52 results found for "monomial-vs-binomial" in Class 10.
Which of the following is a monomial?
A. \(3x^2\)
एक पद वाला बहुपद एकपदी कहलाता है। \(3x^2\) में केवल एक पद है। / A polynomial with one term is called a monomial. \(3x^2\) has only one term.
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Which polynomial is a monomial?
A. \(3x^2\)
एकपदी में केवल एक पद होता है। \(3x^2\) एक ही पद है। / A monomial has only one term. The expression \(3x^2\) has one term.
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Which of the following is a binomial?
A. \(x^2+3\)
दो पदों वाला बहुपद द्विपदी कहलाता है। \(x^2+3\) में दो पद हैं। / A polynomial with two terms is a binomial. \(x^2+3\) has two terms.
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Which polynomial is a binomial?
B. (5x-7)
द्विपदी में दो पद होते हैं। (5x-7) में (5x) और (-7) दो पद हैं। / A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
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What is the simplified form of (\frac{\(2x^2y^{-2}\)3}{8x-3y^{-7}}) if \(x\neq0\) and \(y\neq0\)?
A. \(x^3y\)
ऊपर (\(2x^2y^{-2}\)3=8x-6y^{-6}) है। भाग देने पर \(x^{6-3}y^{-6-(-7)}=x^3y\) मिलता है। / The numerator is (\(2x^2y^{-2}\)3=8x-6y^{-6}). Dividing gives \(x^{6-3}y^{-6-(-7)}=x^3y\).
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What is the product of (\(6x^2y\)\(3xy^4\))?
A. \(18x^3y^5\)
गुणांक (18), \(x^{2+1}=x^3\) और \(y^{1+4}=y^5\) है। समान आधार की घातें जोड़ें। / The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.
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What is the simplified form of \(\frac{18x^5y^3}{6x^2y}\) if \(x\neq0\) and \(y\neq0\)?
A. \(3x^3y^2\)
गुणांक \(\frac{18}{6}=3\), \(x^{5-2}=x^3\) और \(y^{3-1}=y^2\) है। इसलिए उत्तर \(3x^3y^2\) है। / The coefficient is \(\frac{18}{6}=3\), \(x^{5-2}=x^3\), and \(y^{3-1}=y^2\). So the answer is \(3x^3y^2\).
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What is the correct expansion of (\(2a^2b^3\)2)?
A. \(4a^4b^6\)
बाहरी घात गुणांक और सभी घातों पर लगती है। इसलिए (\(2a^2b^3\)2=4a-4b-6) है। / The outside exponent applies to the coefficient and all powers. Thus (\(2a^2b^3\)2=4a-4b-6).
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What is the product of (\(5x^3y\)\(2xy^2\))?
A. \(10x^4y^3\)
गुणांक (10), \(x^{3+1}=x^4\) और \(y^{1+2}=y^3\) है। समान आधार की घातें जोड़ें। / The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.
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What is the simplified form of \(24a^5b^3\div6a^2b^2\) if \(a\neq0\) and \(b\neq0\)?
A. \(4a^3b\)
गुणांक \(\frac{24}{6}=4\), \(a^{5-2}=a^3\) और \(b^{3-2}=b\) है। इसलिए उत्तर \(4a^3b\) है। / The coefficient is \(\frac{24}{6}=4\), \(a^{5-2}=a^3\), and \(b^{3-2}=b\). So the answer is \(4a^3b\).
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What is the simplified form of (\frac{\(3x^2\)2}{9x}) if \(x\neq0\)?
B. \(x^3\)
(\(3x^2\)2=9x-4) होता है। फिर \(\frac{9x^4}{9x}=x^3\) है। / (\(3x^2\)2=9x-4). Then \(\frac{9x^4}{9x}=x^3\).
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What is the correct simplified form of (\(a^3b^2\)3)?
A. \(a^9b^6\)
बाहरी घात प्रत्येक कारक की घात से गुणा होती है। इसलिए (\(a^3b^2\)3=a-9b-6) है। / The outside exponent multiplies the exponent of each factor. Hence (\(a^3b^2\)3=a-9b-6).
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What is the simplified form of (\frac{\(3x^2y^{-1}\)2}{9xy^{-3}}) if \(x\neq0\) and \(y\neq0\)?
A. \(x^3y\)
ऊपर (\(3x^2y^{-1}\)2=9x-4y^{-2}) है। भाग देने पर \(x^{4-1}y^{-2-(-3)}=x^3y\) मिलता है। / The numerator is (\(3x^2y^{-1}\)2=9x-4y^{-2}). Dividing gives \(x^{4-1}y^{-2-(-3)}=x^3y\).
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What is the product of (\(3x^2y\)\(4xy^3\))?
A. \(12x^3y^4\)
गुणांक (12), \(x^{2+1}=x^3\) और \(y^{1+3}=y^4\) है। समान आधार की घातें जोड़ें। / The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.
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What is the simplified form of \(15a^4b^2\div5a^2b\) if \(a\neq0\) and \(b\neq0\)?
A. \(3a^2b\)
गुणांक \(\frac{15}{5}=3\), \(a^{4-2}=a^2\) और \(b^{2-1}=b\) है। इसलिए उत्तर \(3a^2b\) है। / The coefficient is \(\frac{15}{5}=3\), \(a^{4-2}=a^2\), and \(b^{2-1}=b\). So the answer is \(3a^2b\).
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What is the simplified form of (\frac{\(2x^3\)2}{4x-2}) if \(x\neq0\)?
B. \(x^4\)
(\(2x^3\)2=4x-6) होता है। फिर \(\frac{4x^6}{4x^2}=x^4\) है। / (\(2x^3\)2=4x-6). Then \(\frac{4x^6}{4x^2}=x^4\).
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What is the correct simplified form of (\(x^2y^3\)2)?
A. \(x^4y^6\)
बाहरी घात दोनों कारकों की घातों से गुणा होती है। इसलिए (\(x^2y^3\)2=x-4y-6) है। / The outside exponent multiplies the exponents of both factors. Hence (\(x^2y^3\)2=x-4y-6).
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What is the simplified form of \(42a^7\div6a^4\) if \(a\neq0\)?
A. \(7a^3\)
\(\frac{42}{6}=7\) और \(\frac{a^7}{a^4}=a^3\) है। इसलिए उत्तर \(7a^3\) है। / \(\frac{42}{6}=7\) and \(\frac{a^7}{a^4}=a^3\). Therefore the answer is \(7a^3\).
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What is the product of \(5x^4\cdot2x^3\)?
B. \(10x^7\)
गुणांक \(5\cdot2=10\) और \(x^4\cdot x^3=x^7\) है। इसलिए गुणनफल \(10x^7\) है। / The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).
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What is the simplified form of \(\frac{35x^6}{7x^3}\) if \(x\neq0\)?
A. \(5x^3\)
गुणांक \(\frac{35}{7}=5\) और चर भाग \(\frac{x^6}{x^3}=x^3\) है। इसलिए सरल रूप \(5x^3\) है। / The coefficient part is \(\frac{35}{7}=5\) and the variable part is \(\frac{x^6}{x^3}=x^3\). Thus the simplified form is \(5x^3\).
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What is the product of \(6x\cdot5x^2\)?
C. \(30x^3\)
गुणांक \(6\cdot5=30\) और \(x\cdot x^2=x^3\) है। इसलिए उत्तर \(30x^3\) है। / The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
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What is the simplified form of \(30a^6\div5a^3\) if \(a\neq0\)?
A. \(6a^3\)
\(\frac{30}{5}=6\) और \(\frac{a^6}{a^3}=a^3\) है। इसलिए उत्तर \(6a^3\) है। / \(\frac{30}{5}=6\) and \(\frac{a^6}{a^3}=a^3\). Therefore the answer is \(6a^3\).
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What is the product of \(4x^3\cdot3x^2\)?
B. \(12x^5\)
गुणांक \(4\cdot3=12\) और \(x^3\cdot x^2=x^5\) है। इसलिए गुणनफल \(12x^5\) है। / The coefficients give \(4\cdot3=12\), and \(x^3\cdot x^2=x^5\). So the product is \(12x^5\).
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What is the simplified form of \(\frac{24x^5}{6x^2}\) if \(x\neq0\)?
A. \(4x^3\)
गुणांक \(\frac{24}{6}=4\) और \(\frac{x^5}{x^2}=x^3\) है। इसलिए सरल रूप \(4x^3\) है। / The coefficient part is \(\frac{24}{6}=4\) and \(\frac{x^5}{x^2}=x^3\). Thus the simplified form is \(4x^3\).
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What is the product of \(5x\cdot4x^3\)?
C. \(20x^4\)
गुणांक \(5\cdot4=20\) और \(x\cdot x^3=x^4\) है। इसलिए उत्तर \(20x^4\) है। / The coefficients give \(5\cdot4=20\), and \(x\cdot x^3=x^4\). Therefore the answer is \(20x^4\).
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What is the simplified form of \(18a^5\div6a^2\) if \(a\neq0\)?
A. \(3a^3\)
\(\frac{18}{6}=3\) और \(\frac{a^5}{a^2}=a^3\) है। इसलिए उत्तर \(3a^3\) है। / \(\frac{18}{6}=3\) and \(\frac{a^5}{a^2}=a^3\). Therefore the answer is \(3a^3\).
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What is the product of \(3x^2\cdot2x\)?
C. \(6x^3\)
गुणांक \(3\cdot2=6\) और \(x^2\cdot x=x^3\) है। इसलिए गुणनफल \(6x^3\) है। / The coefficients give \(3\cdot2=6\), and \(x^2\cdot x=x^3\). So the product is \(6x^3\).
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What is the simplified form of \(\frac{15x^4}{5x^2}\) if \(x\neq0\)?
A. \(3x^2\)
गुणांक \(\frac{15}{5}=3\) और चर भाग \(\frac{x^4}{x^2}=x^2\) है। इसलिए सरल रूप \(3x^2\) है। / The coefficient part is \(\frac{15}{5}=3\) and the variable part is \(\frac{x^4}{x^2}=x^2\). Thus the simplified form is \(3x^2\).
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What is the product of \(4x\cdot3x^2\)?
C. \(12x^3\)
पहले गुणांक \(4\cdot3=12\) और फिर \(x\cdot x^2=x^3\) करें। इसलिए उत्तर \(12x^3\) है। / First multiply coefficients \(4\cdot3=12\), then \(x\cdot x^2=x^3\). Therefore the answer is \(12x^3\).
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What is obtained by simplifying ((3x+2)(x-4))?
A. \(3x^2-10x-8\)
((3x+2)(x-4)=3x-2-12x+2x-8=3x-2-10x-8)। प्रत्येक पद का हर पद से गुणा करें। / ((3x+2)(x-4)=3x-2-12x+2x-8=3x-2-10x-8). Multiply each term by each term.
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What is the polynomial form of ((x-5)(x+2))?
A. \(x^2-3x-10\)
((x-5)(x+2)=x-2+2x-5x-10=x-2-3x-10)। मध्य पदों को संकेत सहित जोड़ें। / ((x-5)(x+2)=x-2+2x-5x-10=x-2-3x-10). Combine the middle terms with signs.
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Which option correctly describes the type of \(x^3-1\)?
C. त्रिघात द्विपदीCubic binomial
\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है। / \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
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What is obtained by simplifying ((2x-1)(x+5))?
A. \(2x^2+9x-5\)
((2x-1)(x+5)=2x-2+10x-x-5=2x-2+9x-5)। हर पद का हर पद से गुणा करें। / ((2x-1)(x+5)=2x-2+10x-x-5=2x-2+9x-5). Multiply each term by each term.
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How many terms are there in \(7x^2+5\)?
B. (2)
पद \(7x^2\) और (5) हैं। इसलिए इसमें (2) पद हैं। / The terms are \(7x^2\) and (5). Therefore it has (2) terms.
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Which of the following is a polynomial with (2) terms?
B. \(5x^3-4\)
\(5x^3-4\) में (2) पद हैं। दो पदों वाला बहुपद द्विपदी कहलाता है। / \(5x^3-4\) has (2) terms. A polynomial with two terms is called a binomial.
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How many terms are there in (p(x)=7x-2-1)?
B. (2)
\(7x^2\) और (-1) दो पद हैं। इसलिए यह द्विपदी भी है। / There are two terms \(7x^2\) and (-1). So it is also a binomial.
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What is the expansion of ((5x+2)2)?
A. \(25x^2+20x+4\)
((a+b)2) में (a=5x) और (b=2) लें। मध्य पद \(2\cdot5x\cdot2=20x\) है। / Take (a=5x) and (b=2) in ((a+b)2). The middle term is \(2\cdot5x\cdot2=20x\).
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What is the expansion of ((4x-5)2)?
A. \(16x^2-40x+25\)
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=4x) और (b=5) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=4x) and (b=5).
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What is the expansion of ((4x+5)(x-3))?
A. \(4x^2-7x-15\)
वितरण से \(4x^2-12x+5x-15=4x^2-7x-15\) है। समान पदों को अंत में जोड़ें। / By distribution, \(4x^2-12x+5x-15=4x^2-7x-15\). Combine like terms at the end.
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What is the expansion of ((x-7)(x+3))?
A. \(x^2-4x-21\)
गुणा करने पर \(x^2+3x-7x-21=x^2-4x-21\) है। चिह्नों पर ध्यान दें। / Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.
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What is the expansion of ((x+6)(x+4))?
A. \(x^2+10x+24\)
वितरण नियम से \(x^2+4x+6x+24=x^2+10x+24\) मिलता है। मध्य पद समान पद जोड़कर बनता है। / By distribution, \(x^2+4x+6x+24=x^2+10x+24\). The middle term forms by combining like terms.
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What is the expansion of ((4x+3)2)?
A. \(16x^2+24x+9\)
((a+b)2) में (a=4x) और (b=3) लें। मध्य पद \(2\cdot4x\cdot3=24x\) है। / Take (a=4x) and (b=3) in ((a+b)2). The middle term is \(2\cdot4x\cdot3=24x\).
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What is the expansion of ((3x-4)2)?
A. \(9x^2-24x+16\)
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=3x) और (b=4) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=3x) and (b=4).
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What is the expansion of ((3x+1)(x-4))?
A. \(3x^2-11x-4\)
वितरण से \(3x^2-12x+x-4=3x^2-11x-4\) है। बीच के समान पद जोड़ें। / By distribution, \(3x^2-12x+x-4=3x^2-11x-4\). Combine the middle like terms.
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What is the expansion of ((x-5)(x+2))?
A. \(x^2-3x-10\)
गुणा करने पर \(x^2+2x-5x-10=x^2-3x-10\) है। चिह्नों पर ध्यान दें। / Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.
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What is the expansion of ((3x+2)2)?
A. \(9x^2+12x+4\)
((a+b)2) में (a=3x) और (b=2) लें। मध्य पद \(2\cdot3x\cdot2=12x\) है। / Take (a=3x) and (b=2) in ((a+b)2). The middle term is \(2\cdot3x\cdot2=12x\).
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What is the expansion of ((2x-3)2)?
A. \(4x^2-12x+9\)
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=2x) और (b=3) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=2x) and (b=3).
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What is the expansion of ((2x+3)(x-2))?
A. \(2x^2-x-6\)
वितरण से \(2x^2-4x+3x-6=2x^2-x-6\) है। समान पदों को अंत में जोड़ें। / By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.
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What is the expansion of ((x-4)(x+1))?
A. \(x^2-3x-4\)
गुणा करने पर \(x^2+x-4x-4=x^2-3x-4\) मिलता है। चिह्नों पर विशेष ध्यान दें। / Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.
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What is the expanded form of ((2x+1)(x-4)=0)?
A. \(2x^2-7x-4=0\)
विस्तार करने पर \(2x^2-8x+x-4=0\) मिलता है। समान पद जोड़कर \(2x^2-7x-4=0\) बनता है। / Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
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What is the expanded form of ((x+4)(x+5)=0)?
A. \(x^2+9x+20=0\)
विस्तार करने पर \(x^2+5x+4x+20=0\) मिलता है। समान पद जोड़कर \(x^2+9x+20=0\) बनता है। / Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
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What is the expanded form of ((x+2)(x+3)=0)?
A. \(x^2+5x+6=0\)
विस्तार से \(x^2+3x+2x+6=0\) मिलता है। समान पद जोड़कर \(x^2+5x+6=0\) बनता है। / Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
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