यदि (p(x)=(a-2)x-3 +5x-7) और (a=2), तो (p(x)) किस प्रकार का बहुपद बनेगा?
If (p(x)=(a-2)x-3 +5x-7) and (a=2), what type of polynomial will (p(x)) become?
#polynomial
#parameter
#linear
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A त्रिघात बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रेखीय बहुपद / Linear polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
C. रेखीय बहुपद / Linear polynomial
Step 1
Concept
Putting (a=2) makes the coefficient of \(x^3\) equal to (0), leaving (5x-7). So it is a linear polynomial.
Step 2
Why this answer is correct
The correct answer is C. रेखीय बहुपद / Linear polynomial. Putting (a=2) makes the coefficient of \(x^3\) equal to (0), leaving (5x-7). So it is a linear polynomial.
Step 3
Exam Tip
(a=2) रखने पर \(x^3\) का गुणांक (0) हो जाता है और (5x-7) बचता है। इसलिए यह रेखीय बहुपद है।
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निम्न में से कौन सा व्यंजक (x) में बहुपद है और उसकी डिग्री (4) है?
Which expression is a polynomial in (x) and has degree (4)?
#polynomial
#degree
#real_coefficient
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A \(\sqrt{x}+x^4\)
B \(3x^4-\sqrt{5}x^2+6\)
C \(\frac{1}{x}+x^4\)
D \(x^{\frac{4}{3}}+2\)
Explanation opens after your attempt
Correct Answer
B. \(3x^4-\sqrt{5}x^2+6\)
Step 1
Concept
In the second expression, the powers are (4), (2), and (0), and the coefficients are real. So it is a polynomial of degree (4).
Step 2
Why this answer is correct
The correct answer is B. \(3x^4-\sqrt{5}x^2+6\). In the second expression, the powers are (4), (2), and (0), and the coefficients are real. So it is a polynomial of degree (4).
Step 3
Exam Tip
दूसरे व्यंजक में घातें (4), (2), और (0) हैं तथा गुणांक वास्तविक हैं। इसलिए यह डिग्री (4) का बहुपद है।
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बहुपद \(9t^5-4t^3+2t-1\) की घात क्या है?
What is the degree of the polynomial \(9t^5-4t^3+2t-1\)?
#definition-polynomial
#degree
#highest-power
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A (3)
B (4)
C (5)
D (9)
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 (5).
Step 2
Why this answer is correct
The correct answer is C. (5). The degree of a polynomial is the highest power of the variable. Here the highest power is (5).
Step 3
Exam Tip
बहुपद की घात सबसे बड़ी चर-घात होती है। यहाँ सबसे बड़ी घात (5) है।
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व्यंजक \(0x^5-3x^2+8x-1\) की डिग्री क्या है?
What is the degree of \(0x^5-3x^2+8x-1\)?
#polynomial
#zero_coefficient
#degree
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A (5)
B (3)
C (2)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(0x^5\) is a zero term, so it is not counted for degree. The remaining highest power is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). \(0x^5\) is a zero term, so it is not counted for degree. The remaining highest power is (2).
Step 3
Exam Tip
\(0x^5\) शून्य पद है, इसलिए इसे डिग्री के लिए नहीं गिनते। बची हुई सबसे बड़ी घात (2) है।
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व्यंजक \(3y^2+\sqrt{5}y-8\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(3y^2+\sqrt{5}y-8\)?
#definition-polynomial
#real-coefficient
#polynomial-in-y
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A यह बहुपद नहीं है क्योंकि \(\sqrt{5}\) है / It is not a polynomial because it has \(\sqrt{5}\)
B यह बहुपद नहीं है क्योंकि स्थिर पद ऋणात्मक है / It is not a polynomial because the constant term is negative
C यह शून्य बहुपद है / It is the zero polynomial
D यह (y) में बहुपद है / It is a polynomial in (y)
Explanation opens after your attempt
Correct Answer
D. यह (y) में बहुपद है / It is a polynomial in (y)
Step 1
Concept
\(\sqrt{5}\) is only a real coefficient and is allowed. The powers of (y) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is D. यह (y) में बहुपद है / It is a polynomial in (y). \(\sqrt{5}\) is only a real coefficient and is allowed. The powers of (y) are (2), (1), and (0).
Step 3
Exam Tip
\(\sqrt{5}\) केवल वास्तविक गुणांक है और मान्य है। (y) की घातें (2), (1) और (0) हैं।
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किस मान पर ((k+4)x-2 +3x-9) रेखीय बहुपद बनेगा?
For which value will ((k+4)x-2 +3x-9) become a linear polynomial?
#polynomial
#parameter
#linear_polynomial
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A (k=4)
B (k=-4)
C (k=0)
D (k=9)
Explanation opens after your attempt
Step 1
Concept
To become linear, the coefficient of \(x^2\) must be (0). From (k+4=0), we get (k=-4).
Step 2
Why this answer is correct
The correct answer is B. (k=-4). To become linear, the coefficient of \(x^2\) must be (0). From (k+4=0), we get (k=-4).
Step 3
Exam Tip
रेखीय बनने के लिए \(x^2\) का गुणांक (0) होना चाहिए। (k+4=0) से (k=-4) मिलता है।
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व्यंजक \(x^2+\frac{x^2-1}{x-1}\) को \(x\neq1\) पर सरल करने से कौन सा बहुपद मिलता है?
Which polynomial is obtained by simplifying \(x^2+\frac{x^2-1}{x-1}\) for \(x\neq1\)?
#polynomial
#simplification
#domain
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A \(x^2+x+1\)
B \(x^2+x-1\)
C \(2x^2-1\)
D \(x^3+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x+1\)
Step 1
Concept
\(\frac{x^2-1}{x-1}=x+1\) when \(x\neq1\). So the simplified form is \(x^2+x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x+1\). \(\frac{x^2-1}{x-1}=x+1\) when \(x\neq1\). So the simplified form is \(x^2+x+1\).
Step 3
Exam Tip
\(\frac{x^2-1}{x-1}=x+1\) जब \(x\neq1\)। इसलिए सरल रूप \(x^2+x+1\) है।
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व्यंजक \(2x^3+|x|+4\) बहुपद क्यों नहीं है?
Why is \(2x^3+|x|+4\) not a polynomial?
#polynomial
#absolute_value
#non_polynomial
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A क्योंकि इसमें \(2x^3\) है / Because it has \(2x^3\)
B क्योंकि (|x|) बहुपद पद नहीं है / Because (|x|) is not a polynomial term
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 (|x|) बहुपद पद नहीं है / Because (|x|) is not a polynomial term
Step 1
Concept
The term (|x|) is not written using non-negative integer powers of (x). Therefore it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि (|x|) बहुपद पद नहीं है / Because (|x|) is not a polynomial term. The term (|x|) is not written using non-negative integer powers of (x). Therefore it is not a polynomial.
Step 3
Exam Tip
(|x|) को (x) की अऋणात्मक पूर्णांक घातों वाले पद के रूप में नहीं लिखा जाता। इसलिए यह बहुपद नहीं है।
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\(2x^3-5x+4\) की सही पहचान कौन-सी है?
Which is the correct identification of \(2x^3-5x+4\)?
#definition-polynomial
#cubic-trinomial
#classification
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A रैखिक त्रिपदी / Linear trinomial
B द्विघात द्विपदी / Quadratic binomial
C घन त्रिपदी बहुपद / Cubic trinomial polynomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
C. घन त्रिपदी बहुपद / Cubic trinomial polynomial
Step 1
Concept
Its highest power is (3) and it has (3) terms. Therefore, it is a cubic trinomial polynomial.
Step 2
Why this answer is correct
The correct answer is C. घन त्रिपदी बहुपद / Cubic trinomial polynomial. Its highest power is (3) and it has (3) terms. Therefore, it is a cubic trinomial polynomial.
Step 3
Exam Tip
इसकी सबसे बड़ी घात (3) है और इसमें (3) पद हैं। इसलिए यह घन त्रिपदी बहुपद है।
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यदि (m=0), तो (mx-4 +(m+2)x-3 -5) की डिग्री क्या होगी?
If (m=0), what will be the degree of (mx-4 +(m+2)x-3 -5)?
#polynomial
#parameter_substitution
#degree
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A (4)
B (3)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
Putting (m=0) removes the \(x^4\) term and leaves \(2x^3-5\). Therefore the degree is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). Putting (m=0) removes the \(x^4\) term and leaves \(2x^3-5\). Therefore the degree is (3).
Step 3
Exam Tip
(m=0) रखने पर \(x^4\) पद हट जाता है और \(2x^3-5\) बचता है। इसलिए डिग्री (3) है।
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कौन-सा व्यंजक (z) में रैखिक बहुपद है?
Which expression is a linear polynomial in (z)?
#definition-polynomial
#linear-polynomial
#degree-one
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A \(z^2+1\)
B \(z^3-z\)
C (14)
D (8z-3)
Explanation opens after your attempt
Step 1
Concept
A linear polynomial has degree (1). In (8z-3), the highest power is (1).
Step 2
Why this answer is correct
The correct answer is D. (8z-3). A linear polynomial has degree (1). In (8z-3), the highest power is (1).
Step 3
Exam Tip
रैखिक बहुपद की घात (1) होती है। (8z-3) में सबसे बड़ी घात (1) है।
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कौन सा कथन \(5x^2-\pi x+\sqrt{3}\) के लिए सही है?
Which statement is correct for \(5x^2-\pi x+\sqrt{3}\)?
#polynomial
#real_coefficients
#degree
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A यह बहुपद नहीं है क्योंकि इसमें \(\pi\) है / It is not a polynomial because it has \(\pi\)
B यह बहुपद नहीं है क्योंकि इसमें \(\sqrt{3}\) है / It is not a polynomial because it has \(\sqrt{3}\)
C यह बहुपद है और डिग्री (2) है / It is a polynomial and degree is (2)
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
C. यह बहुपद है और डिग्री (2) है / It is a polynomial and degree is (2)
Step 1
Concept
\(\pi\) and \(\sqrt{3}\) are real coefficients. The powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is C. यह बहुपद है और डिग्री (2) है / It is a polynomial and degree is (2). \(\pi\) and \(\sqrt{3}\) are real coefficients. The powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
\(\pi\) और \(\sqrt{3}\) वास्तविक गुणांक हैं। (x) की घातें (2), (1), और (0) हैं।
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बहुपद \(4x^5-7x^3+2\) में \(x^4\) और (x) के गुणांक क्रमशः क्या हैं?
In \(4x^5-7x^3+2\), what are the coefficients of \(x^4\) and (x) respectively?
#polynomial
#missing_terms
#coefficients
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A (4) और (-7) / (4) and (-7)
B (0) और (0) / (0) and (0)
C (5) और (1) / (5) and (1)
D (2) और (0) / (2) and (0)
Explanation opens after your attempt
Correct Answer
B. (0) और (0) / (0) and (0)
Step 1
Concept
The \(x^4\) and (x) terms are absent in this polynomial. Coefficients of absent terms are taken as (0).
Step 2
Why this answer is correct
The correct answer is B. (0) और (0) / (0) and (0). The \(x^4\) and (x) terms are absent in this polynomial. Coefficients of absent terms are taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^4\) और (x) पद नहीं हैं। अनुपस्थित पदों के गुणांक (0) माने जाते हैं।
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यदि (p(x)=6x-4 +0x-6 -3x-2 +5), तो (p(x)) की घात क्या है?
If (p(x)=6x-4 +0x-6 -3x-2 +5), what is the degree of (p(x))?
#definition-polynomial
#zero-coefficient
#degree
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A (6)
B (4)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(0x^6\) is a zero term, so it does not determine the degree. The highest non-zero power is (4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(0x^6\) is a zero term, so it does not determine the degree. The highest non-zero power is (4).
Step 3
Exam Tip
\(0x^6\) शून्य पद है इसलिए घात तय नहीं करता। सबसे बड़ी अशून्य घात (4) है।
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किस विकल्प में व्यंजक मूल रूप में बहुपद नहीं है क्योंकि चर हर में है?
Which option is not a polynomial in its original form because the variable is in the denominator?
#polynomial
#denominator
#non_polynomial
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A \(x^3-2x+5\)
B \(\frac{x^2+4}{x+1}\)
C \(\sqrt{2}x^2-1\)
D \(7x^4+3\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{x^2+4}{x+1}\)
Step 1
Concept
In \(\frac{x^2+4}{x+1}\), the variable is in the denominator. Such an original expression does not satisfy the definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{x^2+4}{x+1}\). In \(\frac{x^2+4}{x+1}\), the variable is in the denominator. Such an original expression does not satisfy the definition of a polynomial.
Step 3
Exam Tip
\(\frac{x^2+4}{x+1}\) में चर हर में है। ऐसा मूल व्यंजक बहुपद की परिभाषा को पूरा नहीं करता।
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व्यंजक \(x^0+3x^2-2x\) की डिग्री क्या है?
What is the degree of \(x^0+3x^2-2x\)?
#polynomial
#zero_power
#degree
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(x^0=1\), and the highest power is (2). Therefore the degree is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). \(x^0=1\), and the highest power is (2). Therefore the degree is (2).
Step 3
Exam Tip
\(x^0=1\) होता है और सबसे बड़ी घात (2) है। इसलिए डिग्री (2) है।
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(7) की बहुपद के रूप में घात क्या होती है?
What is the degree of (7) as a polynomial?
#definition-polynomial
#constant-polynomial
#degree-zero
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A परिभाषित नहीं / Not defined
B (1)
C (7)
D (0)
Explanation opens after your attempt
Step 1
Concept
(7) is a non-zero constant polynomial. Such a polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is D. (0). (7) is a non-zero constant polynomial. Such a polynomial has degree (0).
Step 3
Exam Tip
(7) शून्य से अलग स्थिर बहुपद है। ऐसे बहुपद की घात (0) होती है।
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कौन-सा विकल्प (x) में बहुपद और उसकी घात दोनों सही दिखाता है?
Which option correctly shows a polynomial in (x) and its degree?
#definition-polynomial
#degree-check
#valid-polynomial
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A \(x^4+x\), घात (4) / \(x^4+x\), degree (4)
B \(x^{-4}+x\), घात (4) / \(x^{-4}+x\), degree (4)
C \(\sqrt{x}+1\), घात (1) / \(\sqrt{x}+1\), degree (1)
D \(\frac{1}{x}+x^2\), घात (2) / \(\frac{1}{x}+x^2\), degree (2)
Explanation opens after your attempt
Correct Answer
A. \(x^4+x\), घात (4) / \(x^4+x\), degree (4)
Step 1
Concept
In \(x^4+x\), the powers are (4) and (1). It is a polynomial and its degree is (4).
Step 2
Why this answer is correct
The correct answer is A. \(x^4+x\), घात (4) / \(x^4+x\), degree (4). In \(x^4+x\), the powers are (4) and (1). It is a polynomial and its degree is (4).
Step 3
Exam Tip
\(x^4+x\) में घातें (4) और (1) हैं। यह बहुपद है और इसकी घात (4) है।
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\(x^2+2x^{3/2}+5\) बहुपद क्यों नहीं है?
Why is \(x^2+2x^{3/2}+5\) not a polynomial?
#definition-polynomial
#fractional-power
#not-polynomial
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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 इसमें तीन पद हैं / Because it has three terms
D क्योंकि (x^{3 / 2}) की घात पूर्णांक नहीं है / Because the power in \(x^{3 / 2}\) is not an integer
Explanation opens after your attempt
Correct Answer
D. क्योंकि (x^{3 / 2}) की घात पूर्णांक नहीं है / Because the power in \(x^{3 / 2}\) is not an integer
Step 1
Concept
In a polynomial, powers of the variable must be integers. In \(x^{3/2}\), the power is \(\frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is D. क्योंकि \(x^{3 / 2}\) की घात पूर्णांक नहीं है / Because the power in \(x^{3 / 2}\) is not an integer. In a polynomial, powers of the variable must be integers. In \(x^{3/2}\), the power is \(\frac{3}{2}\).
Step 3
Exam Tip
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{3/2}\) में घात \(\frac{3}{2}\) है।
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कौन-सा व्यंजक (x) में बहुपद है यदि (k) को स्थिर माना जाए?
Which expression is a polynomial in (x) if (k) is treated as a constant?
#definition-polynomial
#parameter
#polynomial-in-x
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A \(kx^3-2x+8\)
B \(\frac{k}{x}+4\)
C \(x^{-2}+k\)
D \(k\sqrt{x}+1\)
Explanation opens after your attempt
Correct Answer
A. \(kx^3-2x+8\)
Step 1
Concept
(k) acts like a constant coefficient. The powers of (x) are (3), (1), and (0), so it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(kx^3-2x+8\). (k) acts like a constant coefficient. The powers of (x) are (3), (1), and (0), so it is a polynomial.
Step 3
Exam Tip
(k) स्थिर की तरह गुणांक है। (x) की घातें (3), (1) और (0) हैं इसलिए यह बहुपद है।
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\(5x^3-2x^2+9x-6\) में कितने पद हैं?
How many terms are there in \(5x^3-2x^2+9x-6\)?
#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: \(5x^3\), \(-2x^2\), (9x), and (-6). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (4). It has four terms: \(5x^3\), \(-2x^2\), (9x), and (-6). Count terms with their signs.
Step 3
Exam Tip
इसमें \(5x^3\), \(-2x^2\), (9x) और (-6) चार पद हैं। पदों को चिन्ह सहित गिनें।
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(p(x)=x-2 -4x+4) की सही पहचान कौन-सी है?
Which is the correct identification of (p(x)=x-2 -4x+4)?
#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 degree is (2) and it has (3) terms. Therefore, it is a quadratic trinomial.
Step 2
Why this answer is correct
The correct answer is B. द्विघात त्रिपदी / Quadratic trinomial. Its degree is (2) and it has (3) terms. Therefore, it is a quadratic trinomial.
Step 3
Exam Tip
इसकी घात (2) है और इसमें (3) पद हैं। इसलिए यह द्विघात त्रिपदी है।
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कौन-सा व्यंजक बहुपद है जिसमें (x) का रैखिक पद नहीं है?
Which expression is a polynomial with no linear (x)-term?
#definition-polynomial
#missing-linear-term
#valid-polynomial
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A \(x^4+3x^2-5\)
B \(x^{-4}+3x^2\)
C \(\sqrt{x}+3\)
D \(\frac{1}{x}+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^4+3x^2-5\)
Step 1
Concept
A polynomial need not have every power term. In \(x^4+3x^2-5\), all present powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^4+3x^2-5\). A polynomial need not have every power term. In \(x^4+3x^2-5\), all present powers are valid.
Step 3
Exam Tip
बहुपद में हर घात का पद होना जरूरी नहीं है। \(x^4+3x^2-5\) में सभी उपस्थित घातें मान्य हैं।
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\(4x^2+\frac{3}{4}x-9\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(4x^2+\frac{3}{4}x-9\)?
#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 variable powers are valid
C यह बहुपद नहीं है क्योंकि स्थिर पद ऋणात्मक है / It is not a polynomial because the constant is negative
D यह शून्य बहुपद है / It is 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 variable powers are valid
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 B. यह बहुपद है क्योंकि चर की घातें मान्य हैं / It is a polynomial because variable powers are valid. 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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किस व्यंजक में \(x^0\) के कारण स्थिर पद बनता है?
In which expression does \(x^0\) form a constant term?
#definition-polynomial
#zero-power
#constant-term
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A \(6x^0+5x\)
B \(6x^{-1}+5x\)
C (6x^{1 / 2}+5x)
D \(6\sqrt{x}+5x\)
Explanation opens after your attempt
Correct Answer
A. \(6x^0+5x\)
Step 1
Concept
\(x^0=1\) when \(x\neq0\). So \(6x^0\) behaves like the constant term (6).
Step 2
Why this answer is correct
The correct answer is A. \(6x^0+5x\). \(x^0=1\) when \(x\neq0\). So \(6x^0\) behaves like the constant term (6).
Step 3
Exam Tip
\(x^0=1\) माना जाता है जब \(x\neq0\)। इसलिए \(6x^0\) स्थिर पद (6) जैसा है।
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कौन-सा व्यंजक बहुपद है पर उसकी घात (1) नहीं है?
Which expression is a polynomial but does not have degree (1)?
#definition-polynomial
#degree-two
#comparison
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A (4x-7)
B \(x^2+6\)
C \(\frac{1}{x}+3\)
D \(\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6\)
Step 1
Concept
\(x^2+6\) is a polynomial and its degree is (2). Therefore, its degree is not (1).
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6\). \(x^2+6\) is a polynomial and its degree is (2). Therefore, its degree is not (1).
Step 3
Exam Tip
\(x^2+6\) बहुपद है और इसकी घात (2) है। इसलिए इसकी घात (1) नहीं है।
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कौन-सा व्यंजक (m) में बहुपद है?
Which expression is a polynomial in (m)?
#definition-polynomial
#polynomial-in-m
#valid-powers
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A \(m^2+\frac{1}{m}\)
B \(m^{-2}+7\)
C \(2m^5-3m+1\)
D \(\sqrt{m}+4\)
Explanation opens after your attempt
Correct Answer
C. \(2m^5-3m+1\)
Step 1
Concept
In \(2m^5-3m+1\), the powers of (m) are (5), (1), and (0). All are valid.
Step 2
Why this answer is correct
The correct answer is C. \(2m^5-3m+1\). In \(2m^5-3m+1\), the powers of (m) are (5), (1), and (0). All are valid.
Step 3
Exam Tip
\(2m^5-3m+1\) में (m) की घातें (5), (1) और (0) हैं। ये सभी मान्य हैं।
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यदि (p(x)=ax-4 +3x-2 -1) में (a=0) हो, तो घात क्या होगी?
If (a=0) in (p(x)=ax-4 +3x-2 -1), what will be the degree?
#definition-polynomial
#parameter
#degree-change
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A (4)
B (3)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
When (a=0), the \(x^4\) term disappears. The remaining polynomial \(3x^2-1\) has degree (2).
Step 2
Why this answer is correct
The correct answer is C. (2). When (a=0), the \(x^4\) term disappears. The remaining polynomial \(3x^2-1\) has degree (2).
Step 3
Exam Tip
(a=0) होने पर \(x^4\) वाला पद हट जाता है। शेष बहुपद \(3x^2-1\) की घात (2) है।
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किस विकल्प में बहुपद की मुख्य शर्त सही है?
Which option gives the main condition of a polynomial correctly?
#definition-polynomial
#condition
#concept
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A चर की घातें ऋणात्मक हो सकती हैं / Variable powers can be negative
B चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए / Variable powers must be zero or positive integers
C चर हमेशा हर में होना चाहिए / The variable must always be in the denominator
D चर की घात हमेशा \(\frac{1}{2}\) होनी चाहिए / The variable power must always be \(\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
B. चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए / Variable powers must be zero or positive integers
Step 1
Concept
In a polynomial, powers of the variable are 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 होनी चाहिए / Variable powers must be zero or positive integers. In a polynomial, powers of the variable are 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 होती हैं। यह परिभाषा की सबसे महत्वपूर्ण शर्त है।
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\(x^3+2x^2+x+5\) की घात क्या है?
What is the degree of \(x^3+2x^2+x+5\)?
#definition-polynomial
#degree
#cubic
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A (1)
B (2)
C (5)
D (3)
Explanation opens after your attempt
Step 1
Concept
The highest power is (3) in \(x^3\). Therefore, the degree of the polynomial is (3).
Step 2
Why this answer is correct
The correct answer is D. (3). The highest power is (3) in \(x^3\). Therefore, the degree of the polynomial is (3).
Step 3
Exam Tip
सबसे बड़ी घात \(x^3\) में (3) है। इसलिए बहुपद की घात (3) है।
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कौन-सा व्यंजक (x) में बहुपद नहीं है लेकिन वास्तविक गुणांक रखता है?
Which expression is not a polynomial in (x) but has real coefficients?
#definition-polynomial
#real-coefficients
#denominator
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A \(2x^3+\sqrt{7}x\)
B \(\frac{4}{x}-3\)
C \(5x^2-1\)
D \(8x^0+2x\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{4}{x}-3\)
Step 1
Concept
Having real coefficients is not enough. In \(\frac{4}{x}\), the power of (x) is (-1), so it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{4}{x}-3\). Having real coefficients is not enough. In \(\frac{4}{x}\), the power of (x) is (-1), so it is not a polynomial.
Step 3
Exam Tip
वास्तविक गुणांक होना पर्याप्त नहीं है। \(\frac{4}{x}\) में (x) की घात (-1) है इसलिए यह बहुपद नहीं है।
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किस व्यंजक में स्थिर पद ऋणात्मक है और फिर भी बहुपद है?
Which expression has a negative constant term and is still a polynomial?
#definition-polynomial
#negative-constant
#valid-polynomial
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A \(x^2-11\)
B \(x^{-2}-11\)
C \(\sqrt{x}-11\)
D \(\frac{1}{x}-11\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11\)
Step 1
Concept
A negative constant term does not prevent an expression from being a polynomial. In \(x^2-11\), all powers are valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-11\). A negative constant term does not prevent an expression from being a polynomial. In \(x^2-11\), all powers are valid.
Step 3
Exam Tip
ऋणात्मक स्थिर पद होने से व्यंजक बहुपद बनने से नहीं रुकता। \(x^2-11\) में सभी घातें मान्य हैं।
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(p(u)=3u-2 -4u+10) की घात और प्रकार क्या है?
What are the degree and type of (p(u)=3u-2 -4u+10)?
#definition-polynomial
#degree-type
#quadratic
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A घात (1), रैखिक / Degree (1), linear
B घात (2), द्विघात / Degree (2), quadratic
C घात (3), घन / Degree (3), cubic
D घात (0), स्थिर / Degree (0), constant
Explanation opens after your attempt
Correct Answer
B. घात (2), द्विघात / Degree (2), quadratic
Step 1
Concept
The highest power is (2). Therefore, it is a quadratic polynomial.
Step 2
Why this answer is correct
The correct answer is B. घात (2), द्विघात / Degree (2), quadratic. The highest power is (2). Therefore, it is a quadratic polynomial.
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है।
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\(2x^5+x^2-3\) में कौन-सी घातें उपस्थित हैं?
Which powers are present in \(2x^5+x^2-3\)?
#definition-polynomial
#powers
#constant-term
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A (5), (2), (0)
B (5), (1), (-3)
C (2), (1), (0)
D (5), \(\frac{1}{2}\), (0)
Explanation opens after your attempt
Correct Answer
A. (5), (2), (0)
Step 1
Concept
The power of \(2x^5\) is (5), the power of \(x^2\) is (2), and the constant term is treated as power (0).
Step 2
Why this answer is correct
The correct answer is A. (5), (2), (0). The power of \(2x^5\) is (5), the power of \(x^2\) is (2), and the constant term is treated as power (0).
Step 3
Exam Tip
\(2x^5\) की घात (5), \(x^2\) की घात (2), और स्थिर पद की घात (0) मानी जाती है।
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कौन-सा व्यंजक बहुपद है और उसकी घात (6) है?
Which expression is a polynomial of degree (6)?
#definition-polynomial
#degree-six
#valid-polynomial
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A (x^{6 / 2}+1)
B \(x^{-6}+4\)
C \(2x^6-x^3+8\)
D \(\frac{1}{x^6}+2\)
Explanation opens after your attempt
Correct Answer
C. \(2x^6-x^3+8\)
Step 1
Concept
In \(2x^6-x^3+8\), all powers are valid and the highest power is (6). So its degree is (6).
Step 2
Why this answer is correct
The correct answer is C. \(2x^6-x^3+8\). In \(2x^6-x^3+8\), all powers are valid and the highest power is (6). So its degree is (6).
Step 3
Exam Tip
\(2x^6-x^3+8\) में सभी घातें मान्य हैं और सबसे बड़ी घात (6) है। इसलिए इसकी घात (6) है।
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कौन-सा कथन बहुपद के लिए गलत है?
Which statement is false for a polynomial?
#definition-polynomial
#false-statement
#denominator
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A गुणांक वास्तविक हो सकते हैं / Coefficients can be real
B चर की घातें धनात्मक पूर्णांक हो सकती हैं / Variable powers can be positive integers
C चर हर में रह सकता है / The variable can be in the denominator
D स्थिर पद हो सकता है / A constant term can be present
Explanation opens after your attempt
Correct Answer
C. चर हर में रह सकता है / The variable can be in the denominator
Step 1
Concept
If the variable appears in the denominator, its power often becomes negative. Negative powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. चर हर में रह सकता है / The variable can be in the denominator. If the variable appears in the denominator, its power often becomes negative. Negative powers are not valid in a polynomial.
Step 3
Exam Tip
यदि चर हर में आता है तो अक्सर उसकी घात ऋणात्मक हो जाती है। बहुपद में ऋणात्मक घात मान्य नहीं होती।
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\(x^2+x^{-1}+1\) बहुपद क्यों नहीं है?
Why is \(x^2+x^{-1}+1\) not a polynomial?
#definition-polynomial
#negative-power
#reason
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A क्योंकि \(x^2\) है / Because it has \(x^2\)
B क्योंकि \(x^{-1}\) की घात ऋणात्मक है / Because the power in \(x^{-1}\) is negative
C क्योंकि स्थिर पद है / Because it has a constant term
D क्योंकि तीन पद हैं / Because it has three terms
Explanation opens after your attempt
Correct Answer
B. 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 B. 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 स्वीकार्य नहीं होती।
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कौन-सा व्यंजक (x) में बहुपद है और दशमलव गुणांक रखता है?
Which expression is a polynomial in (x) with a decimal coefficient?
#definition-polynomial
#decimal-coefficient
#real-coefficients
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A \(1.5x^2-4x+3\)
B \(1.5x^{-2}+3\)
C \(\sqrt{x}+1.5\)
D \(\frac{1.5}{x}+2\)
Explanation opens after your attempt
Correct Answer
A. \(1.5x^2-4x+3\)
Step 1
Concept
The decimal (1.5) is a real coefficient. The powers of (x) are (2), (1), and (0), which are valid.
Step 2
Why this answer is correct
The correct answer is A. \(1.5x^2-4x+3\). The decimal (1.5) is a real coefficient. The powers of (x) are (2), (1), and (0), which are valid.
Step 3
Exam Tip
दशमलव (1.5) वास्तविक गुणांक है। (x) की घातें (2), (1) और (0) मान्य हैं।
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किस बहुपद में \(x^2\) का पद नहीं है लेकिन घात (4) है?
Which polynomial has no \(x^2\) term but has degree (4)?
#definition-polynomial
#missing-term
#degree-four
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A \(x^4+3x-2\)
B \(x^2+3x-2\)
C \(x^{-4}+3x\)
D \(\sqrt{x}+x^4\)
Explanation opens after your attempt
Correct Answer
A. \(x^4+3x-2\)
Step 1
Concept
In \(x^4+3x-2\), the \(x^2\) term is missing but the highest power is (4). A missing term does not affect validity.
Step 2
Why this answer is correct
The correct answer is A. \(x^4+3x-2\). In \(x^4+3x-2\), the \(x^2\) term is missing but the highest power is (4). A missing term does not affect validity.
Step 3
Exam Tip
\(x^4+3x-2\) में \(x^2\) पद नहीं है पर सबसे बड़ी घात (4) है। गायब पद घात को नहीं रोकता।
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(p(x)=5x-2 ) की सही पहचान कौन-सी है?
Which is the correct identification of (p(x)=5x-2 )?
#definition-polynomial
#quadratic-monomial
#classification
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A द्विघात एकपदी / Quadratic monomial
B रैखिक एकपदी / Linear monomial
C स्थिर बहुपद / Constant polynomial
D घन द्विपदी / Cubic binomial
Explanation opens after your attempt
Correct Answer
A. द्विघात एकपदी / Quadratic monomial
Step 1
Concept
\(5x^2\) has one term and degree (2). Therefore, it is a quadratic monomial.
Step 2
Why this answer is correct
The correct answer is A. द्विघात एकपदी / Quadratic monomial. \(5x^2\) has one term and degree (2). Therefore, it is a quadratic monomial.
Step 3
Exam Tip
\(5x^2\) में एक पद है और घात (2) है। इसलिए यह द्विघात एकपदी है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि इसमें \(\frac{1}{x^3}\) है?
Which expression is not a polynomial because it contains \(\frac{1}{x^3}\)?
#definition-polynomial
#denominator
#negative-exponent
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A \(x^3+1\)
B \(4+\frac{1}{x^3}\)
C \(x^0+x^3\)
D \(7x^2-5\)
Explanation opens after your attempt
Correct Answer
B. \(4+\frac{1}{x^3}\)
Step 1
Concept
\(\frac{1}{x^3}=x^{-3}\). Due to the negative power, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(4+\frac{1}{x^3}\). \(\frac{1}{x^3}=x^{-3}\). Due to the negative power, it is not a polynomial.
Step 3
Exam Tip
\(\frac{1}{x^3}=x^{-3}\) होता है। ऋणात्मक घात के कारण यह बहुपद नहीं है।
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\(3x^2-7\) में पदों की संख्या और घात क्या है?
What are the number of terms and degree in \(3x^2-7\)?
#definition-polynomial
#term-count
#degree
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A (2) पद और घात (2) / (2) terms and degree (2)
B (3) पद और घात (2) / (3) terms and degree (2)
C (2) पद और घात (7) / (2) terms and degree (7)
D (1) पद और घात (0) / (1) term and degree (0)
Explanation opens after your attempt
Correct Answer
A. (2) पद और घात (2) / (2) terms and degree (2)
Step 1
Concept
\(3x^2-7\) has two terms and the highest power is (2). So it is a quadratic binomial.
Step 2
Why this answer is correct
The correct answer is A. (2) पद और घात (2) / (2) terms and degree (2). \(3x^2-7\) has two terms and the highest power is (2). So it is a quadratic binomial.
Step 3
Exam Tip
\(3x^2-7\) में दो पद हैं और सबसे बड़ी घात (2) है। इसलिए यह द्विघात द्विपदी है।
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कौन-सा व्यंजक (n) में बहुपद नहीं है?
Which expression is not a polynomial in (n)?
#definition-polynomial
#fractional-exponent
#not-polynomial
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A \(n^4-2n^2+1\)
B (6n+5)
C (n^{4 / 3}+2)
D \(9n^0-1\)
Explanation opens after your attempt
Correct Answer
C. (n^{4 / 3}+2)
Step 1
Concept
The power in \(n^{4/3}\) is not an integer. In a polynomial, variable powers must be non-negative integers.
Step 2
Why this answer is correct
The correct answer is C. \(n^{4 / 3}+2\). The power in \(n^{4/3}\) is not an integer. In a polynomial, variable powers must be non-negative integers.
Step 3
Exam Tip
\(n^{4/3}\) की घात पूर्णांक नहीं है। बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए।
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यदि (p(x)=2x-3 +ax-2 +5) में (a=0) हो, तो कौन-सा कथन सही है?
If (a=0) in (p(x)=2x-3 +ax-2 +5), which statement is correct?
#definition-polynomial
#parameter
#degree
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A घात (2) हो जाएगी / The degree becomes (2)
B घात (3) रहेगी / The degree remains (3)
C यह शून्य बहुपद बन जाएगा / It becomes the zero polynomial
D यह बहुपद नहीं रहेगा / It will not remain a polynomial
Explanation opens after your attempt
Correct Answer
B. घात (3) रहेगी / The degree remains (3)
Step 1
Concept
When (a=0), the \(x^2\) term disappears but \(2x^3\) remains. Therefore, the degree stays (3).
Step 2
Why this answer is correct
The correct answer is B. घात (3) रहेगी / The degree remains (3). When (a=0), the \(x^2\) term disappears but \(2x^3\) remains. Therefore, the degree stays (3).
Step 3
Exam Tip
(a=0) पर \(x^2\) वाला पद हटता है लेकिन \(2x^3\) रहता है। इसलिए घात (3) ही रहेगी।
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कौन-सा विकल्प बहुपद की परिभाषा के अनुसार सही उदाहरण देता है?
Which option gives a correct example according to the definition of polynomial?
#definition-polynomial
#example
#valid-powers
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A \(x^2+4x+4\) क्योंकि घातें (2), (1), (0) हैं / \(x^2+4x+4\) because powers are (2), (1), (0)
B \(x^{-2}+4\) क्योंकि घात (-2) है / \(x^{-2}+4\) because power is (-2)
C \(\sqrt{x}+4\) क्योंकि मूल है / \(\sqrt{x}+4\) because it has a root
D \(\frac{1}{x}+4\) क्योंकि हर है / \(\frac{1}{x}+4\) because it has denominator
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+4\) क्योंकि घातें (2), (1), (0) हैं / \(x^2+4x+4\) because powers are (2), (1), (0)
Step 1
Concept
In \(x^2+4x+4\), all powers are non-negative integers. So it is a correct polynomial example.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+4\) क्योंकि घातें (2), (1), (0) हैं / \(x^2+4x+4\) because powers are (2), (1), (0). In \(x^2+4x+4\), all powers are non-negative integers. So it is a correct polynomial example.
Step 3
Exam Tip
\(x^2+4x+4\) में सभी घातें शून्य या धनात्मक पूर्णांक हैं। इसलिए यह सही बहुपद उदाहरण है।
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कौन-सा व्यंजक (x) में बहुपद है जबकि (y) गुणांक की तरह है?
Which expression is a polynomial in (x) while (y) acts like a coefficient?
#definition-polynomial
#polynomial-in-x
#coefficient-parameter
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A \(y^2x^3-4x+6\)
B \(\frac{y}{x}+3\)
C \(x^{-1}+y\)
D \(\sqrt{x}+y^2\)
Explanation opens after your attempt
Correct Answer
A. \(y^2x^3-4x+6\)
Step 1
Concept
With respect to (x), \(y^2\) 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. \(y^2x^3-4x+6\). With respect to (x), \(y^2\) can be treated like a coefficient. The powers of (x) are (3), (1), and (0).
Step 3
Exam Tip
(x) के संदर्भ में \(y^2\) गुणांक की तरह माना जा सकता है। (x) की घातें (3), (1) और (0) हैं।
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कौन-सा व्यंजक बहुपद है जिसमें केवल सम घातें हैं?
Which expression is a polynomial having only even powers?
#definition-polynomial
#even-powers
#valid-polynomial
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A \(x^6+2x^4-x^2+9\)
B \(x^5+x^3+1\)
C \(x^{-2}+x^4\)
D \(\sqrt{x}+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^6+2x^4-x^2+9\)
Step 1
Concept
In \(x^6+2x^4-x^2+9\), the powers are (6), (4), (2), and (0). All are even and valid.
Step 2
Why this answer is correct
The correct answer is A. \(x^6+2x^4-x^2+9\). In \(x^6+2x^4-x^2+9\), the powers are (6), (4), (2), and (0). All are even and valid.
Step 3
Exam Tip
\(x^6+2x^4-x^2+9\) में घातें (6), (4), (2) और (0) हैं। ये सभी सम और मान्य हैं।
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\(x^4+2x^3+x^2+x+1\) में कितने पद हैं?
How many terms are there in \(x^4+2x^3+x^2+x+1\)?
#definition-polynomial
#term-count
#five-terms
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
This polynomial has (5) distinct terms. Use plus signs to identify the terms separately.
Step 2
Why this answer is correct
The correct answer is C. (5). This polynomial has (5) distinct terms. Use plus signs to identify the terms separately.
Step 3
Exam Tip
इस बहुपद में (5) अलग-अलग पद हैं। जोड़ के चिन्हों से पदों को अलग पहचानें।
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\(x^2-3x+2\) की सही पहचान क्या है?
What is the correct identification of \(x^2-3x+2\)?
#definition-polynomial
#quadratic-trinomial
#identification
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A द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial
B रैखिक द्विपदी / Linear binomial
C घन त्रिपदी / Cubic trinomial
D स्थिर बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial
Step 1
Concept
Its degree is (2) and it has (3) terms. Therefore, it is a quadratic trinomial polynomial.
Step 2
Why this answer is correct
The correct answer is A. द्विघात त्रिपदी बहुपद / Quadratic trinomial polynomial. Its degree is (2) and it has (3) terms. Therefore, it is a quadratic trinomial polynomial.
Step 3
Exam Tip
इसकी घात (2) है और इसमें (3) पद हैं। इसलिए यह द्विघात त्रिपदी बहुपद है।
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कौन-सा व्यंजक (x) में बहुपद नहीं है क्योंकि उसमें (x) हर में है?
Which expression is not a polynomial in (x) because it has (x) in the denominator?
#definition-polynomial
#denominator
#not-polynomial
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A \(2x^2+5\)
B \(3x^3-x\)
C \(\frac{x^2+1}{x}\)
D \(7x^0+4x\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{x^2+1}{x}\)
Step 1
Concept
\(\frac{x^2+1}{x}=x+\frac{1}{x}\) contains \(\frac{1}{x}\), whose power is (-1). Therefore, it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{x^2+1}{x}\). \(\frac{x^2+1}{x}=x+\frac{1}{x}\) contains \(\frac{1}{x}\), whose power is (-1). Therefore, it is not a polynomial.
Step 3
Exam Tip
\(\frac{x^2+1}{x}=x+\frac{1}{x}\) में \(\frac{1}{x}\) की घात (-1) है। इसलिए यह बहुपद नहीं है।
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