((4x+3)\(x^2-2x+5\)) में अचर पद क्या है?
What is the constant term in ((4x+3)\(x^2-2x+5\))?
#constant term
#multiplication
#polynomial
A (3)
B (5)
C (8)
D (15)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is D. (15). The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल \(3\cdot5=15\) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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((3x-2)\(2x^2+x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((3x-2)\(2x^2+x-5\))?
#multiplication
#coefficient
#expansion
A (-1)
B (1)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-1). ((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 3
Exam Tip
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), इसलिए \(x^2\) का गुणांक (-1) है। विस्तार के बाद समान पद मिलाएं।
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((3x-2)\(x^2+5x-1\)) में अचर पद क्या है?
What is the constant term in ((3x-2)\(x^2+5x-1\))?
#constant term
#multiplication
#polynomial
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is C. (2). The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल ((-2)(-1)=2) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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((2x-1)\(x^2-3x+4\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((2x-1)\(x^2-3x+4\))?
#multiplication
#coefficient
#expansion
A (-7)
B (-6)
C (-5)
D (8)
Explanation opens after your attempt
Step 1
Concept
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-7). ((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 3
Exam Tip
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), इसलिए गुणांक (-7) है। विस्तार के बाद समान पद मिलाएं।
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((2x-3)\(x^2+x+1\)) में अचर पद क्या है?
What is the constant term in ((2x-3)\(x^2+x+1\))?
#constant term
#multiplication
#polynomial
A (-3)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is A. (-3). The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल ((-3)\cdot1=-3) से आता है। अचर पद के लिए अचर पदों का गुणन देखें।
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((x-2)\(3x^2+4x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((x-2)\(3x^2+4x-5\))?
#multiplication
#coefficient
#expansion
A (-4)
B (-2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is B. (-2). ((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 3
Exam Tip
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), इसलिए \(x^2\) का गुणांक (-2) है। विस्तार में समान पद मिलाएं।
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(-3x\(2x^2-4x+5\)) का सरल रूप क्या है?
What is the simplified form of (-3x\(2x^2-4x+5\))?
#multiplication
#distributive property
#polynomial
A \(-6x^3+12x^2-15x\)
B \(-6x^3-12x^2-15x\)
C \(6x^3+12x^2-15x\)
D \(-6x^2+12x-15\)
Explanation opens after your attempt
Correct Answer
A. \(-6x^3+12x^2-15x\)
Step 1
Concept
Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
Step 2
Why this answer is correct
The correct answer is A. \(-6x^3+12x^2-15x\). Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
Step 3
Exam Tip
प्रत्येक पद को (-3x) से गुणा करने पर \(-6x^3+12x^2-15x\) मिलता है। ऋणात्मक गुणक के संकेत ध्यान से लगाएं।
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((x+3)(x-4)) का बहुपद रूप क्या है?
What is the polynomial form of ((x+3)(x-4))?
#multiplication
#binomials
#polynomial
A \(x^2-x-12\)
B \(x^2+7x-12\)
C \(x^2-x+12\)
D \(x^2-7x-12\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-x-12\)
Step 1
Concept
((x+3)(x-4)=x-2 -4x+3x-12=x-2 -x-12). Watch signs while combining middle terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-x-12\). ((x+3)(x-4)=x-2 -4x+3x-12=x-2 -x-12). Watch signs while combining middle terms.
Step 3
Exam Tip
((x+3)(x-4)=x-2 -4x+3x-12=x-2 -x-12)। मध्य पद जोड़ते समय संकेत देखें।
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(2x\(3x^2-5x+1\)) का सरल रूप क्या है?
What is the simplified form of (2x\(3x^2-5x+1\))?
#multiplication
#distributive property
#polynomial
A \(6x^3-10x^2+2x\)
B \(6x^2-10x+2\)
C \(5x^3-7x^2+x\)
D \(6x^3+10x^2+2x\)
Explanation opens after your attempt
Correct Answer
A. \(6x^3-10x^2+2x\)
Step 1
Concept
Multiplying each term by (2x) gives \(6x^3-10x^2+2x\). Use the distributive property.
Step 2
Why this answer is correct
The correct answer is A. \(6x^3-10x^2+2x\). Multiplying each term by (2x) gives \(6x^3-10x^2+2x\). Use the distributive property.
Step 3
Exam Tip
प्रत्येक पद को (2x) से गुणा करने पर \(6x^3-10x^2+2x\) मिलता है। वितरण नियम का प्रयोग करें।
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सरलीकृत कीजिए: (2\sqrt{3}\(\sqrt{12}-\sqrt{27}\)) का मान क्या है?
Simplify: what is the value of (2\sqrt{3}\(\sqrt{12}-\sqrt{27}\))?
#polynomials
#surds
#multiplication
#real-numbers
A (,-6,)
B (,6,)
C \(,-2\sqrt{3},\)
D \(,2\sqrt{3},\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so the inside value is \(-\sqrt{3}\) and the product is (-6). In exams, simplify the surds first.
Step 2
Why this answer is correct
The correct answer is A. (,-6,). \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so the inside value is \(-\sqrt{3}\) and the product is (-6). In exams, simplify the surds first.
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\), इसलिए अंदर का मान \(-\sqrt{3}\) है और गुणनफल (-6) है। परीक्षा में पहले surd को सरल करें।
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(\(-4a^2b^{-3}\)\(3a^{-1}b^5\)) का गुणनफल क्या है?
What is the product of (\(-4a^2b^{-3}\)\(3a^{-1}b^5\))?
#polynomials
#monomials
#multiplication
#negative-exponents
A \(,-12ab^2,\)
B \(,-12a^3b^2,\)
C \(,12ab^{-8},\)
D \(,-a b^2,\)
Explanation opens after your attempt
Correct Answer
A. \(,-12ab^2,\)
Step 1
Concept
The product of coefficients (-4) and (3) is (-12), and \(a^{2-1}b^{-3+5}=ab^2\). In exams, handle coefficients and exponents separately.
Step 2
Why this answer is correct
The correct answer is A. \(,-12ab^2,\). The product of coefficients (-4) and (3) is (-12), and \(a^{2-1}b^{-3+5}=ab^2\). In exams, handle coefficients and exponents separately.
Step 3
Exam Tip
गुणांक (-4) और (3) का गुणनफल (-12) है, और \(a^{2-1}b^{-3+5}=ab^2\) है। परीक्षा में गुणांक और घातांक अलग-अलग संभालें।
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((2x-1)(3x+4)) का विस्तार क्या होगा?
What is the expansion of ((2x-1)(3x+4))?
#polynomials
#multiplication
#binomials
#expansion
A \(,6x^2+5x-4,\)
B \(,6x^2-5x-4,\)
C \(,6x^2+11x-4,\)
D \(,6x^2+5x+4,\)
Explanation opens after your attempt
Correct Answer
A. \(,6x^2+5x-4,\)
Step 1
Concept
By distribution, \(6x^2+8x-3x-4=6x^2+5x-4\). In exams, combine cross terms with the correct sign.
Step 2
Why this answer is correct
The correct answer is A. \(,6x^2+5x-4,\). By distribution, \(6x^2+8x-3x-4=6x^2+5x-4\). In exams, combine cross terms with the correct sign.
Step 3
Exam Tip
वितरण से \(6x^2+8x-3x-4=6x^2+5x-4\) मिलता है। परीक्षा में cross terms को सही sign के साथ जोड़ें।
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((x+2)(x-3)) का विस्तार क्या है?
What is the expansion of ((x+2)(x-3))?
#polynomials
#multiplication
#expansion
#real-numbers
A \(,x^2-x-6,\)
B \(,x^2+x-6,\)
C \(,x^2-x+6,\)
D \(,x^2-5x-6,\)
Explanation opens after your attempt
Correct Answer
A. \(,x^2-x-6,\)
Step 1
Concept
Using the distributive law, (x(x-3)+2(x-3)=x-2 -x-6). In exams, check the sign of the middle term carefully.
Step 2
Why this answer is correct
The correct answer is A. \(,x^2-x-6,\). Using the distributive law, (x(x-3)+2(x-3)=x-2 -x-6). In exams, check the sign of the middle term carefully.
Step 3
Exam Tip
वितरण नियम से (x(x-3)+2(x-3)=x-2 -x-6) मिलता है। परीक्षा में middle term का sign ध्यान से जांचें।
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(\(2x^2y\)\(-3xy^2\)) का गुणनफल क्या है?
What is the product of (\(2x^2y\)\(-3xy^2\))?
#polynomials
#monomials
#multiplication
#exponents
A \(,-6x^3y^3,\)
B \(,-6x^2y^2,\)
C \(,6x^3y^3,\)
D \(,-x^3y^3,\)
Explanation opens after your attempt
Correct Answer
A. \(,-6x^3y^3,\)
Step 1
Concept
The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.
Step 2
Why this answer is correct
The correct answer is A. \(,-6x^3y^3,\). The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.
Step 3
Exam Tip
गुणांक (2) और (-3) का गुणनफल (-6) है, और समान चरों की घातें जुड़ती हैं। परीक्षा में sign और exponents दोनों ध्यान से देखें।
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((x+4)(x+3)) का विस्तार क्या है?
What is the expansion of ((x+4)(x+3))?
#polynomials
#multiplication
#binomials
A \(x^2+7x+12\)
B \(x^2+12x+7\)
C \(x^2+7\)
D (2x+7)
Explanation opens after your attempt
Correct Answer
A. \(x^2+7x+12\)
Step 1
Concept
By distribution, \(x^2+3x+4x+12=x^2+7x+12\). Combine like terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+7x+12\). By distribution, \(x^2+3x+4x+12=x^2+7x+12\). Combine like terms.
Step 3
Exam Tip
वितरण नियम से \(x^2+3x+4x+12=x^2+7x+12\) मिलता है। समान पदों को जोड़ें।
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((x+3)(x+2)) का विस्तार क्या है?
What is the expansion of ((x+3)(x+2))?
#polynomials
#multiplication
#binomials
A \(x^2+5x+6\)
B \(x^2+6x+5\)
C \(x^2+5\)
D (2x+5)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x+6\)
Step 1
Concept
By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x+6\). By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.
Step 3
Exam Tip
वितरण नियम से \(x^2+2x+3x+6=x^2+5x+6\)। मध्य पद समान पद जोड़कर बनता है।
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कौन सा विकल्प (\sqrt{2}\times\(\sqrt{18}-\sqrt{8}\)) का मान है?
Which option is the value of (\sqrt{2}\times\(\sqrt{18}-\sqrt{8}\))?
#surds
#multiplication
#rational-result
A (2)
B (4)
C \(\sqrt{10}\)
D \(2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the bracket is \(\sqrt{2}\). The product is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the bracket is \(\sqrt{2}\). The product is (2).
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए कोष्ठक \(\sqrt{2}\) है। गुणनफल (2) है।
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कौन सा विकल्प \(3\sqrt{6}\times2\sqrt{6}\) का मान है?
Which option is the value of \(3\sqrt{6}\times2\sqrt{6}\)?
#surds
#multiplication
#rational-result
A (36)
B \(6\sqrt{6}\)
C \(36\sqrt{6}\)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (36). \(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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कौन सा विकल्प \(\sqrt{18}\times\sqrt{50}\) का मान है?
Which option is the value of \(\sqrt{18}\times\sqrt{50}\)?
#multiplication
#irrational-numbers
#rational-result
A (30)
B \(\sqrt{68}\)
C \(15\sqrt{2}\)
D \(50\sqrt{18}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (30). \(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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कौन सा विकल्प \(2\sqrt{5}\times3\sqrt{5}\) का मान है?
Which option is the value of \(2\sqrt{5}\times3\sqrt{5}\)?
#surds
#multiplication
#rational-result
A (30)
B \(6\sqrt{5}\)
C \(30\sqrt{5}\)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (30). \(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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कौन सा विकल्प \(\sqrt{10}\times\sqrt{40}\) का मान है?
Which option is the value of \(\sqrt{10}\times\sqrt{40}\)?
#multiplication
#irrational-numbers
#rational-result
A (20)
B \(\sqrt{50}\)
C \(10\sqrt{40}\)
D \(40\sqrt{10}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (20). \(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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कौन सा विकल्प \(\sqrt{24}\times\sqrt{6}\) का मान है?
Which option is the value of \(\sqrt{24}\times\sqrt{6}\)?
#surds
#multiplication
#rational-result
A (12)
B \(6\sqrt{24}\)
C \(\sqrt{30}\)
D \(24\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
Step 2
Why this answer is correct
The correct answer is A. (12). \(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
Step 3
Exam Tip
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\) है। जड़ों के गुणन में अंदर की संख्याएँ गुणा करें।
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कौन सा कथन दो अपरिमेय संख्याओं के गुणनफल के बारे में सही है?
Which statement is correct about the product of two irrational numbers?
#irrational-numbers
#multiplication
#properties
A गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational
B गुणनफल हमेशा अपरिमेय होता है / The product is always irrational
C गुणनफल हमेशा शून्य होता है / The product is always zero
D गुणनफल हमेशा ऋणात्मक होता है / The product is always negative
Explanation opens after your attempt
Correct Answer
A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational
Step 1
Concept
\(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.
Step 2
Why this answer is correct
The correct answer is A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational. \(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.
Step 3
Exam Tip
\(\sqrt{5}\times\sqrt{5}=5\) परिमेय है पर \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) अपरिमेय है। इसलिए स्थिति पर निर्भर करता है।
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कौन सा विकल्प \(\sqrt{3}\) और \(\sqrt{27}\) का गुणनफल बताता है?
Which option gives the product of \(\sqrt{3}\) and \(\sqrt{27}\)?
#surds
#multiplication
#rational-result
A (9)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D \(27\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
Step 2
Why this answer is correct
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
Step 3
Exam Tip
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। गुणन में जड़ों के अंदर के संख्याओं को गुणा करें।
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कौन सा विकल्प दो अपरिमेय संख्याओं का गुणनफल परिमेय बनने का उदाहरण है?
Which option is an example where the product of two irrational numbers is rational?
#irrational-numbers
#multiplication
#rational-result
A \(\sqrt{12}\times\sqrt{3}\)
B \(\sqrt{2}\times\sqrt{5}\)
C \(\sqrt{7}\times\sqrt{3}\)
D \(\sqrt{11}\times\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{12}\times\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{12}\times\sqrt{3}\). \(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.
Step 3
Exam Tip
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\) है। दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता।
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कौन सा विकल्प \(3\sqrt{2}\times2\sqrt{2}\) का मान है?
Which option is the value of \(3\sqrt{2}\times2\sqrt{2}\)?
#surds
#multiplication
#rational-result
A (12)
B \(6\sqrt{2}\)
C \(12\sqrt{2}\)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (12). \(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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यदि (r) गैर शून्य परिमेय संख्या है और (s) अपरिमेय संख्या है तो (rs) कैसा होगा?
If (r) is a non zero rational number and (s) is irrational then what is (rs)?
#multiplication
#properties
#irrational-numbers
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C हमेशा शून्य / Always zero
D हमेशा प्राकृतिक संख्या / Always natural number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
A non zero rational multiplier keeps an irrational number irrational. The condition \(r\neq0\) is important.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. A non zero rational multiplier keeps an irrational number irrational. The condition \(r\neq0\) is important.
Step 3
Exam Tip
गैर शून्य परिमेय गुणक अपरिमेय संख्या को अपरिमेय ही रखता है। शर्त \(r\neq0\) महत्वपूर्ण है।
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\(\sqrt{7}\times\sqrt{11}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{7}\times\sqrt{11}\)?
#multiplication
#irrational-numbers
#classification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{7}\times\sqrt{11}=\sqrt{77}\) and (77) is not a perfect square. So the result is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(\sqrt{7}\times\sqrt{11}=\sqrt{77}\) and (77) is not a perfect square. So the result is irrational.
Step 3
Exam Tip
\(\sqrt{7}\times\sqrt{11}=\sqrt{77}\) है और (77) पूर्ण वर्ग नहीं है। इसलिए परिणाम अपरिमेय है।
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\(\sqrt{5}\times\sqrt{45}\) का मान क्या है?
What is the value of \(\sqrt{5}\times\sqrt{45}\)?
#multiplication
#irrational-numbers
#rational-result
A (15)
B \(5\sqrt{45}\)
C \(\sqrt{50}\)
D \(45\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (15). \(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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यदि (m) और (n) परिमेय संख्याएँ हैं तो \(m\times n\) किस प्रकार की संख्या होगी?
If (m) and (n) are rational numbers then what type of number will \(m\times n\) be?
#rational-numbers
#multiplication
#closure
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C हमेशा पूर्णांक / Always integer
D हमेशा ऋणात्मक / Always negative
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The product of two rational numbers is rational. But the result is not always an integer.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The product of two rational numbers is rational. But the result is not always an integer.
Step 3
Exam Tip
दो परिमेय संख्याओं का गुणनफल परिमेय होता है। लेकिन परिणाम हमेशा पूर्णांक नहीं होता।
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