निम्न में से कौन-सा व्यंजक (x) में बहुपद है?
Which of the following expressions is a polynomial in (x)?
#definition-polynomial
#nonnegative-powers
#basics
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A \(x^2+3x-5\)
B \(\frac{1}{x}+2\)
C \(\sqrt{x}+4\)
D \(x^{-1}+7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-5\)
Step 1
Concept
In a polynomial, powers of the variable are non-negative integers. Check the power of every term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-5\). In a polynomial, powers of the variable are non-negative integers. Check the power of every term.
Step 3
Exam Tip
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होती हैं। हर पद की घात जाँचें।
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कौन-सा व्यंजक (x) में बहुपद नहीं है?
Which expression is not a polynomial in (x)?
#definition-polynomial
#negative-power
#not-polynomial
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A \(4x^3-2x+1\)
B \(7x^2\)
C \(\frac{5}{x}+3\)
D (9)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5}{x}+3\)
Step 1
Concept
In \(\frac{5}{x}\), the power of (x) is (-1). An expression with a negative power is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5}{x}+3\). In \(\frac{5}{x}\), the power of (x) is (-1). An expression with a negative power is not a polynomial.
Step 3
Exam Tip
\(\frac{5}{x}\) में (x) की घात (-1) है। ऋणात्मक घात वाला व्यंजक बहुपद नहीं होता।
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व्यंजक \(6x^4-3x^2+x-8\) की घात क्या है?
What is the degree of \(6x^4-3x^2+x-8\)?
#definition-polynomial
#degree
#highest-power
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A (2)
B (4)
C (6)
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 (4).
Step 2
Why this answer is correct
The correct answer is B. (4). The degree of a polynomial is the highest power of the variable. Here the highest power is (4).
Step 3
Exam Tip
बहुपद की घात चर की सबसे बड़ी घात होती है। यहाँ सबसे बड़ी घात (4) है।
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(11) किस प्रकार का बहुपद है?
What type of polynomial is (11)?
#definition-polynomial
#constant-polynomial
#degree-zero
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A शून्य बहुपद / Zero polynomial
B रैखिक बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
D. स्थिर बहुपद / Constant polynomial
Step 1
Concept
(11) 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. स्थिर बहुपद / Constant polynomial. (11) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
(11) 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 चर की घात पूर्णांक तो है लेकिन बहुपद बनने के लिए स्वीकार्य नहीं है?
In which expression is the variable's power an integer but not acceptable for being a polynomial?
#definition-polynomial
#negative-exponent
#condition
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A \(x^5+1\)
B \(3x^{-2}+4\)
C \(2x^0+7\)
D \(9x^3-x\)
Explanation opens after your attempt
Correct Answer
B. \(3x^{-2}+4\)
Step 1
Concept
In a polynomial, powers must be zero or positive integers. (-2) is an integer but not acceptable because it is negative.
Step 2
Why this answer is correct
The correct answer is B. \(3x^{-2}+4\). In a polynomial, powers must be zero or positive integers. (-2) is an integer but not acceptable because it is negative.
Step 3
Exam Tip
बहुपद में घातें केवल शून्य या धनात्मक पूर्णांक होनी चाहिए। (-2) पूर्णांक है पर धनात्मक नहीं है।
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कौन-सा व्यंजक द्विघात बहुपद है?
Which expression is a quadratic polynomial?
#definition-polynomial
#quadratic-polynomial
#degree-two
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A \(x^3+2x+1\)
B \(4x^2-5x+9\)
C (7x-1)
D \(\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2-5x+9\)
Step 1
Concept
A quadratic polynomial has degree (2). In \(4x^2-5x+9\), the highest power is (2).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2-5x+9\). A quadratic polynomial has degree (2). In \(4x^2-5x+9\), the highest power is (2).
Step 3
Exam Tip
द्विघात बहुपद की घात (2) होती है। \(4x^2-5x+9\) में सबसे बड़ी घात (2) है।
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कौन-सा व्यंजक घन बहुपद है?
Which expression is a cubic polynomial?
#definition-polynomial
#cubic-polynomial
#degree-three
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A \(2x^3-x+4\)
B \(x^2+5\)
C (8x-3)
D \(x^{-3}+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3-x+4\)
Step 1
Concept
A cubic polynomial has degree (3). In \(2x^3-x+4\), the highest power is (3).
Step 2
Why this answer is correct
The correct answer is A. \(2x^3-x+4\). A cubic polynomial has degree (3). In \(2x^3-x+4\), the highest power is (3).
Step 3
Exam Tip
घन बहुपद की घात (3) होती है। \(2x^3-x+4\) में सबसे बड़ी घात (3) है।
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बहुपद (0) के बारे में कौन-सा कथन सही है?
Which statement is correct about the polynomial (0)?
#definition-polynomial
#zero-polynomial
#undefined-degree
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A इसकी घात (1) है / Its degree is (1)
B इसकी घात (0) है / Its degree is (0)
C इसकी घात परिभाषित नहीं होती / Its degree is not defined
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
(0) is the zero polynomial but its degree is not defined. In exams, keep zero polynomial and constant polynomial separate.
Step 2
Why this answer is correct
The correct answer is C. इसकी घात परिभाषित नहीं होती / Its degree is not defined. (0) is the zero polynomial but its degree is not defined. In exams, keep zero polynomial and constant polynomial separate.
Step 3
Exam Tip
(0) शून्य बहुपद है लेकिन उसकी घात परिभाषित नहीं होती। परीक्षा में शून्य बहुपद और स्थिर बहुपद को अलग रखें।
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\(5x^0+2x\) को बहुपद मानते समय \(x^0\) किसके बराबर माना जाता है?
While treating \(5x^0+2x\) as a polynomial, \(x^0\) is considered equal to what?
#definition-polynomial
#zero-power
#constant-term
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A (x)
B (0)
C (1)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(x^0=1\) when \(x\neq0\). So \(5x^0\) acts like a constant term.
Step 2
Why this answer is correct
The correct answer is C. (1). \(x^0=1\) when \(x\neq0\). So \(5x^0\) acts like a constant term.
Step 3
Exam Tip
\(x^0=1\) होता है जब \(x\neq0\) हो। इसलिए \(5x^0\) स्थिर पद की तरह काम करता है।
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कौन-सा व्यंजक बहुपद है जिसमें गुणांक अपरिमेय संख्या है?
Which expression is a polynomial with an irrational coefficient?
#definition-polynomial
#irrational-coefficient
#real-coefficients
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A (x^{1 / 2}+2)
B \(\sqrt{2}x^2+3x-1\)
C \(\frac{1}{x}+ \sqrt{2}\)
D \(x^{-2}+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{2}x^2+3x-1\)
Step 1
Concept
Coefficients may be real numbers, so \(\sqrt{2}\) is allowed. Powers of the variable must be non-negative integers.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{2}x^2+3x-1\). Coefficients may be real numbers, so \(\sqrt{2}\) is allowed. Powers of the variable must be non-negative integers.
Step 3
Exam Tip
गुणांक वास्तविक संख्या हो सकते हैं इसलिए \(\sqrt{2}\) स्वीकार्य है। चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर मूल के अंदर है?
Which expression is not a polynomial because the variable is inside a root?
#definition-polynomial
#radical
#not-polynomial
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A \(x^2+\sqrt{5}\)
B \(\sqrt{x}+3\)
C \(5x+\sqrt{2}\)
D \(x^3-1\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{x}+3\)
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 B. \(\sqrt{x}+3\). \(\sqrt{x}=x^{1/2}\), 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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बहुपद \(7x^5-2x^3+x-4\) में कितने पद हैं?
How many terms are there in the polynomial \(7x^5-2x^3+x-4\)?
#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: \(7x^5\), \(-2x^3\), (x), and (-4). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (4). It has four terms: \(7x^5\), \(-2x^3\), (x), and (-4). Count terms with their signs.
Step 3
Exam Tip
इसमें \(7x^5\), \(-2x^3\), (x) और (-4) चार पद हैं। पदों को चिन्ह सहित गिनें।
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कौन-सा बहुपद एकपदी है?
Which polynomial is a monomial?
#definition-polynomial
#monomial
#term-count
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A \(6x^4\)
B \(x^2+1\)
C \(x+2x^2\)
D \(3x^2-5x+7\)
Explanation opens after your attempt
Correct Answer
A. \(6x^4\)
Step 1
Concept
A monomial has only one term. \(6x^4\) is a polynomial with a single term.
Step 2
Why this answer is correct
The correct answer is A. \(6x^4\). A monomial has only one term. \(6x^4\) is a polynomial with a single term.
Step 3
Exam Tip
एकपदी में केवल एक पद होता है। \(6x^4\) एक ही पद वाला बहुपद है।
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कौन-सा बहुपद द्विपदी है?
Which polynomial is a binomial?
#definition-polynomial
#binomial
#term-count
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A \(x^2+3x+2\)
B \(4x^3-9\)
C (7x)
D \(x^4+x^2+x+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-9\)
Step 1
Concept
A binomial has two terms. \(4x^3-9\) has the two terms \(4x^3\) and (-9).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-9\). A binomial has two terms. \(4x^3-9\) has the two terms \(4x^3\) and (-9).
Step 3
Exam Tip
द्विपदी में दो पद होते हैं। \(4x^3-9\) में \(4x^3\) और (-9) दो पद हैं।
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कौन-सा बहुपद त्रिपदी है?
Which polynomial is a trinomial?
#definition-polynomial
#trinomial
#term-count
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A \(2x^2-5x+6\)
B \(9x^2-4\)
C \(8x^5\)
D \(x^3+x^2+x+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+6\)
Step 1
Concept
A trinomial has three terms. \(2x^2-5x+6\) has three terms.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+6\). A trinomial has three terms. \(2x^2-5x+6\) has three terms.
Step 3
Exam Tip
त्रिपदी में तीन पद होते हैं। \(2x^2-5x+6\) में तीन पद हैं।
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\(3x^2+\frac{2}{5}x-1\) के बारे में सही कथन क्या है?
Which statement is correct about \(3x^2+\frac{2}{5}x-1\)?
#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 घातें शून्य या धनात्मक पूर्णांक हैं / It is a polynomial because powers are non-negative integers
C यह बहुपद नहीं है क्योंकि स्थिर पद है / It is not a polynomial because it has a constant term
D यह बहुपद नहीं है क्योंकि इसमें (x) है / It is not a polynomial because it has (x)
Explanation opens after your attempt
Correct Answer
B. यह बहुपद है क्योंकि घातें शून्य या धनात्मक पूर्णांक हैं / It is a polynomial because powers are non-negative integers
Step 1
Concept
Coefficients can be fractions. Here the powers of (x) are (2), (1), and (0), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is B. यह बहुपद है क्योंकि घातें शून्य या धनात्मक पूर्णांक हैं / It is a polynomial because powers are non-negative integers. Coefficients can be fractions. Here the powers of (x) are (2), (1), and (0), so it is a polynomial.
Step 3
Exam Tip
गुणांक भिन्न हो सकते हैं। यहाँ (x) की घातें (2), (1) और (0) हैं इसलिए यह बहुपद है।
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निम्न में से कौन-सा (x) में बहुपद है लेकिन (x) में रैखिक बहुपद नहीं है?
Which of the following is a polynomial in (x) but not a linear polynomial in (x)?
#definition-polynomial
#linear-vs-quadratic
#degree
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A (5x-2)
B \(x^2+4\)
C \(\frac{1}{x}+1\)
D \(\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+4\)
Step 1
Concept
\(x^2+4\) is a polynomial but its degree is (2). A linear polynomial has degree (1).
Step 2
Why this answer is correct
The correct answer is B. \(x^2+4\). \(x^2+4\) is a polynomial but its degree is (2). A linear polynomial has degree (1).
Step 3
Exam Tip
\(x^2+4\) बहुपद है लेकिन इसकी घात (2) है। रैखिक बहुपद की घात (1) होती है।
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किस विकल्प में बहुपद की सामान्य शर्त सही दी गई है?
Which option gives the correct general condition for 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 भिन्न हों / Powers of the variable are fractions
C चर की घातें शून्य या धनात्मक पूर्णांक हों / Powers of the variable are zero or positive integers
D चर हमेशा हर में हो / The variable is always in the denominator
Explanation opens after your attempt
Correct Answer
C. 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 are zero or positive integers. This is the key point of the definition.
Step 2
Why this answer is correct
The correct answer is C. चर की घातें शून्य या धनात्मक पूर्णांक हों / Powers of the variable are zero or positive integers. In a polynomial, powers of the variable are zero or positive integers. This is the key point of the definition.
Step 3
Exam Tip
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होती हैं। यही परिभाषा का मुख्य बिंदु है।
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व्यंजक \(x^2+\frac{1}{x^2}\) बहुपद क्यों नहीं है?
Why is \(x^2+\frac{1}{x^2}\) 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 स्थिर पद नहीं है / Because it has no constant term
C क्योंकि \(\frac{1}{x^2}=x^{-2}\) है / Because \(\frac{1}{x^2}=x^{-2}\)
D क्योंकि इसमें दो पद हैं / Because it has two terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि \(\frac{1}{x^2}=x^{-2}\) है / Because \(\frac{1}{x^2}=x^{-2}\)
Step 1
Concept
In \(\frac{1}{x^2}\), the power of (x) is (-2). Due to the negative power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(\frac{1}{x^2}=x^{-2}\) है / Because \(\frac{1}{x^2}=x^{-2}\). In \(\frac{1}{x^2}\), the power of (x) is (-2). Due to the negative power, it is not a polynomial.
Step 3
Exam Tip
\(\frac{1}{x^2}\) में (x) की घात (-2) है। ऋणात्मक घात के कारण यह बहुपद नहीं है।
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कौन-सा व्यंजक (y) में बहुपद है?
Which expression is a polynomial in (y)?
#definition-polynomial
#polynomial-in-y
#valid-polynomial
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A \(y^3-2y+6\)
B \(\frac{4}{y}+1\)
C \(y^{-2}+5\)
D \(\sqrt{y}+3\)
Explanation opens after your attempt
Correct Answer
A. \(y^3-2y+6\)
Step 1
Concept
In \(y^3-2y+6\), the powers of (y) are (3), (1), and (0). All are non-negative integers.
Step 2
Why this answer is correct
The correct answer is A. \(y^3-2y+6\). In \(y^3-2y+6\), the powers of (y) are (3), (1), and (0). All are non-negative integers.
Step 3
Exam Tip
\(y^3-2y+6\) में (y) की घातें (3), (1) और (0) हैं। ये सभी शून्य या धनात्मक पूर्णांक हैं।
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\(2t^2-7t+10\) की घात क्या है?
What is the degree of \(2t^2-7t+10\)?
#definition-polynomial
#degree
#quadratic
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A (0)
B (1)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2) in \(t^2\). 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) in \(t^2\). Therefore, the degree of the polynomial is (2).
Step 3
Exam Tip
सबसे बड़ी घात \(t^2\) में (2) है। इसलिए बहुपद की घात (2) है।
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कौन-सा स्थिर बहुपद नहीं है?
Which is not a constant polynomial?
#definition-polynomial
#constant-polynomial
#variable
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A (12)
B (-5)
C (0)
D (x+1)
Explanation opens after your attempt
Step 1
Concept
A constant polynomial has no variable. (x+1) contains (x), so it is not a constant polynomial.
Step 2
Why this answer is correct
The correct answer is D. (x+1). A constant polynomial has no variable. (x+1) contains (x), so it is not a constant polynomial.
Step 3
Exam Tip
स्थिर बहुपद में चर नहीं होता। (x+1) में (x) है इसलिए यह स्थिर बहुपद नहीं है।
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\(4x^3+0x^2-2\) की घात क्या है?
What is the degree of \(4x^3+0x^2-2\)?
#definition-polynomial
#zero-coefficient
#degree
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A (0)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
\(0x^2\) is a zero term, so it does not determine the degree. The highest non-zero term is \(4x^3\).
Step 2
Why this answer is correct
The correct answer is C. (3). \(0x^2\) is a zero term, so it does not determine the degree. The highest non-zero term is \(4x^3\).
Step 3
Exam Tip
\(0x^2\) शून्य पद है इसलिए घात तय नहीं करता। सबसे बड़ा अशून्य पद \(4x^3\) है।
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कौन-सा व्यंजक बहुपद है हालांकि उसमें (x) का पद नहीं है?
Which expression is a polynomial although it has no (x)-term?
#definition-polynomial
#missing-term
#valid-polynomial
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A \(3x^4+5\)
B \(\frac{1}{x}+5\)
C \(x^{-4}+5\)
D \(\sqrt{x^4}+5\)
Explanation opens after your attempt
Correct Answer
A. \(3x^4+5\)
Step 1
Concept
A polynomial need not contain every power. \(3x^4+5\) has powers (4) and (0), which are valid.
Step 2
Why this answer is correct
The correct answer is A. \(3x^4+5\). A polynomial need not contain every power. \(3x^4+5\) has powers (4) and (0), which are valid.
Step 3
Exam Tip
बहुपद में सभी घातें होना जरूरी नहीं है। \(3x^4+5\) में घात (4) और (0) हैं जो मान्य हैं।
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\(x^2+x^{1/2}+1\) बहुपद क्यों नहीं है?
Why is \(x^2+x^{1/2}+1\) not a polynomial?
#definition-polynomial
#fractional-power
#not-polynomial
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A क्योंकि \(x^2\) है / Because it has \(x^2\)
B क्योंकि (x^{1 / 2}) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 2}\) is not an integer
C क्योंकि इसमें तीन पद हैं / Because it has three terms
D क्योंकि इसमें स्थिर पद है / Because it has a constant term
Explanation opens after your attempt
Correct Answer
B. क्योंकि (x^{1 / 2}) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 2}\) is not an integer
Step 1
Concept
In a polynomial, powers of the variable must be integers. \(x^{1/2}\) has power \(\frac{1}{2}\), so it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(x^{1 / 2}\) की घात पूर्णांक नहीं है / Because the power in \(x^{1 / 2}\) is not an integer. In a polynomial, powers of the variable must be integers. \(x^{1/2}\) has power \(\frac{1}{2}\), so it is not a polynomial.
Step 3
Exam Tip
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{1/2}\) की घात \(\frac{1}{2}\) है इसलिए यह बहुपद नहीं है।
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कौन-सा व्यंजक बहुपद है और उसकी घात (0) है?
Which expression is a polynomial of degree (0)?
#definition-polynomial
#degree-zero
#constant
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A (0)
B (8)
C (x)
D \(x^0+x\)
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). (8) is such a constant polynomial.
Step 2
Why this answer is correct
The correct answer is B. (8). A non-zero constant polynomial has degree (0). (8) is such a constant polynomial.
Step 3
Exam Tip
शून्य से अलग स्थिर बहुपद की घात (0) होती है। (8) ऐसा ही स्थिर बहुपद है।
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निम्न में से किसमें बहुपद की घात (1) है?
Which of the following has degree (1)?
#definition-polynomial
#degree-one
#linear
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A (9x-4)
B \(x^2-1\)
C (7)
D \(x^3+x\)
Explanation opens after your attempt
Step 1
Concept
In (9x-4), the highest power is (1). So it is a polynomial of degree (1).
Step 2
Why this answer is correct
The correct answer is A. (9x-4). In (9x-4), the highest power is (1). So it is a polynomial of degree (1).
Step 3
Exam Tip
(9x-4) में सबसे बड़ी घात (1) है। इसलिए यह घात (1) का बहुपद है।
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कौन-सा व्यंजक बहुपद है पर एकपदी नहीं है?
Which expression is a polynomial but not a monomial?
#definition-polynomial
#monomial-vs-binomial
#term-count
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A \(5x^3\)
B \(x^2+4\)
C \(\frac{1}{x}\)
D \(x^{-1}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+4\)
Step 1
Concept
\(x^2+4\) is a polynomial and has two terms. Therefore, it is not a monomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+4\). \(x^2+4\) is a polynomial and has two terms. Therefore, it is not a monomial.
Step 3
Exam Tip
\(x^2+4\) बहुपद है और इसमें दो पद हैं। इसलिए यह एकपदी नहीं है।
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\(2x^3-5x^2+x-1\) किस प्रकार का बहुपद है?
What type of polynomial is \(2x^3-5x^2+x-1\)?
#definition-polynomial
#cubic
#classification
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A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C घन बहुपद / Cubic polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. घन बहुपद / Cubic polynomial
Step 1
Concept
The highest power of this polynomial is (3). A polynomial of degree (3) is called a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is C. घन 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 घन बहुपद कहलाता है।
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\(x^5+x^2+1\) में कौन-सा पद घात तय करता है?
Which term determines the degree of \(x^5+x^2+1\)?
#definition-polynomial
#degree-determining-term
#highest-power
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A \(x^5\)
B \(x^2\)
C (1)
D \(x^5+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^5\)
Step 1
Concept
The degree is determined by the highest power of the variable. The term \(x^5\) has the highest power (5).
Step 2
Why this answer is correct
The correct answer is A. \(x^5\). The degree is determined by the highest power of the variable. The term \(x^5\) has the highest power (5).
Step 3
Exam Tip
घात सबसे बड़ी चर-घात से तय होती है। \(x^5\) में सबसे बड़ी घात (5) है।
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\(3x^2-7\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(3x^2-7\)?
#definition-polynomial
#quadratic
#classification
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A यह बहुपद नहीं है / It is not a polynomial
B यह (x) में द्विघात बहुपद है / It is a quadratic polynomial in (x)
C यह (x) में रैखिक बहुपद है / It is a linear polynomial in (x)
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
B. यह (x) में द्विघात बहुपद है / It is a quadratic polynomial in (x)
Step 1
Concept
In \(3x^2-7\), the highest power is (2). Therefore, it is a quadratic polynomial.
Step 2
Why this answer is correct
The correct answer is B. यह (x) में द्विघात बहुपद है / It is a quadratic polynomial in (x). In \(3x^2-7\), the highest power is (2). Therefore, it is a quadratic polynomial.
Step 3
Exam Tip
\(3x^2-7\) में सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है।
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कौन-सा विकल्प ऐसा बहुपद दिखाता है जिसकी घात (4) है?
Which option shows a polynomial of degree (4)?
#definition-polynomial
#degree-four
#classification
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A \(x^4-3x+2\)
B \(4x^3+x^2\)
C \(x^2+x+4\)
D (4x+1)
Explanation opens after your attempt
Correct Answer
A. \(x^4-3x+2\)
Step 1
Concept
The degree is obtained from the highest power. In \(x^4-3x+2\), the highest power is (4).
Step 2
Why this answer is correct
The correct answer is A. \(x^4-3x+2\). The degree is obtained from the highest power. In \(x^4-3x+2\), the highest power is (4).
Step 3
Exam Tip
घात सबसे बड़ी शक्ति से मिलती है। \(x^4-3x+2\) में सबसे बड़ी घात (4) है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर की घात ऋणात्मक है?
Which expression is not a polynomial because the variable has a negative power?
#definition-polynomial
#negative-power
#not-polynomial
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A \(x^2-3\)
B \(5x^{-3}+2\)
C \(7x^0+1\)
D \(9x^4\)
Explanation opens after your attempt
Correct Answer
B. \(5x^{-3}+2\)
Step 1
Concept
The power in \(x^{-3}\) is negative. Negative powers are not allowed in polynomials.
Step 2
Why this answer is correct
The correct answer is B. \(5x^{-3}+2\). The power in \(x^{-3}\) is negative. Negative powers are not allowed in polynomials.
Step 3
Exam Tip
\(x^{-3}\) की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार्य नहीं होती।
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\(2x^2+3x+1\) में (x) की कौन-कौन सी घातें आती हैं?
Which powers of (x) appear in \(2x^2+3x+1\)?
#definition-polynomial
#powers
#constant-term
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A (2), (1), (0)
B (2), (3), (1)
C (1), (0), (-1)
D (2), \(\frac{1}{2}\), (0)
Explanation opens after your attempt
Correct Answer
A. (2), (1), (0)
Step 1
Concept
The powers are (2) for \(2x^2\), (1) for (3x), and (0) for (1). This makes it a polynomial.
Step 2
Why this answer is correct
The correct answer is A. (2), (1), (0). The powers are (2) for \(2x^2\), (1) for (3x), and (0) for (1). This makes it a polynomial.
Step 3
Exam Tip
\(2x^2\) की घात (2), (3x) की घात (1) और (1) की घात (0) मानी जाती है। यही इसे बहुपद बनाता है।
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कौन-सा व्यंजक (x) में बहुपद है और (y) को स्थिर मानने पर भी वैध रहेगा?
Which expression is a polynomial in (x) if (y) is treated as a constant?
#definition-polynomial
#polynomial-in-x
#parameter
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A \(x^2+yx+3\)
B \(\frac{1}{x}+y\)
C \(\sqrt{x}+y\)
D \(x^{-1}+y^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+yx+3\)
Step 1
Concept
Treating (y) as a constant, the term (yx) has (x)-power (1). All powers of (x) are non-negative integers.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+yx+3\). Treating (y) as a constant, the term (yx) has (x)-power (1). All powers of (x) are non-negative integers.
Step 3
Exam Tip
(y) को स्थिर मानने पर (yx) में (x) की घात (1) है। सभी (x) घातें शून्य या धनात्मक पूर्णांक हैं।
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कौन-सा व्यंजक (x) में बहुपद नहीं है जबकि देखने में बीजीय लगता है?
Which expression is not a polynomial in (x) though it looks algebraic?
#definition-polynomial
#denominator
#not-polynomial
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A \(2x^3+x\)
B \(5x^2-1\)
C \(x+\frac{2}{x}\)
D \(7x^0+4\)
Explanation opens after your attempt
Correct Answer
C. \(x+\frac{2}{x}\)
Step 1
Concept
In \(\frac{2}{x}\), the power of (x) is (-1). Hence the whole expression is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(x+\frac{2}{x}\). In \(\frac{2}{x}\), the power of (x) is (-1). Hence the whole expression is not a polynomial.
Step 3
Exam Tip
\(\frac{2}{x}\) में (x) की घात (-1) है। इसलिए पूरा व्यंजक बहुपद नहीं है।
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यदि (p(x)=4x-2 -9x+2), तो यह किस घात का बहुपद है?
If (p(x)=4x-2 -9x+2), what is the degree of this polynomial?
#definition-polynomial
#function-notation
#degree
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A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2) in \(x^2\). Therefore, the degree of (p(x)) is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). The highest power is (2) in \(x^2\). Therefore, the degree of (p(x)) is (2).
Step 3
Exam Tip
सबसे बड़ी घात \(x^2\) में (2) है। इसलिए (p(x)) की घात (2) है।
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कौन-सा बहुपद (x) में नहीं बल्कि (z) में दिया गया है?
Which polynomial is given in (z) instead of (x)?
#definition-polynomial
#polynomial-in-z
#variable
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A \(3x^2+1\)
B \(4z^3-z+8\)
C (7x-2)
D \(x^4+z^{-1}\)
Explanation opens after your attempt
Correct Answer
B. \(4z^3-z+8\)
Step 1
Concept
In \(4z^3-z+8\), the variable is (z) and its powers are (3), (1), (0). So it is a polynomial in (z).
Step 2
Why this answer is correct
The correct answer is B. \(4z^3-z+8\). In \(4z^3-z+8\), the variable is (z) and its powers are (3), (1), (0). So it is a polynomial in (z).
Step 3
Exam Tip
\(4z^3-z+8\) में चर (z) है और उसकी घातें (3), (1), (0) हैं। इसलिए यह (z) में बहुपद है।
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\(7x^2-4x^{-1}+3\) बहुपद क्यों नहीं है?
Why is \(7x^2-4x^{-1}+3\) not a polynomial?
#definition-polynomial
#negative-exponent
#reason
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A क्योंकि \(7x^2\) है / Because it has \(7x^2\)
B क्योंकि (3) स्थिर पद है / Because (3) is a constant term
C क्योंकि \(x^{-1}\) की घात ऋणात्मक है / Because the power in \(x^{-1}\) is negative
D क्योंकि इसमें तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
C. क्योंकि \(x^{-1}\) की घात ऋणात्मक है / Because the power in \(x^{-1}\) is negative
Step 1
Concept
The power in \(x^{-1}\) is negative. Such a power is not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(x^{-1}\) की घात ऋणात्मक है / Because the power in \(x^{-1}\) is negative. The power in \(x^{-1}\) is negative. Such a power is not allowed in a polynomial.
Step 3
Exam Tip
\(x^{-1}\) की घात ऋणात्मक है। बहुपद में ऐसी घात मान्य नहीं होती।
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कौन-सा विकल्प बहुपद की सही पहचान करता है?
Which option correctly identifies a polynomial?
#definition-polynomial
#real-coefficient
#valid-polynomial
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A \(x^2+\sqrt{3}x+5\)
B \(\sqrt{x}+x\)
C \(x^{-2}+1\)
D \(\frac{x+1}{x}\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+\sqrt{3}x+5\)
Step 1
Concept
\(\sqrt{3}\) is a coefficient and is an allowed real number. The powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+\sqrt{3}x+5\). \(\sqrt{3}\) is a coefficient and is an allowed real number. The powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
\(\sqrt{3}\) गुणांक है और यह स्वीकार्य वास्तविक संख्या है। (x) की घातें (2), (1), (0) हैं।
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कौन-सा व्यंजक बहुपद है लेकिन उसकी घात (2) नहीं है?
Which expression is a polynomial but does not have degree (2)?
#definition-polynomial
#degree-four
#classification
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A \(x^2+x+1\)
B \(5x^4-x+2\)
C \(\sqrt{x}+1\)
D \(\frac{1}{x}+x^2\)
Explanation opens after your attempt
Correct Answer
B. \(5x^4-x+2\)
Step 1
Concept
\(5x^4-x+2\) is a polynomial and its degree is (4). Therefore, its degree is not (2).
Step 2
Why this answer is correct
The correct answer is B. \(5x^4-x+2\). \(5x^4-x+2\) is a polynomial and its degree is (4). Therefore, its degree is not (2).
Step 3
Exam Tip
\(5x^4-x+2\) बहुपद है और इसकी घात (4) है। इसलिए इसकी घात (2) नहीं है।
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यदि बहुपद में सबसे बड़ी घात (1) है, तो उसे क्या कहते हैं?
If the highest power in a polynomial is (1), what is it called?
#definition-polynomial
#linear-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
B. रैखिक बहुपद / Linear polynomial
Step 1
Concept
A polynomial with highest power (1) is called linear. Focus on the degree to remember the name.
Step 2
Why this answer is correct
The correct answer is B. रैखिक बहुपद / Linear polynomial. A polynomial with highest power (1) is called linear. Focus on the degree to remember the name.
Step 3
Exam Tip
सबसे बड़ी घात (1) होने पर बहुपद रैखिक कहलाता है। नाम याद करने के लिए घात पर ध्यान दें।
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यदि बहुपद में सबसे बड़ी घात (2) है, तो उसे क्या कहते हैं?
If the highest power in a polynomial is (2), what is it called?
#definition-polynomial
#quadratic-polynomial
#classification
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A रैखिक बहुपद / Linear polynomial
B घन बहुपद / Cubic polynomial
C द्विघात बहुपद / Quadratic polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
A polynomial with highest power (2) is called quadratic. Connect degree (2) with quadratic.
Step 2
Why this answer is correct
The correct answer is C. द्विघात बहुपद / Quadratic polynomial. A polynomial with highest power (2) is called quadratic. Connect degree (2) with quadratic.
Step 3
Exam Tip
सबसे बड़ी घात (2) होने पर बहुपद द्विघात कहलाता है। घात (2) को द्विघात से जोड़ें।
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यदि बहुपद में सबसे बड़ी घात (3) है, तो उसे क्या कहते हैं?
If the highest power in a polynomial is (3), what is it called?
#definition-polynomial
#cubic-polynomial
#classification
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A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रैखिक बहुपद / Linear polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
A polynomial with highest power (3) is called cubic. Identify the type from the degree.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. A polynomial with highest power (3) is called cubic. Identify the type from the degree.
Step 3
Exam Tip
सबसे बड़ी घात (3) होने पर बहुपद घन कहलाता है। घात से बहुपद का प्रकार पहचानें।
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कौन-सा बहुपद (x) में चार पदों वाला है?
Which polynomial in (x) has four terms?
#definition-polynomial
#term-count
#four-terms
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A \(x^3+x^2+x+1\)
B \(x^2+x+1\)
C \(x^4-1\)
D (7x)
Explanation opens after your attempt
Correct Answer
A. \(x^3+x^2+x+1\)
Step 1
Concept
\(x^3+x^2+x+1\) has four distinct terms. Identify terms by the plus signs.
Step 2
Why this answer is correct
The correct answer is A. \(x^3+x^2+x+1\). \(x^3+x^2+x+1\) has four distinct terms. Identify terms by the plus signs.
Step 3
Exam Tip
\(x^3+x^2+x+1\) में चार अलग पद हैं। पदों को जोड़ के चिन्हों से पहचानें।
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(p(x)=0) को कौन-सा बहुपद कहा जाता है?
What is (p(x)=0) called?
#definition-polynomial
#zero-polynomial
#notation
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A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C शून्य बहुपद / Zero polynomial
D घन बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
C. शून्य बहुपद / Zero polynomial
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. शून्य बहुपद / Zero polynomial. (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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कौन-सा विकल्प \(x^2-5x+6\) की सही पहचान है?
Which option correctly identifies \(x^2-5x+6\)?
#definition-polynomial
#quadratic-trinomial
#classification
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A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात त्रिपदी बहुपद है / It is a quadratic trinomial polynomial
C यह बहुपद नहीं है / It is not a polynomial
D यह स्थिर बहुपद है / It is a constant polynomial
Explanation opens after your attempt
Correct Answer
B. यह द्विघात त्रिपदी बहुपद है / It is a 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. यह द्विघात त्रिपदी बहुपद है / It is a 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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कौन-सा व्यंजक (x) में बहुपद है क्योंकि चर की सभी घातें धनात्मक पूर्णांक या शून्य हैं?
Which expression is a polynomial in (x) because all powers of the variable are positive integers or zero?
#definition-polynomial
#valid-polynomial
#powers
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A \(2x^6-4x^2+9\)
B \(x^{-4}+3x\)
C \(\frac{7}{x}+x^2\)
D (x^{2 / 3}+5)
Explanation opens after your attempt
Correct Answer
A. \(2x^6-4x^2+9\)
Step 1
Concept
In \(2x^6-4x^2+9\), the powers of (x) are (6), (2), and (0). All satisfy the condition of a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(2x^6-4x^2+9\). In \(2x^6-4x^2+9\), the powers of (x) are (6), (2), and (0). All satisfy the condition of a polynomial.
Step 3
Exam Tip
\(2x^6-4x^2+9\) में (x) की घातें (6), (2) और (0) हैं। ये सभी बहुपद की शर्त पूरी करती हैं।
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(p(x)=5x-3 -2x-2 +8) में (x) का पद नहीं है। इसकी घात क्या होगी?
In (p(x)=5x-3 -2x-2 +8), the (x)-term is missing. What will be its degree?
#definition-polynomial
#missing-term
#degree
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A (1)
B (2)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
The absence of a term does not change the degree. The highest present power is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). The absence of a term does not change the degree. The highest present power is (3).
Step 3
Exam Tip
किसी पद के न होने से घात नहीं बदलती। सबसे बड़ी उपस्थित घात (3) है।
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कौन-सा व्यंजक (t) में बहुपद नहीं है क्योंकि (t) हर में है?
Which expression is not a polynomial in (t) because (t) is in the denominator?
#definition-polynomial
#denominator
#not-polynomial
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A \(t^4-2t+1\)
B \(6+\frac{3}{t}\)
C \(9t^0-5t\)
D \(2t^3+7\)
Explanation opens after your attempt
Correct Answer
B. \(6+\frac{3}{t}\)
Step 1
Concept
\(\frac{3}{t}=3t^{-1}\), so 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 B. \(6+\frac{3}{t}\). \(\frac{3}{t}=3t^{-1}\), so the power is (-1). An expression with a negative power is not a polynomial.
Step 3
Exam Tip
\(\frac{3}{t}=3t^{-1}\) होता है और घात (-1) है। ऋणात्मक घात वाला व्यंजक बहुपद नहीं होता।
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