कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि चर की घात ऋणात्मक है?
Which expression is not a polynomial in (x) because the variable has a negative power?
#definition-polynomial
#negative-exponent
#not-polynomial
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A \(3x^2+5\)
B \(7x^0-4x\)
C \(9x^4-x+2\)
D \(5x^{-3}+1\)
Explanation opens after your attempt
Correct Answer
D. \(5x^{-3}+1\)
Step 1
Concept
The power in \(x^{-3}\) is negative. Negative powers are not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is D. \(5x^{-3}+1\). The power in \(x^{-3}\) is negative. Negative powers are not allowed in a polynomial.
Step 3
Exam Tip
\(x^{-3}\) की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार्य नहीं होती।
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बहुपद \(6x^7-4x^3+x-8\) की घात क्या है?
What is the degree of the polynomial \(6x^7-4x^3+x-8\)?
#definition-polynomial
#degree
#highest-power
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A (3)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The degree of a polynomial is the highest power of the variable. Here the highest power is (7).
Step 2
Why this answer is correct
The correct answer is C. (7). The degree of a polynomial is the highest power of the variable. Here the highest power is (7).
Step 3
Exam Tip
बहुपद की घात सबसे बड़ी चर-घात होती है। यहाँ सबसे बड़ी घात (7) है।
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(23) को किस प्रकार का बहुपद माना जाता है?
What type of polynomial is (23) considered?
#definition-polynomial
#constant-polynomial
#degree-zero
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A स्थिर बहुपद / Constant polynomial
B रैखिक बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
A. स्थिर बहुपद / Constant polynomial
Step 1
Concept
(23) 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 A. स्थिर बहुपद / Constant polynomial. (23) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
(23) में कोई चर नहीं है इसलिए यह स्थिर बहुपद है। शून्य से अलग स्थिर बहुपद की घात (0) होती है।
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कौन-सा व्यंजक (t) में रैखिक बहुपद है?
Which expression is a linear polynomial in (t)?
#definition-polynomial
#linear-polynomial
#degree-one
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A \(t^2+1\)
B \(t^3-t\)
C (12)
D (5t-9)
Explanation opens after your attempt
Step 1
Concept
A linear polynomial has degree (1). In (5t-9), the highest power is (1).
Step 2
Why this answer is correct
The correct answer is D. (5t-9). A linear polynomial has degree (1). In (5t-9), the highest power is (1).
Step 3
Exam Tip
रैखिक बहुपद की घात (1) होती है। (5t-9) में सबसे बड़ी घात (1) है।
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शून्य बहुपद (0) की घात के बारे में सही कथन कौन-सा है?
Which statement is correct about the degree of the zero polynomial (0)?
#definition-polynomial
#zero-polynomial
#undefined-degree
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A इसकी घात (0) है / Its degree is (0)
B इसकी घात परिभाषित नहीं होती / Its degree is not defined
C इसकी घात (1) है / Its degree is (1)
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
B. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
(0) is the zero polynomial but its degree is not defined. Keep it separate from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is B. इसकी घात परिभाषित नहीं होती / Its degree is not defined. (0) is the zero polynomial but its degree is not defined. Keep it separate from a non-zero constant polynomial.
Step 3
Exam Tip
(0) शून्य बहुपद है लेकिन उसकी घात परिभाषित नहीं होती। इसे शून्य से अलग स्थिर बहुपद से अलग रखें।
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\(9x^0+4x\) में \(x^0\) किसके बराबर माना जाता है?
In \(9x^0+4x\), \(x^0\) is considered equal to what?
#definition-polynomial
#zero-power
#constant-term
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A (x)
B (0)
C (9)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(x^0=1\) when \(x\neq0\). So \(9x^0\) acts like a constant term.
Step 2
Why this answer is correct
The correct answer is D. (1). \(x^0=1\) when \(x\neq0\). So \(9x^0\) acts like a constant term.
Step 3
Exam Tip
\(x^0=1\) माना जाता है जब \(x\neq0\)। इसलिए \(9x^0\) स्थिर पद की तरह काम करता है।
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कौन-सा व्यंजक भिन्न गुणांक होने के बाद भी बहुपद है?
Which expression is a polynomial even though it has a fractional coefficient?
#definition-polynomial
#fractional-coefficient
#valid-polynomial
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A \(3x^2+\frac{5}{8}x-2\)
B \(\frac{3}{x}+2\)
C (x^{1 / 2}+5)
D \(x^{-1}+\frac{5}{8}\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+\frac{5}{8}x-2\)
Step 1
Concept
Fractional coefficients are allowed in polynomials. Here the powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+\frac{5}{8}x-2\). Fractional coefficients are allowed in polynomials. Here the powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
भिन्न गुणांक बहुपद में मान्य होते हैं। यहाँ (x) की घातें (2), (1) और (0) हैं।
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बहुपद \(x^4-3x^2+2x-11\) में कितने पद हैं?
How many terms are there in the polynomial \(x^4-3x^2+2x-11\)?
#definition-polynomial
#terms
#counting
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A (3)
B (4)
C (5)
D (2)
Explanation opens after your attempt
Step 1
Concept
It has four terms: \(x^4\), \(-3x^2\), (2x), and (-11). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is B. (4). It has four terms: \(x^4\), \(-3x^2\), (2x), and (-11). Count terms with their signs.
Step 3
Exam Tip
इसमें \(x^4\), \(-3x^2\), (2x) और (-11) चार पद हैं। पदों को चिन्ह सहित गिनें।
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(p(x)=7x-5 -2x+4) में \(x^4\), \(x^3\) और \(x^2\) पद नहीं हैं। इसकी घात क्या है?
In (p(x)=7x-5 -2x+4), the \(x^4\), \(x^3\), and \(x^2\) terms are missing. What is its degree?
#definition-polynomial
#missing-terms
#degree
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A (1)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Missing terms do not change the degree. The highest present power is (5).
Step 2
Why this answer is correct
The correct answer is D. (5). Missing terms do not change the degree. The highest present power is (5).
Step 3
Exam Tip
गायब पद घात को नहीं बदलते। सबसे बड़ी उपस्थित घात (5) है।
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कौन-सा विकल्प बहुपद की मुख्य शर्त सही बताता है?
Which option correctly states the main condition of a polynomial?
#definition-polynomial
#condition
#concept
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A चर की घातें ऋणात्मक पूर्णांक हों / Powers of the variable are negative integers
B चर की घातें शून्य या धनात्मक पूर्णांक हों / Powers of the variable are zero or positive integers
C चर हमेशा हर में हो / The variable is always in the denominator
D चर की घात हमेशा \(\frac{1}{2}\) हो / The variable power is always \(\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
B. चर की घातें शून्य या धनात्मक पूर्णांक हों / Powers of the variable are zero or positive integers
Step 1
Concept
In a polynomial, powers of the variable must be zero or positive integers. This is the most important condition in the definition.
Step 2
Why this answer is correct
The correct answer is B. चर की घातें शून्य या धनात्मक पूर्णांक हों / Powers of the variable are zero or positive integers. In a polynomial, powers of the variable must be zero or positive integers. This is the most important condition in the definition.
Step 3
Exam Tip
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए। यही परिभाषा की सबसे जरूरी शर्त है।
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\(x^3+x^{2/5}+1\) बहुपद क्यों नहीं है?
Why is \(x^3+x^{2/5}+1\) not a polynomial?
#definition-polynomial
#fractional-power
#not-polynomial
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A क्योंकि इसमें \(x^3\) है / Because it has \(x^3\)
B क्योंकि इसमें (1) है / Because it has (1)
C क्योंकि (x^{2 / 5}) की घात पूर्णांक नहीं है / Because the power in \(x^{2 / 5}\) 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^{2 / 5}) की घात पूर्णांक नहीं है / Because the power in \(x^{2 / 5}\) is not an integer
Step 1
Concept
In a polynomial, powers of the variable must be integers. The power in \(x^{2/5}\) is \(\frac{2}{5}\), which is not an integer.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(x^{2 / 5}\) की घात पूर्णांक नहीं है / Because the power in \(x^{2 / 5}\) is not an integer. In a polynomial, powers of the variable must be integers. The power in \(x^{2/5}\) is \(\frac{2}{5}\), which is not an integer.
Step 3
Exam Tip
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{2/5}\) की घात \(\frac{2}{5}\) है, जो पूर्णांक नहीं है।
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\(4x^3+0x^5-6x+2\) की घात क्या है?
What is the degree of \(4x^3+0x^5-6x+2\)?
#definition-polynomial
#zero-coefficient
#degree
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A (5)
B (3)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(0x^5\) is a zero term and does not determine the degree. The highest non-zero power is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). \(0x^5\) is a zero term and does not determine the degree. The highest non-zero power is (3).
Step 3
Exam Tip
\(0x^5\) शून्य पद है और घात तय नहीं करता। सबसे बड़ी अशून्य घात (3) है।
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कौन-सा व्यंजक (x) में बहुपद नहीं है लेकिन स्थिर पद रखता है?
Which expression is not a polynomial in (x) but has a constant term?
#definition-polynomial
#negative-exponent
#constant-term
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A \(x^2+3\)
B (4x+9)
C \(x^{-4}+8\)
D \(7x^3-1\)
Explanation opens after your attempt
Correct Answer
C. \(x^{-4}+8\)
Step 1
Concept
The power in \(x^{-4}\) is negative, so it is not a polynomial. (8) is only a constant term.
Step 2
Why this answer is correct
The correct answer is C. \(x^{-4}+8\). The power in \(x^{-4}\) is negative, so it is not a polynomial. (8) is only a constant term.
Step 3
Exam Tip
\(x^{-4}\) की घात ऋणात्मक है इसलिए यह बहुपद नहीं है। (8) केवल स्थिर पद है।
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कौन-सा विकल्प \(x^2-6x+9\) की सही पहचान है?
Which option correctly identifies \(x^2-6x+9\)?
#definition-polynomial
#quadratic-trinomial
#classification
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A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial
C घन त्रिपदी / Cubic trinomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial
Step 1
Concept
Its degree is (2) and it has three terms. Therefore, it is a quadratic trinomial polynomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial. Its degree is (2) and it has three terms. Therefore, it is a quadratic trinomial polynomial.
Step 3
Exam Tip
इसकी घात (2) है और इसमें तीन पद हैं। इसलिए यह द्विघात त्रिपदी बहुपद है।
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\(x^5+2x^3-7\) में कौन-सी घातें उपस्थित हैं?
Which powers are present in \(x^5+2x^3-7\)?
#definition-polynomial
#powers
#constant-term
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A (5), (3), (0)
B (5), (2), (-7)
C (3), (1), (0)
D (5), \(\frac{1}{2}\), (0)
Explanation opens after your attempt
Correct Answer
A. (5), (3), (0)
Step 1
Concept
The power of \(x^5\) is (5), the power of \(2x^3\) is (3), and the constant term is treated as power (0).
Step 2
Why this answer is correct
The correct answer is A. (5), (3), (0). The power of \(x^5\) is (5), the power of \(2x^3\) is (3), and the constant term is treated as power (0).
Step 3
Exam Tip
\(x^5\) की घात (5), \(2x^3\) की घात (3), और स्थिर पद की घात (0) मानी जाती है।
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कौन-सा व्यंजक बहुपद है लेकिन घात (2) का नहीं है?
Which expression is a polynomial but not of degree (2)?
#definition-polynomial
#degree-four
#comparison
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A \(x^2+5x+6\)
B \(6x^4-x+3\)
C \(\sqrt{x}+2\)
D \(\frac{1}{x}+x^2\)
Explanation opens after your attempt
Correct Answer
B. \(6x^4-x+3\)
Step 1
Concept
\(6x^4-x+3\) is a polynomial and its degree is (4). Therefore, it is not of degree (2).
Step 2
Why this answer is correct
The correct answer is B. \(6x^4-x+3\). \(6x^4-x+3\) is a polynomial and its degree is (4). Therefore, it is not of degree (2).
Step 3
Exam Tip
\(6x^4-x+3\) बहुपद है और इसकी घात (4) है। इसलिए इसकी घात (2) नहीं है।
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कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि (x) हर में है?
Which expression is not a polynomial in (x) because (x) is in the denominator?
#definition-polynomial
#denominator
#not-polynomial
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A \(x^3+2x\)
B \(5x^2-1\)
C \(\frac{x+4}{x}\)
D \(7x^0+3x\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{x+4}{x}\)
Step 1
Concept
\(\frac{x+4}{x}=1+\frac{4}{x}\) and \(\frac{4}{x}=4x^{-1}\). Due to the negative power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{x+4}{x}\). \(\frac{x+4}{x}=1+\frac{4}{x}\) and \(\frac{4}{x}=4x^{-1}\). Due to the negative power, it is not a polynomial.
Step 3
Exam Tip
\(\frac{x+4}{x}=1+\frac{4}{x}\) है और \(\frac{4}{x}=4x^{-1}\) है। ऋणात्मक घात के कारण यह बहुपद नहीं है।
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यदि बहुपद की सबसे बड़ी घात (3) हो, तो उसे क्या कहते हैं?
If the highest power of a polynomial is (3), what is it called?
#definition-polynomial
#cubic-polynomial
#classification
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A स्थिर बहुपद / Constant polynomial
B रैखिक बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D घन बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
D. घन बहुपद / Cubic polynomial
Step 1
Concept
A polynomial with highest power (3) is called cubic. Identify the type of polynomial from its degree.
Step 2
Why this answer is correct
The correct answer is D. घन बहुपद / Cubic polynomial. A polynomial with highest power (3) is called cubic. Identify the type of polynomial from its degree.
Step 3
Exam Tip
सबसे बड़ी घात (3) होने पर बहुपद घन कहलाता है। बहुपद का प्रकार घात से पहचानें।
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कौन-सा व्यंजक (x) में बहुपद है और \(x^2\) पद नहीं रखता?
Which expression is a polynomial in (x) and does not have an \(x^2\) term?
#definition-polynomial
#missing-term
#valid-polynomial
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A \(x^4+3x-5\)
B \(x^{-4}+3x\)
C \(\sqrt{x}+3x\)
D \(\frac{1}{x^2}+x\)
Explanation opens after your attempt
Correct Answer
A. \(x^4+3x-5\)
Step 1
Concept
A polynomial need not contain every power term. In \(x^4+3x-5\), the present powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^4+3x-5\). A polynomial need not contain every power term. In \(x^4+3x-5\), the present powers are valid.
Step 3
Exam Tip
बहुपद में हर घात का पद होना जरूरी नहीं है। \(x^4+3x-5\) में उपस्थित घातें मान्य हैं।
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(p(x)=2x-2 -5) की सही पहचान कौन-सी है?
Which is the correct identification of (p(x)=2x-2 -5)?
#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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(p(x)=9x-4) की घात और प्रकार क्या है?
What are the degree and type of (p(x)=9x-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 (9x-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 (9x-4) is (1). Therefore, it is a linear polynomial.
Step 3
Exam Tip
(9x-4) में सबसे बड़ी घात (1) है। इसलिए यह रैखिक बहुपद है।
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कौन-सा व्यंजक बहुपद है और उसकी घात (5) है?
Which expression is a polynomial of degree (5)?
#definition-polynomial
#degree-five
#valid-polynomial
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A (x^{5 / 2}+2)
B \(x^{-5}+4\)
C \(2x^5-x^2+3\)
D \(\frac{1}{x^5}+1\)
Explanation opens after your attempt
Correct Answer
C. \(2x^5-x^2+3\)
Step 1
Concept
In \(2x^5-x^2+3\), all powers are valid and the highest power is (5).
Step 2
Why this answer is correct
The correct answer is C. \(2x^5-x^2+3\). In \(2x^5-x^2+3\), all powers are valid and the highest power is (5).
Step 3
Exam Tip
\(2x^5-x^2+3\) में सभी घातें मान्य हैं और सबसे बड़ी घात (5) है।
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\(x^2+\frac{1}{x^3}+5\) बहुपद क्यों नहीं है?
Why is \(x^2+\frac{1}{x^3}+5\) not a polynomial?
#definition-polynomial
#negative-power
#denominator
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A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (5) है / Because it has (5)
C क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\)
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\)
Step 1
Concept
In \(\frac{1}{x^3}\), the power of (x) is (-3). Due to the negative power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(\frac{1}{x^3}=x^{-3}\) है / Because \(\frac{1}{x^3}=x^{-3}\). In \(\frac{1}{x^3}\), the power of (x) is (-3). Due to the negative power, it is not a polynomial.
Step 3
Exam Tip
\(\frac{1}{x^3}\) में (x) की घात (-3) है। ऋणात्मक घात के कारण यह बहुपद नहीं है।
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यदि (p(x)=3x-4 +2x-2 +1), तो यह किस घात का बहुपद है?
If (p(x)=3x-4 +2x-2 +1), what is the degree of this polynomial?
#definition-polynomial
#function-notation
#degree
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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) in \(x^4\). Therefore, the degree of (p(x)) is (4).
Step 2
Why this answer is correct
The correct answer is D. (4). The highest power is (4) in \(x^4\). Therefore, the degree of (p(x)) is (4).
Step 3
Exam Tip
सबसे बड़ी घात \(x^4\) में (4) है। इसलिए (p(x)) की घात (4) है।
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कौन-सा व्यंजक (z) में बहुपद है लेकिन (x) में नहीं पूछा गया है?
Which expression is a polynomial in (z), not asked in (x)?
#definition-polynomial
#polynomial-in-z
#variable
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A \(3x^2+z^{-1}\)
B \(4z^3-2z+9\)
C \(\frac{1}{z}+2\)
D \(\sqrt{z}+5\)
Explanation opens after your attempt
Correct Answer
B. \(4z^3-2z+9\)
Step 1
Concept
In \(4z^3-2z+9\), the powers of (z) are (3), (1), and (0). So it is a polynomial in (z).
Step 2
Why this answer is correct
The correct answer is B. \(4z^3-2z+9\). In \(4z^3-2z+9\), the powers of (z) are (3), (1), and (0). So it is a polynomial in (z).
Step 3
Exam Tip
\(4z^3-2z+9\) में (z) की घातें (3), (1) और (0) हैं। इसलिए यह (z) में बहुपद है।
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किस व्यंजक में (x) की घातें (6), (4) और (0) हैं?
In which expression are the powers of (x) (6), (4), and (0)?
#definition-polynomial
#powers
#constant-term
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A \(x^6+3x^4-5\)
B \(x^6+3x^{-4}-5\)
C (x^{6 / 4}+3x-4 -5)
D \(x^6+\frac{3}{x^4}-5\)
Explanation opens after your attempt
Correct Answer
A. \(x^6+3x^4-5\)
Step 1
Concept
In \(x^6+3x^4-5\), the powers of (x) are (6), (4), and (0) for the constant term.
Step 2
Why this answer is correct
The correct answer is A. \(x^6+3x^4-5\). In \(x^6+3x^4-5\), the powers of (x) are (6), (4), and (0) for the constant term.
Step 3
Exam Tip
\(x^6+3x^4-5\) में (x) की घातें (6), (4) और स्थिर पद के लिए (0) हैं।
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कौन-सा व्यंजक बहुपद है जिसमें अपरिमेय स्थिर पद है?
Which expression is a polynomial with an irrational constant term?
#definition-polynomial
#irrational-constant
#real-coefficients
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A \(x^2+\sqrt{x}\)
B \(x^{-2}+\sqrt{3}\)
C \(2x^3-5x+\sqrt{7}\)
D \(\frac{1}{x}+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
C. \(2x^3-5x+\sqrt{7}\)
Step 1
Concept
\(\sqrt{7}\) is a real constant term and is allowed. All powers of the variable are non-negative integers.
Step 2
Why this answer is correct
The correct answer is C. \(2x^3-5x+\sqrt{7}\). \(\sqrt{7}\) is a real constant term and is allowed. All powers of the variable are non-negative integers.
Step 3
Exam Tip
\(\sqrt{7}\) एक वास्तविक स्थिर पद है और मान्य है। चर की सभी घातें शून्य या धनात्मक पूर्णांक हैं।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि उसमें \(\log x\) है?
Which expression is not a polynomial because it contains \(\log x\)?
#definition-polynomial
#logarithmic-term
#not-polynomial
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A \(x^2+\log x\)
B \(x^2+5x+1\)
C \(7x^3-\sqrt{2}\)
D \(x^0+4x\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+\log x\)
Step 1
Concept
\(\log x\) is not a term with a non-negative integer power of the variable. Therefore, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+\log x\). \(\log x\) is not a term with a non-negative integer power of the variable. Therefore, it is not a polynomial.
Step 3
Exam Tip
\(\log x\) चर की शून्य या धनात्मक पूर्णांक घात वाला पद नहीं है। इसलिए यह बहुपद नहीं है।
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(p(x)=0x-3 +0x-2 +0x) के बारे में सही कथन कौन-सा है?
Which statement is correct about (p(x)=0x-3 +0x-2 +0x)?
#definition-polynomial
#zero-polynomial
#zero-coefficients
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A यह घात (3) का बहुपद है / It is a polynomial of degree (3)
B यह घात (2) का बहुपद है / It is a polynomial of degree (2)
C यह शून्य बहुपद है जिसकी घात परिभाषित नहीं है / It is the zero polynomial whose degree is not defined
D यह स्थिर बहुपद (1) है / It is constant polynomial (1)
Explanation opens after your attempt
Correct Answer
C. यह शून्य बहुपद है जिसकी घात परिभाषित नहीं है / It is the zero polynomial whose degree is not defined
Step 1
Concept
All terms have zero coefficients, so it is the zero polynomial. The degree of the zero polynomial is not defined.
Step 2
Why this answer is correct
The correct answer is C. यह शून्य बहुपद है जिसकी घात परिभाषित नहीं है / It is the zero polynomial whose degree is not defined. All terms have zero coefficients, so it is the zero polynomial. The degree of the zero polynomial is not defined.
Step 3
Exam Tip
सभी पदों के गुणांक शून्य हैं, इसलिए यह शून्य बहुपद है। शून्य बहुपद की घात परिभाषित नहीं होती।
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कौन-सा व्यंजक केवल सम घातों वाला बहुपद है?
Which expression is a polynomial with only even powers?
#definition-polynomial
#even-powers
#valid-polynomial
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A \(x^6-4x^2+9\)
B \(x^5+x^2+1\)
C \(x^{-2}+x^4\)
D \(\sqrt{x}+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^6-4x^2+9\)
Step 1
Concept
In the first option, the powers are (6), (2), and (0). All are even and valid for a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(x^6-4x^2+9\). In the first option, the powers are (6), (2), and (0). All are even and valid for a polynomial.
Step 3
Exam Tip
पहले विकल्प में घातें (6), (2) और (0) हैं। ये सभी सम और बहुपद के लिए मान्य हैं।
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कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि उसमें \(\sin x\) है?
Which expression is not a polynomial in (x) because it contains \(\sin x\)?
#definition-polynomial
#trigonometric-term
#not-polynomial
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A \(3x^2+\sin x\)
B \(3x^2+x+1\)
C \(7x^0-2x\)
D \(\sqrt{5}x^3+4\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+\sin x\)
Step 1
Concept
Polynomial terms use fixed non-negative integer powers of the variable. \(\sin x\) is not such a term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+\sin x\). Polynomial terms use fixed non-negative integer powers of the variable. \(\sin x\) is not such a term.
Step 3
Exam Tip
बहुपद के पद चर की निश्चित शून्य या धनात्मक पूर्णांक घातों में होते हैं। \(\sin x\) ऐसा पद नहीं है।
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किस व्यंजक को \(x\neq0\) पर सरल करने के बाद बहुपद \(x^2+1\) मिलेगा?
Which expression gives the polynomial \(x^2+1\) after simplification for \(x\neq0\)?
#definition-polynomial
#simplification
#valid-polynomial
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A \(\frac{x^3+x}{x}\)
B \(\frac{x^2+1}{x}\)
C \(\frac{x+1}{x^2}\)
D \(\frac{1}{x}+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{x^3+x}{x}\)
Step 1
Concept
\(\frac{x^3+x}{x}=x^2+1\). In the simplified form, the powers are (2) and (0), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{x^3+x}{x}\). \(\frac{x^3+x}{x}=x^2+1\). In the simplified form, the powers are (2) and (0), so it is a polynomial.
Step 3
Exam Tip
\(\frac{x^3+x}{x}=x^2+1\) है। सरल रूप में घातें (2) और (0) हैं, इसलिए यह बहुपद है।
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कौन-सा विकल्प \(x^3-2x^2+5x-7\) की सही पहचान देता है?
Which option gives the correct identification of \(x^3-2x^2+5x-7\)?
#definition-polynomial
#cubic
#term-count
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A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी / Quadratic trinomial
C घन चार-पदी बहुपद / Cubic four-term polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. 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 C. 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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यदि (p(x)=0x-5 +8x-3 -2x+6), तो (p(x)) की घात क्या होगी?
If (p(x)=0x-5 +8x-3 -2x+6), what will be the degree of (p(x))?
#definition-polynomial
#zero-coefficient
#degree
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A (5)
B (3)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(0x^5\) is a zero term and does not determine the degree. The highest non-zero power is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). \(0x^5\) is a zero term and does not determine the degree. The highest non-zero power is (3).
Step 3
Exam Tip
\(0x^5\) शून्य पद है और घात तय नहीं करता। सबसे बड़ी अशून्य घात (3) है।
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कौन-सा व्यंजक बहुपद है क्योंकि \(\sqrt{13}\) केवल गुणांक है?
Which expression is a polynomial because \(\sqrt{13}\) is only a coefficient?
#definition-polynomial
#irrational-coefficient
#valid-polynomial
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A \(\sqrt{13}x^2-4x+1\)
B \(\sqrt{x}+13\)
C \(x^{-2}+\sqrt{13}\)
D \(\frac{\sqrt{13}}{x}+2\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{13}x^2-4x+1\)
Step 1
Concept
\(\sqrt{13}\) is a real coefficient and is allowed in a polynomial. The powers of the variable are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{13}x^2-4x+1\). \(\sqrt{13}\) is a real coefficient and is allowed in a polynomial. The powers of the variable are (2), (1), and (0).
Step 3
Exam Tip
\(\sqrt{13}\) वास्तविक गुणांक है और बहुपद में मान्य है। चर की घातें (2), (1) और (0) हैं।
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किस व्यंजक में (x) की घातें (4), (1) और (0) हैं?
In which expression are the powers of (x) (4), (1), and (0)?
#definition-polynomial
#powers
#constant-term
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A \(x^4+7x-3\)
B \(x^4+7x^{-1}-3\)
C (x^{4 / 1}+7x^{1 / 2}-3)
D \(\frac{x^4+7}{x}-3\)
Explanation opens after your attempt
Correct Answer
A. \(x^4+7x-3\)
Step 1
Concept
In \(x^4+7x-3\), the powers are (4), (1), and (0) for the constant term. All powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^4+7x-3\). In \(x^4+7x-3\), the powers are (4), (1), and (0) for the constant term. All powers are valid.
Step 3
Exam Tip
\(x^4+7x-3\) में घातें (4), (1) और स्थिर पद के लिए (0) हैं। सभी घातें मान्य हैं।
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कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि उसमें (x) भाजक में छिपा है?
Which expression is not a polynomial in (x) because (x) is hidden in the divisor?
#definition-polynomial
#hidden-denominator
#not-polynomial
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A \(x^2+\frac{x}{3}+1\)
B \(\frac{2x^2+5}{x}\)
C \(5x^3-2x+1\)
D \(4x^0+7x\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{2x^2+5}{x}\)
Step 1
Concept
\(\frac{2x^2+5}{x}=2x+\frac{5}{x}\). In \(\frac{5}{x}\), the power of (x) is (-1).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2x^2+5}{x}\). \(\frac{2x^2+5}{x}=2x+\frac{5}{x}\). In \(\frac{5}{x}\), the power of (x) is (-1).
Step 3
Exam Tip
\(\frac{2x^2+5}{x}=2x+\frac{5}{x}\) है। \(\frac{5}{x}\) में (x) की घात (-1) है।
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(p(x)=4x-2 -9x+11) की सही पहचान कौन-सी है?
Which is the correct identification of (p(x)=4x-2 -9x+11)?
#definition-polynomial
#quadratic-trinomial
#classification
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A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी / Quadratic trinomial
C घन त्रिपदी / Cubic trinomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात त्रिपदी / Quadratic trinomial
Step 1
Concept
Its highest power is (2) and it has three terms. Therefore, it is a quadratic trinomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात त्रिपदी / Quadratic trinomial. Its highest power is (2) and it has three terms. Therefore, it is a quadratic trinomial.
Step 3
Exam Tip
इसकी सबसे बड़ी घात (2) है और इसमें तीन पद हैं। इसलिए यह द्विघात त्रिपदी है।
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कौन-सा व्यंजक बहुपद है लेकिन एकपदी नहीं है और द्विपदी भी नहीं है?
Which expression is a polynomial but neither a monomial nor a binomial?
#definition-polynomial
#trinomial
#term-count
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A \(6x^2\)
B \(x^3-8\)
C \(2x^2+x-5\)
D \(x^{-1}+2\)
Explanation opens after your attempt
Correct Answer
C. \(2x^2+x-5\)
Step 1
Concept
\(2x^2+x-5\) has three terms, so it is a trinomial. All its powers are valid.
Step 2
Why this answer is correct
The correct answer is C. \(2x^2+x-5\). \(2x^2+x-5\) has three terms, so it is a trinomial. All its powers are valid.
Step 3
Exam Tip
\(2x^2+x-5\) में तीन पद हैं इसलिए यह त्रिपदी है। इसकी सभी घातें मान्य हैं।
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किस व्यंजक में \(\frac{1}{2}\) गुणांक है लेकिन वह बहुपद है?
Which expression has coefficient \(\frac{1}{2}\) but is still a polynomial?
#definition-polynomial
#fractional-coefficient
#valid-powers
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A \(\frac{1}{2}x^3+4x-6\)
B \(\frac{1}{2x}+4\)
C (x^{1 / 2}+4x)
D \(x^{-2}+\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}x^3+4x-6\)
Step 1
Concept
Fractional coefficients are allowed. In \(\frac{1}{2}x^3+4x-6\), the powers of (x) are (3), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}x^3+4x-6\). Fractional coefficients are allowed. In \(\frac{1}{2}x^3+4x-6\), the powers of (x) are (3), (1), and (0).
Step 3
Exam Tip
भिन्न गुणांक मान्य होते हैं। \(\frac{1}{2}x^3+4x-6\) में (x) की घातें (3), (1) और (0) हैं।
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यदि (q(x)=x-6 +2x-4 +3x-2 +4), तो यह किस प्रकार की घातों वाला बहुपद है?
If (q(x)=x-6 +2x-4 +3x-2 +4), what type of powers does this polynomial have?
#definition-polynomial
#even-powers
#valid-polynomial
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A केवल सम घातें / Only even powers
B केवल विषम घातें / Only odd powers
C ऋणात्मक घातें / Negative powers
D भिन्न घातें / Fractional powers
Explanation opens after your attempt
Correct Answer
A. केवल सम घातें / Only even powers
Step 1
Concept
It has powers (6), (4), (2), and (0). All are even and valid for a polynomial.
Step 2
Why this answer is correct
The correct answer is A. केवल सम घातें / Only even powers. It has powers (6), (4), (2), and (0). All are even and valid for a polynomial.
Step 3
Exam Tip
इसमें घातें (6), (4), (2) और (0) हैं। ये सभी सम और बहुपद के लिए मान्य हैं।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि उसमें (x) की घात \(-\frac{1}{2}\) है?
Which expression is not a polynomial because it has power \(-\frac{1}{2}\) of (x)?
#definition-polynomial
#fractional-negative-power
#not-polynomial
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A \(x^2+3x+1\)
B (x^{-1 / 2}+5)
C \(x^0+2x\)
D \(4x^3-7\)
Explanation opens after your attempt
Correct Answer
B. (x^{-1 / 2}+5)
Step 1
Concept
\(-\frac{1}{2}\) is neither zero nor a positive integer. So this power is not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^{-1 / 2}+5\). \(-\frac{1}{2}\) is neither zero nor a positive integer. So this power is not valid in a polynomial.
Step 3
Exam Tip
\(-\frac{1}{2}\) न तो शून्य है और न धनात्मक पूर्णांक। इसलिए यह घात बहुपद में मान्य नहीं है।
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कौन-सा व्यंजक (x) में बहुपद है यदि (b) को स्थिर माना जाए?
Which expression is a polynomial in (x) if (b) is treated as a constant?
#definition-polynomial
#parameter
#polynomial-in-x
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A \(b x^4-3b x+2\)
B \(\frac{b}{x}+2\)
C \(x^{-4}+b\)
D \(b\sqrt{x}+1\)
Explanation opens after your attempt
Correct Answer
A. \(b x^4-3b x+2\)
Step 1
Concept
(b) can be treated as a coefficient with respect to (x). The powers of (x) are (4), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(b x^4-3b x+2\). (b) can be treated as a coefficient with respect to (x). The powers of (x) are (4), (1), and (0).
Step 3
Exam Tip
(b) को (x) के संदर्भ में गुणांक माना जा सकता है। (x) की घातें (4), (1) और (0) हैं।
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\(x^3+x^2+x+1\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(x^3+x^2+x+1\)?
#definition-polynomial
#cubic
#term-count
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A यह चार पदों वाला घन बहुपद है / It is a cubic polynomial with four terms
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह स्थिर बहुपद है / It is a constant polynomial
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
A. यह चार पदों वाला घन बहुपद है / It is a cubic polynomial with four terms
Step 1
Concept
It has four terms and the highest power is (3). Therefore, it is a cubic polynomial with four terms.
Step 2
Why this answer is correct
The correct answer is A. यह चार पदों वाला घन बहुपद है / It is a cubic polynomial with four terms. It has four terms and the highest power is (3). Therefore, it is a cubic polynomial with four terms.
Step 3
Exam Tip
इसमें चार पद हैं और सबसे बड़ी घात (3) है। इसलिए यह चार पदों वाला घन बहुपद है।
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कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि उसमें \(\tan x\) है?
Which expression is not a polynomial in (x) because it contains \(\tan x\)?
#definition-polynomial
#trigonometric-term
#not-polynomial
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A \(x^2+\tan x\)
B \(x^2+5x+4\)
C \(7x^0-3x\)
D \(\sqrt{3}x^2+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+\tan x\)
Step 1
Concept
Polynomial terms use fixed non-negative integer powers of the variable. \(\tan x\) is not such a term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+\tan x\). Polynomial terms use fixed non-negative integer powers of the variable. \(\tan x\) is not such a term.
Step 3
Exam Tip
बहुपद के पद चर की निश्चित शून्य या धनात्मक पूर्णांक घातों में होते हैं। \(\tan x\) ऐसा पद नहीं है।
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यदि (p(x)=5x-3 +0x-2 +0x-12), तो (p(x)) में कितने अशून्य पद हैं?
If (p(x)=5x-3 +0x-2 +0x-12), how many non-zero terms are there in (p(x))?
#definition-polynomial
#zero-coefficient
#term-count
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
\(0x^2\) and (0x) are zero terms. The non-zero terms are \(5x^3\) and (-12).
Step 2
Why this answer is correct
The correct answer is B. (2). \(0x^2\) and (0x) are zero terms. The non-zero terms are \(5x^3\) and (-12).
Step 3
Exam Tip
\(0x^2\) और (0x) शून्य पद हैं। अशून्य पद \(5x^3\) और (-12) हैं।
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कौन-सा व्यंजक (x) में बहुपद है लेकिन उसका स्थिर पद नहीं लिखा गया है?
Which expression is a polynomial in (x) but its constant term is not written?
#definition-polynomial
#constant-term
#valid-polynomial
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A \(4x^4-3x^2\)
B \(4x^4-3\)
C \(x^{-4}+3x\)
D \(\sqrt{x}+3x\)
Explanation opens after your attempt
Correct Answer
A. \(4x^4-3x^2\)
Step 1
Concept
In \(4x^4-3x^2\), there is no separate constant term, so the constant term is considered (0). All powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(4x^4-3x^2\). In \(4x^4-3x^2\), there is no separate constant term, so the constant term is considered (0). All powers are valid.
Step 3
Exam Tip
\(4x^4-3x^2\) में कोई अलग स्थिर पद नहीं है, इसलिए स्थिर पद (0) माना जाता है। सभी घातें मान्य हैं।
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\(\frac{x^4+x^3}{x^2}\) को \(x\neq0\) पर सरल करने के बाद यह बहुपद क्यों नहीं है?
Why is \(\frac{x^4+x^3}{x^2}\) not a polynomial after simplifying for \(x\neq0\)?
#definition-polynomial
#simplification
#valid-polynomial
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A क्योंकि यह \(x^2+x\) बनता है / Because it becomes \(x^2+x\)
B क्योंकि यह \(x^2+\frac{1}{x}\) बनता है / Because it becomes \(x^2+\frac{1}{x}\)
C क्योंकि यह \(x^4+x^3\) रहता है / Because it remains \(x^4+x^3\)
D यह बहुपद नहीं बल्कि शून्य है / It is zero, not a polynomial
Explanation opens after your attempt
Correct Answer
A. क्योंकि यह \(x^2+x\) बनता है / Because it becomes \(x^2+x\)
Step 1
Concept
\(\frac{x^4+x^3}{x^2}=x^2+x\). It is a polynomial, so the correct reason is that powers (2) and (1) are valid.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि यह \(x^2+x\) बनता है / Because it becomes \(x^2+x\). \(\frac{x^4+x^3}{x^2}=x^2+x\). It is a polynomial, so the correct reason is that powers (2) and (1) are valid.
Step 3
Exam Tip
\(\frac{x^4+x^3}{x^2}=x^2+x\) है। यह बहुपद है, इसलिए सही कारण यह है कि इसमें घातें (2) और (1) मान्य हैं।
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((x+2)2 ) के बारे में सही कथन कौन-सा है?
Which statement is correct about ((x+2)2 )?
#definition-polynomial
#expanded-form
#quadratic
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A यह बहुपद नहीं है क्योंकि इसमें कोष्ठक है / It is not a polynomial because it has brackets
B यह रैखिक बहुपद है / It is a linear polynomial
C यह द्विघात बहुपद है / It is a quadratic polynomial
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
C. यह द्विघात बहुपद है / It is a quadratic polynomial
Step 1
Concept
The expanded form is \(x^2+4x+4\). The highest power is (2), so it is a quadratic polynomial.
Step 2
Why this answer is correct
The correct answer is C. यह द्विघात बहुपद है / It is a quadratic polynomial. The expanded form is \(x^2+4x+4\). The highest power is (2), so it is a quadratic polynomial.
Step 3
Exam Tip
विस्तारित रूप \(x^2+4x+4\) है। सबसे बड़ी घात (2) है, इसलिए यह द्विघात बहुपद है।
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कौन-सा व्यंजक (x) में बहुपद है लेकिन लिखे हुए रूप में घातें घटते क्रम में नहीं हैं?
Which expression is a polynomial in (x) but is not written in descending powers?
#definition-polynomial
#order-of-terms
#valid-polynomial
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A \(5+x^3-2x\)
B \(x^{-1}+x^2\)
C \(\sqrt{x}+x^2\)
D \(\frac{1}{x}+5\)
Explanation opens after your attempt
Correct Answer
A. \(5+x^3-2x\)
Step 1
Concept
In \(5+x^3-2x\), the powers are (0), (3), and (1), but all are valid. Writing in descending order is not required.
Step 2
Why this answer is correct
The correct answer is A. \(5+x^3-2x\). In \(5+x^3-2x\), the powers are (0), (3), and (1), but all are valid. Writing in descending order is not required.
Step 3
Exam Tip
\(5+x^3-2x\) में घातें (0), (3), (1) हैं, पर सभी मान्य हैं। घटते क्रम में लिखना जरूरी नहीं है।
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