\), the powers are (2) and (0), which are valid. The other options contain invalid powers.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+1\) क्योंकि घातें (2) और (0) हैं / \(x^2+1\) because powers are (2) and (0). In \(x^2+1\), the powers are (2) and (0), which are valid. The other options contain invalid powers.
Step 3
Exam Tip
\(x^2+1\) में घातें (2) और (0) हैं जो मान्य हैं। बाकी विकल्पों में अमान्य घातें हैं।
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कौन-सा व्यंजक (x) में बहुपद है लेकिन (y) भी गुणांक की तरह शामिल है?
Which expression is a polynomial in (x) but includes (y) as a coefficient-like quantity?
#definition-polynomial
#polynomial-in-x
#coefficient-parameter
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A \(y x^3+2x-5\)
B \(\frac{y}{x}+2\)
C \(x^{-2}+y\)
D \(\sqrt{x}+y\)
Explanation opens after your attempt
Correct Answer
A. \(y x^3+2x-5\)
Step 1
Concept
With respect to (x), (y) can be treated like a coefficient. The powers of (x) are (3), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(y x^3+2x-5\). With respect to (x), (y) can be treated like a coefficient. The powers of (x) are (3), (1), and (0).
Step 3
Exam Tip
(x) के संदर्भ में (y) को गुणांक की तरह माना जा सकता है। (x) की घातें (3), (1) और (0) हैं।
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कौन-सा विकल्प \(x^3-2x+5\) की सही पहचान है?
Which option correctly identifies \(x^3-2x+5\)?
#definition-polynomial
#cubic-trinomial
#classification
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A यह रैखिक त्रिपदी है / It is a linear trinomial
B यह द्विघात द्विपदी है / It is a quadratic binomial
C यह घन त्रिपदी बहुपद है / It is a cubic trinomial polynomial
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. यह घन त्रिपदी बहुपद है / It is a cubic trinomial polynomial
Step 1
Concept
Its degree is (3) and it has three terms. Therefore, it is a cubic trinomial polynomial.
Step 2
Why this answer is correct
The correct answer is C. यह घन त्रिपदी बहुपद है / It is a cubic trinomial polynomial. Its degree is (3) and it has three terms. Therefore, it is a cubic trinomial polynomial.
Step 3
Exam Tip
इसकी घात (3) है और इसमें तीन पद हैं। इसलिए यह घन त्रिपदी बहुपद है।
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यदि (p(x)=0x-5 +4x-2 -3x+8), तो (p(x)) की घात क्या होगी?
If (p(x)=0x-5 +4x-2 -3x+8), what will be the degree of (p(x))?
#definition-polynomial
#zero-coefficient
#degree
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A (5)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(0x^5\) is a zero term, so it does not determine the degree. The highest non-zero power is (2).
Step 2
Why this answer is correct
The correct answer is B. (2). \(0x^5\) is a zero term, so it does not determine the degree. The highest non-zero power is (2).
Step 3
Exam Tip
\(0x^5\) शून्य पद है इसलिए घात तय नहीं करता। सबसे बड़ी अशून्य घात (2) है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर घात में है?
Which expression is not a polynomial because the variable is in the exponent?
#definition-polynomial
#variable-exponent
#not-polynomial
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A \(x^2+8\)
B \(2^x+x\)
C \(5x^4-1\)
D \(\sqrt{2}x+3\)
Explanation opens after your attempt
Correct Answer
B. \(2^x+x\)
Step 1
Concept
In a polynomial, the variable has fixed non-negative integer powers. In \(2^x\), the variable is in the exponent, so it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(2^x+x\). In a polynomial, the variable has fixed non-negative integer powers. In \(2^x\), the variable is in the exponent, so it is not a polynomial.
Step 3
Exam Tip
बहुपद में चर की घात निश्चित शून्य या धनात्मक पूर्णांक होती है। \(2^x\) में चर घात में है इसलिए यह बहुपद नहीं है।
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यदि (p(x)=ax-3 +2x-1) में (a=0) हो, तो बहुपद की घात क्या होगी?
If (a=0) in (p(x)=ax-3 +2x-1), what will be the degree of the polynomial?
#definition-polynomial
#parameter
#degree
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A (3)
B (2)
C (1)
D (0)
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Step 1
Concept
When (a=0), the \(x^3\) term disappears. The remaining polynomial (2x-1) has degree (1).
Step 2
Why this answer is correct
The correct answer is C. (1). When (a=0), the \(x^3\) term disappears. The remaining polynomial (2x-1) has degree (1).
Step 3
Exam Tip
(a=0) रखने पर \(x^3\) वाला पद हट जाता है। शेष बहुपद (2x-1) की घात (1) है।
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