89 results found for "binomial multiplication" in Class 10.
Which of the following is a binomial?
A. \(x^2+3\)
A polynomial with two terms is a binomial. \(x^2+3\) has two terms.
The correct answer is A. \(x^2+3\). A polynomial with two terms is a binomial. \(x^2+3\) has two terms.
दो पदों वाला बहुपद द्विपदी कहलाता है। \(x^2+3\) में दो पद हैं।
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Which polynomial is a binomial?
B. (5x-7)
A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
The correct answer is B. (5x-7). A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
द्विपदी में दो पद होते हैं। (5x-7) में (5x) और (-7) दो पद हैं।
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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). Multiply each term by each term.
The correct answer is A. \(3x^2-10x-8\). ((3x+2)(x-4)=3x-2-12x+2x-8=3x-2-10x-8). Multiply each term by each term.
((3x+2)(x-4)=3x-2-12x+2x-8=3x-2-10x-8)। प्रत्येक पद का हर पद से गुणा करें।
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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). Combine the middle terms with signs.
The correct answer is A. \(x^2-3x-10\). ((x-5)(x+2)=x-2+2x-5x-10=x-2-3x-10). Combine the middle terms with signs.
((x-5)(x+2)=x-2+2x-5x-10=x-2-3x-10)। मध्य पदों को संकेत सहित जोड़ें।
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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). Multiply each term by each term.
The correct answer is A. \(2x^2+9x-5\). ((2x-1)(x+5)=2x-2+10x-x-5=2x-2+9x-5). Multiply each term by each term.
((2x-1)(x+5)=2x-2+10x-x-5=2x-2+9x-5)। हर पद का हर पद से गुणा करें।
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What is the expansion of ((4x+5)(x-3))?
A. \(4x^2-7x-15\)
By distribution, \(4x^2-12x+5x-15=4x^2-7x-15\). Combine like terms at the end.
The correct answer is A. \(4x^2-7x-15\). By distribution, \(4x^2-12x+5x-15=4x^2-7x-15\). Combine like terms at the end.
वितरण से \(4x^2-12x+5x-15=4x^2-7x-15\) है। समान पदों को अंत में जोड़ें।
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What is the expansion of ((x-7)(x+3))?
A. \(x^2-4x-21\)
Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.
The correct answer is A. \(x^2-4x-21\). Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.
गुणा करने पर \(x^2+3x-7x-21=x^2-4x-21\) है। चिह्नों पर ध्यान दें।
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What is the expansion of ((x+6)(x+4))?
A. \(x^2+10x+24\)
By distribution, \(x^2+4x+6x+24=x^2+10x+24\). The middle term forms by combining like terms.
The correct answer is A. \(x^2+10x+24\). By distribution, \(x^2+4x+6x+24=x^2+10x+24\). The middle term forms by combining like terms.
वितरण नियम से \(x^2+4x+6x+24=x^2+10x+24\) मिलता है। मध्य पद समान पद जोड़कर बनता है।
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What is the expansion of ((3x+1)(x-4))?
A. \(3x^2-11x-4\)
By distribution, \(3x^2-12x+x-4=3x^2-11x-4\). Combine the middle like terms.
The correct answer is A. \(3x^2-11x-4\). By distribution, \(3x^2-12x+x-4=3x^2-11x-4\). Combine the middle like terms.
वितरण से \(3x^2-12x+x-4=3x^2-11x-4\) है। बीच के समान पद जोड़ें।
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What is the expansion of ((x-5)(x+2))?
A. \(x^2-3x-10\)
Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.
The correct answer is A. \(x^2-3x-10\). Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.
गुणा करने पर \(x^2+2x-5x-10=x^2-3x-10\) है। चिह्नों पर ध्यान दें।
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What is the expansion of ((2x+3)(x-2))?
A. \(2x^2-x-6\)
By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.
The correct answer is A. \(2x^2-x-6\). By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.
वितरण से \(2x^2-4x+3x-6=2x^2-x-6\) है। समान पदों को अंत में जोड़ें।
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What is the expansion of ((x-4)(x+1))?
A. \(x^2-3x-4\)
Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.
The correct answer is A. \(x^2-3x-4\). Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.
गुणा करने पर \(x^2+x-4x-4=x^2-3x-4\) मिलता है। चिह्नों पर विशेष ध्यान दें।
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What is the constant term in ((4x+3)\(x^2-2x+5\))?
D. (15)
The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
The correct answer is D. (15). The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
अचर पद केवल \(3\cdot5=15\) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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What is the coefficient of \(x^2\) in ((3x-2)\(2x^2+x-5\))?
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.
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.
((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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What is the constant term in ((3x-2)\(x^2+5x-1\))?
C. (2)
The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
The correct answer is C. (2). The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
अचर पद केवल ((-2)(-1)=2) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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What is the coefficient of \(x^2\) in ((2x-1)\(x^2-3x+4\))?
A. (-7)
((2x-1)\(x^2-3x+4\)=2x-3-7x-2+11x-4), so the coefficient is (-7). Combine like terms after expansion.
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.
((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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What is the constant term in ((2x-3)\(x^2+x+1\))?
A. (-3)
The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
The correct answer is A. (-3). The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
अचर पद केवल ((-3)\cdot1=-3) से आता है। अचर पद के लिए अचर पदों का गुणन देखें।
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What is the coefficient of \(x^2\) in ((x-2)\(3x^2+4x-5\))?
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.
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.
((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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What is the simplified form of (-3x\(2x^2-4x+5\))?
A. \(-6x^3+12x^2-15x\)
Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
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.
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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What is the polynomial form of ((x+3)(x-4))?
A. \(x^2-x-12\)
((x+3)(x-4)=x-2-4x+3x-12=x-2-x-12). Watch signs while combining middle terms.
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.
((x+3)(x-4)=x-2-4x+3x-12=x-2-x-12)। मध्य पद जोड़ते समय संकेत देखें।
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What is the simplified form of (2x\(3x^2-5x+1\))?
A. \(6x^3-10x^2+2x\)
Multiplying each term by (2x) gives \(6x^3-10x^2+2x\). Use the distributive property.
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.
प्रत्येक पद को (2x) से गुणा करने पर \(6x^3-10x^2+2x\) मिलता है। वितरण नियम का प्रयोग करें।
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Simplify: what is the value of (2\sqrt{3}\(\sqrt{12}-\sqrt{27}\))?
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.
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.
\(\sqrt{12}=2\sqrt{3}\) 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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What is the product of (\(-4a^2b^{-3}\)\(3a^{-1}b^5\))?
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.
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.
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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What is the expansion of ((2x-1)(3x+4))?
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.
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.
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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What is the expansion of ((x+2)(x-3))?
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.
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.
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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What is the product of (\(2x^2y\)\(-3xy^2\))?
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.
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.
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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What is the product of (\(6x^2y\)\(3xy^4\))?
A. \(18x^3y^5\)
The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.
The correct answer is A. \(18x^3y^5\). The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.
गुणांक (18), \(x^{2+1}=x^3\) और \(y^{1+4}=y^5\) है। समान आधार की घातें जोड़ें।
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What is the product of (\(5x^3y\)\(2xy^2\))?
A. \(10x^4y^3\)
The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.
The correct answer is A. \(10x^4y^3\). The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.
गुणांक (10), \(x^{3+1}=x^4\) और \(y^{1+2}=y^3\) है। समान आधार की घातें जोड़ें।
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What is the expansion of ((x+4)(x+3))?
A. \(x^2+7x+12\)
By distribution, \(x^2+3x+4x+12=x^2+7x+12\). Combine like terms.
The correct answer is A. \(x^2+7x+12\). By distribution, \(x^2+3x+4x+12=x^2+7x+12\). Combine like terms.
वितरण नियम से \(x^2+3x+4x+12=x^2+7x+12\) मिलता है। समान पदों को जोड़ें।
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What is the product of (\(3x^2y\)\(4xy^3\))?
A. \(12x^3y^4\)
The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.
The correct answer is A. \(12x^3y^4\). The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.
गुणांक (12), \(x^{2+1}=x^3\) और \(y^{1+3}=y^4\) है। समान आधार की घातें जोड़ें।
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What is the expansion of ((x+3)(x+2))?
A. \(x^2+5x+6\)
By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.
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.
वितरण नियम से \(x^2+2x+3x+6=x^2+5x+6\)। मध्य पद समान पद जोड़कर बनता है।
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What is the product of \(5x^4\cdot2x^3\)?
B. \(10x^7\)
The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).
The correct answer is B. \(10x^7\). The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).
गुणांक \(5\cdot2=10\) और \(x^4\cdot x^3=x^7\) है। इसलिए गुणनफल \(10x^7\) है।
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What is the value of \(\frac{5}{8}\cdot\frac{16}{15}\)?
A. \(\frac{2}{3}\)
Multiply and simplify: \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\). Cancelling first makes calculation easier.
The correct answer is A. \(\frac{2}{3}\). Multiply and simplify: \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\). Cancelling first makes calculation easier.
गुणा करके सरल करें \(\frac{5}{8}\cdot\frac{16}{15}=\frac{80}{120}=\frac{2}{3}\)। पहले काटने से गणना आसान होती है।
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What is the product of \(6x\cdot5x^2\)?
C. \(30x^3\)
The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
The correct answer is C. \(30x^3\). The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
गुणांक \(6\cdot5=30\) और \(x\cdot x^2=x^3\) है। इसलिए उत्तर \(30x^3\) है।
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C. \(5\cdot5\cdot5\cdot5\)
\(5^4\) means multiplying (5) by itself (4) times. An exponent shows repeated multiplication.
The correct answer is C. \(5\cdot5\cdot5\cdot5\). \(5^4\) means multiplying (5) by itself (4) times. An exponent shows repeated multiplication.
\(5^4\) का अर्थ (5) को (4) बार गुणा करना है। घात बार-बार गुणा को दिखाती है।
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What is the product of \(4x^3\cdot3x^2\)?
B. \(12x^5\)
The coefficients give \(4\cdot3=12\), and \(x^3\cdot x^2=x^5\). So the product is \(12x^5\).
The correct answer is B. \(12x^5\). The coefficients give \(4\cdot3=12\), and \(x^3\cdot x^2=x^5\). So the product is \(12x^5\).
गुणांक \(4\cdot3=12\) और \(x^3\cdot x^2=x^5\) है। इसलिए गुणनफल \(12x^5\) है।
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What is the value of \(\frac{4}{7}\cdot\frac{14}{5}\)?
A. \(\frac{8}{5}\)
Multiply and simplify: \(\frac{4}{7}\cdot\frac{14}{5}=\frac{56}{35}=\frac{8}{5}\). Cancelling first makes calculation easier.
The correct answer is A. \(\frac{8}{5}\). Multiply and simplify: \(\frac{4}{7}\cdot\frac{14}{5}=\frac{56}{35}=\frac{8}{5}\). Cancelling first makes calculation easier.
गुणा करके सरल करें \(\frac{4}{7}\cdot\frac{14}{5}=\frac{56}{35}=\frac{8}{5}\)। पहले काटने से गणना आसान होती है।
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What is the product of \(5x\cdot4x^3\)?
C. \(20x^4\)
The coefficients give \(5\cdot4=20\), and \(x\cdot x^3=x^4\). Therefore the answer is \(20x^4\).
The correct answer is C. \(20x^4\). The coefficients give \(5\cdot4=20\), and \(x\cdot x^3=x^4\). Therefore the answer is \(20x^4\).
गुणांक \(5\cdot4=20\) और \(x\cdot x^3=x^4\) है। इसलिए उत्तर \(20x^4\) है।
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C. \(4\cdot4\cdot4\)
\(4^3\) means multiplying (4) by itself (3) times. An exponent shows repeated multiplication.
The correct answer is C. \(4\cdot4\cdot4\). \(4^3\) means multiplying (4) by itself (3) times. An exponent shows repeated multiplication.
\(4^3\) का अर्थ (4) को (3) बार गुणा करना है। घात बार-बार गुणा को दिखाती है।
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What is the product of \(3x^2\cdot2x\)?
C. \(6x^3\)
The coefficients give \(3\cdot2=6\), and \(x^2\cdot x=x^3\). So the product is \(6x^3\).
The correct answer is C. \(6x^3\). The coefficients give \(3\cdot2=6\), and \(x^2\cdot x=x^3\). So the product is \(6x^3\).
गुणांक \(3\cdot2=6\) और \(x^2\cdot x=x^3\) है। इसलिए गुणनफल \(6x^3\) है।
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What is the value of \(\frac{3}{5}\cdot\frac{10}{9}\)?
A. \(\frac{2}{3}\)
Multiply and simplify: \(\frac{3}{5}\cdot\frac{10}{9}=\frac{30}{45}=\frac{2}{3}\). Cancelling first saves time.
The correct answer is A. \(\frac{2}{3}\). Multiply and simplify: \(\frac{3}{5}\cdot\frac{10}{9}=\frac{30}{45}=\frac{2}{3}\). Cancelling first saves time.
गुणा करके सरल करें \(\frac{3}{5}\cdot\frac{10}{9}=\frac{30}{45}=\frac{2}{3}\)। पहले काटना समय बचाता है।
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What is the product of \(4x\cdot3x^2\)?
C. \(12x^3\)
First multiply coefficients \(4\cdot3=12\), then \(x\cdot x^2=x^3\). Therefore the answer is \(12x^3\).
The correct answer is C. \(12x^3\). First multiply coefficients \(4\cdot3=12\), then \(x\cdot x^2=x^3\). Therefore the answer is \(12x^3\).
पहले गुणांक \(4\cdot3=12\) और फिर \(x\cdot x^2=x^3\) करें। इसलिए उत्तर \(12x^3\) है।
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B. \(2\cdot2\cdot2\cdot2\cdot2\)
\(2^5\) means multiplying (2) by itself (5) times. An exponent shows repeated multiplication.
The correct answer is B. \(2\cdot2\cdot2\cdot2\cdot2\). \(2^5\) means multiplying (2) by itself (5) times. An exponent shows repeated multiplication.
\(2^5\) का अर्थ (2) को (5) बार गुणा करना है। घात बार-बार गुणा को दिखाती है।
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If \(x=\sqrt{6}+\sqrt{2}\) and \(y=\sqrt{6}-\sqrt{2}\), what is (xy)?
A. (4)
(xy=\(\sqrt{6}\)2-\(\sqrt{2}\)2=6-2=4). Conjugate multiplication saves time in exams.
The correct answer is A. (4). (xy=\(\sqrt{6}\)2-\(\sqrt{2}\)2=6-2=4). Conjugate multiplication saves time in exams.
(xy=\(\sqrt{6}\)2-\(\sqrt{2}\)2=6-2=4) है। परीक्षा में संयुग्मी गुणन से समय बचता है।
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Which option is the value of (\sqrt{2}\times\(\sqrt{18}-\sqrt{8}\))?
A. (2)
\(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the bracket is \(\sqrt{2}\). The product is (2).
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).
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए कोष्ठक \(\sqrt{2}\) है। गुणनफल (2) है।
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Which option is the value of \(3\sqrt{6}\times2\sqrt{6}\)?
A. (36)
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
The correct answer is A. (36). \(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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Which option is the value of \(\sqrt{18}\times\sqrt{50}\)?
A. (30)
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
The correct answer is A. (30). \(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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Which option is the value of \(2\sqrt{5}\times3\sqrt{5}\)?
A. (30)
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
The correct answer is A. (30). \(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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Which option is the value of \(\sqrt{10}\times\sqrt{40}\)?
A. (20)
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
The correct answer is A. (20). \(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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Which option is the value of \(\sqrt{24}\times\sqrt{6}\)?
A. (12)
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
The correct answer is A. (12). \(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\) है। जड़ों के गुणन में अंदर की संख्याएँ गुणा करें।
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Which statement is correct about the product of two irrational numbers?
A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता हैThe 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.
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.
\(\sqrt{5}\times\sqrt{5}=5\) परिमेय है पर \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) अपरिमेय है। इसलिए स्थिति पर निर्भर करता है।
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Which option gives the product of \(\sqrt{3}\) and \(\sqrt{27}\)?
A. (9)
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। गुणन में जड़ों के अंदर के संख्याओं को गुणा करें।
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Which option is an example where the product of two irrational numbers is rational?
A. \(\sqrt{12}\times\sqrt{3}\)
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.
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.
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\) है। दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता।
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Which option is the value of \(3\sqrt{2}\times2\sqrt{2}\)?
A. (12)
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
The correct answer is A. (12). \(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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If (r) is a non zero rational number and (s) is irrational then what is (rs)?
A. अपरिमेय संख्याIrrational number
A non zero rational multiplier keeps an irrational number irrational. The condition \(r\neq0\) is important.
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.
गैर शून्य परिमेय गुणक अपरिमेय संख्या को अपरिमेय ही रखता है। शर्त \(r\neq0\) महत्वपूर्ण है।
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What type of number is \(\sqrt{7}\times\sqrt{11}\)?
A. अपरिमेय संख्याIrrational number
\(\sqrt{7}\times\sqrt{11}=\sqrt{77}\) and (77) is not a perfect square. So the result is irrational.
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.
\(\sqrt{7}\times\sqrt{11}=\sqrt{77}\) है और (77) पूर्ण वर्ग नहीं है। इसलिए परिणाम अपरिमेय है।
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What is the value of \(\sqrt{5}\times\sqrt{45}\)?
A. (15)
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
The correct answer is A. (15). \(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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If (m) and (n) are rational numbers then what type of number will \(m\times n\) be?
A. परिमेय संख्याRational number
The product of two rational numbers is rational. But the result is not always an integer.
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.
दो परिमेय संख्याओं का गुणनफल परिमेय होता है। लेकिन परिणाम हमेशा पूर्णांक नहीं होता।
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Which option is an example where the product of two irrational numbers is irrational?
A. \(\sqrt{2}\times\sqrt{5}\)
\(\sqrt{2}\times\sqrt{5}=\sqrt{10}\), which is irrational. Multiplying equal roots can often give a rational number.
The correct answer is A. \(\sqrt{2}\times\sqrt{5}\). \(\sqrt{2}\times\sqrt{5}=\sqrt{10}\), which is irrational. Multiplying equal roots can often give a rational number.
\(\sqrt{2}\times\sqrt{5}=\sqrt{10}\) है जो अपरिमेय है। समान जड़ों का गुणन अक्सर परिमेय दे सकता है।
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Which option shows the result of multiplying an irrational number by zero?
A. (0) जो परिमेय है(0) which is rational
Multiplying any real number by (0) gives (0). (0) is a rational number.
The correct answer is A. (0) जो परिमेय है / (0) which is rational. Multiplying any real number by (0) gives (0). (0) is a rational number.
किसी भी वास्तविक संख्या को (0) से गुणा करने पर (0) मिलता है। (0) परिमेय संख्या है।
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What is the value of \(\sqrt{3}\times\sqrt{27}\)?
A. (9)
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrational numbers can be rational.
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrational numbers can be rational.
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय भी हो सकता है।
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What is the product of two irrational numbers always?
A. हमेशा निश्चित नहींNot always fixed
\(\sqrt{2}\times\sqrt{2}=2\) is rational but \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) is irrational. So it is not always one type.
The correct answer is A. हमेशा निश्चित नहीं / Not always fixed. \(\sqrt{2}\times\sqrt{2}=2\) is rational but \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) is irrational. So it is not always one type.
\(\sqrt{2}\times\sqrt{2}=2\) परिमेय है लेकिन \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\) अपरिमेय है। इसलिए हमेशा एक जैसा नहीं होता।
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What type of number is \(3\sqrt{5}\)?
A. अपरिमेय संख्याIrrational number
Multiplying an irrational by a non zero rational gives an irrational result. Here \(3\neq0\).
The correct answer is A. अपरिमेय संख्या / Irrational number. Multiplying an irrational by a non zero rational gives an irrational result. Here \(3\neq0\).
गैर शून्य परिमेय संख्या से अपरिमेय को गुणा करने पर परिणाम अपरिमेय होता है। यहाँ \(3\neq0\) है।
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Which statement is correct about \(\sqrt{2}\cdot \sqrt{3}\)?
B. यह \(\sqrt{6}\) है और अपरिमेय हैIt is \(\sqrt{6}\) and irrational
The product of radicals is \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\).
Since (6) is not a perfect square \(\sqrt{6}\) is irrational.
In multiplication the numbers inside radicals multiply, not add. चरण 1: वर्गमूलों का गुणनफल \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\) है। चरण 2: (6) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{6}\) अपरिमेय है। चरण 3: गुणन में भीतर की संख्याएं गुणा होती हैं जोड़ नहीं।
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Which option gives the correct value of (\sqrt{3}\(2+\sqrt{3}\))?
A. \(2\sqrt{3}+3\)
Use the distributive law.
(\sqrt{3}\(2+\sqrt{3}\)=2\sqrt{3}+\(\sqrt{3}\)2=2\sqrt{3}+3).
Remember that \(\sqrt{3}\times\sqrt{3}=3\). चरण 1: वितरण नियम लगाएँ। चरण 2: (\sqrt{3}\(2+\sqrt{3}\)=2\sqrt{3}+\(\sqrt{3}\)2=2\sqrt{3}+3)। चरण 3: \(\sqrt{3}\times\sqrt{3}\) को (3) लिखना न भूलें।
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What is the value of (\sqrt{7}\(4+\sqrt{7}\))?
A. \(4\sqrt{7}+7\)
Apply distribution: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\).
This becomes \(4\sqrt{7}+7\).
In such multiplication, remember \(\sqrt{7}\times\sqrt{7}=7\). चरण 1: वितरण नियम लगाएं: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\)। चरण 2: यह \(4\sqrt{7}+7\) बनता है। चरण 3: समान वर्गमूलों के गुणन में \(\sqrt{7}\times\sqrt{7}=7\) याद रखें।
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What is the value of (\sqrt{5}\(3+\sqrt{5}\))?
A. \(3\sqrt{5}+5\)
Apply distribution: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\).
This becomes \(3\sqrt{5}+5\).
In such multiplication, remember \(\sqrt{5}\times\sqrt{5}=5\). चरण 1: वितरण नियम लगाएं: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\)। चरण 2: यह \(3\sqrt{5}+5\) बनता है। चरण 3: समान वर्गमूलों के गुणन में \(\sqrt{5}\times\sqrt{5}=5\) याद रखें।
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What is the value of (\sqrt{3}\(2+\sqrt{3}\))?
A. \(2\sqrt{3}+3\)
Use distribution: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\).
This becomes \(2\sqrt{3}+3\).
In radical multiplication, remember \(\sqrt{3}\times\sqrt{3}=3\). चरण 1: वितरण नियम लगाएं: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\)। चरण 2: यह \(2\sqrt{3}+3\) बनता है। चरण 3: वर्गमूल वाले गुणन में \(\sqrt{3}\times\sqrt{3}=3\) याद रखें।
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A. \(2\times3\times7^2\)
In a perfect cube, every prime exponent must be a multiple of (3).
\(2^5\) needs one more (2), \(3^2\) needs one more (3), and \(7^1\) needs \(7^2\).
Complete each exponent to the next multiple of (3). चरण 1: पूर्ण घन में हर अभाज्य गुणनखंड की घात (3) की गुणज होनी चाहिए। चरण 2: \(2^5\) को \(2^6\) बनाने के लिए (2), \(3^2\) को \(3^3\) बनाने के लिए (3), और \(7^1\) को \(7^3\) बनाने के लिए \(7^2\) चाहिए। चरण 3: घातों को अगली (3) की गुणज तक पूरा करें।
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If (x) leaves remainder 7 when divided by 10, what is the remainder when (3x) is divided by 10?
A. 1
Write (x=10q+7).
(3x=30q+21=10(3q+2)+1), so the remainder is 1.
In multiplication questions, multiply the remainder and reduce it by the divisor. चरण 1: (x=10q+7) लिखें। चरण 2: (3x=30q+21=10(3q+2)+1), इसलिए शेषफल 1 है। चरण 3: गुणा के सवालों में शेषफल को गुणा करके फिर भाजक से घटाएं।
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If (a) leaves remainder (5) when divided by (6), what is the remainder when (2a) is divided by (6)?
B. (4)
Let (a=6q+5).
(2a=12q+10=6(2q+1)+4), so the remainder is (4).
(10) cannot be the remainder because it is greater than (6). चरण 1: (a=6q+5) मानें। चरण 2: (2a=12q+10=6(2q+1)+4), इसलिए शेषफल (4) है। चरण 3: (10) शेषफल नहीं हो सकता क्योंकि यह (6) से बड़ा है।
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If (a) leaves remainder (3) when divided by (4), what is the remainder when (2a) is divided by (4)?
C. (2)
Write (a=4q+3).
(2a=8q+6=4(2q+1)+2), so the remainder is (2).
After multiplication, do not forget to convert the remainder into the correct range. चरण 1: (a=4q+3) लिखें। चरण 2: (2a=8q+6=4(2q+1)+2), इसलिए शेषफल (2) है। चरण 3: गुणा करने के बाद शेषफल को सही सीमा में बदलना न भूलें।
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If (a=7q+5), what is the remainder when (3a) is divided by (7)?
A. (1)
The remainder of (a) is (5), so for (3a), check \(3 \times 5=15\).
\(15=7 \times 2+1\), so the remainder is (1).
In such questions, work with the remainder instead of the whole number. चरण 1: (a) का शेषफल (5) है, इसलिए (3a) के लिए \(3 \times 5=15\) देखें। चरण 2: \(15=7 \times 2+1\), इसलिए शेषफल (1) होगा। चरण 3: ऐसे सवाल में पूरी संख्या नहीं, केवल शेषफल पर काम करें।
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If (a=5q+4), what is the remainder when (2a) is divided by (5)?
A. (3)
(2a=2(5q+4)=10q+8).
(8=5+3), so (2a=5(2q+1)+3) and the remainder is (3).
In multiplication-based questions, first multiply the old remainder and then divide by the divisor. चरण 1: (2a=2(5q+4)=10q+8)। चरण 2: (8=5+3), इसलिए (2a=5(2q+1)+3) और शेषफल (3) है। चरण 3: गुणा वाले प्रश्न में पहले शेषफल को गुणा करके फिर भाजक से बाँटें।
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In which condition can asexual reproduction be very beneficial?
A. जब वातावरण स्थिर हो और तेजी से समान संतानें बनानी होंWhen the environment is stable and similar offspring are needed quickly
Asexual reproduction can produce offspring quickly from one parent.
Offspring can be similar to the parent.
This method can be successful in a stable environment. चरण 1: अलैंगिक जनन में एक जनक से जल्दी संतानें बन सकती हैं। चरण 2: संतानें जनक जैसी हो सकती हैं। चरण 3: स्थिर वातावरण में यह तरीका सफल हो सकता है।
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Why is asexual reproduction useful for rapid increase in number?
A. एक जनक से कम समय में संतान बन सकती हैOffspring can form from one parent in less time
Asexual reproduction does not need a mate.
One parent alone can form new organisms.
Thus numbers can increase rapidly in favourable conditions. चरण 1: अलैंगिक प्रजनन में साथी की आवश्यकता नहीं होती। चरण 2: एक जनक ही नए जीव बना सकता है। चरण 3: इसलिए अनुकूल दशा में संख्या तेजी से बढ़ सकती है।
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Which option correctly describes the type of \(x^3-1\)?
C. त्रिघात द्विपदीCubic binomial
\(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
The correct answer is C. त्रिघात द्विपदी / Cubic binomial. \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है।
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How many terms are there in \(7x^2+5\)?
B. (2)
The terms are \(7x^2\) and (5). Therefore it has (2) terms.
The correct answer is B. (2). The terms are \(7x^2\) and (5). Therefore it has (2) terms.
पद \(7x^2\) और (5) हैं। इसलिए इसमें (2) पद हैं।
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Which of the following is a polynomial with (2) terms?
B. \(5x^3-4\)
\(5x^3-4\) has (2) terms. A polynomial with two terms is called a binomial.
The correct answer is B. \(5x^3-4\). \(5x^3-4\) has (2) terms. A polynomial with two terms is called a binomial.
\(5x^3-4\) में (2) पद हैं। दो पदों वाला बहुपद द्विपदी कहलाता है।
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How many terms are there in (p(x)=7x-2-1)?
B. (2)
There are two terms \(7x^2\) and (-1). So it is also a binomial.
The correct answer is B. (2). There are two terms \(7x^2\) and (-1). So it is also a binomial.
\(7x^2\) और (-1) दो पद हैं। इसलिए यह द्विपदी भी है।
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What is the expansion of ((5x+2)2)?
A. \(25x^2+20x+4\)
Take (a=5x) and (b=2) in ((a+b)2). The middle term is \(2\cdot5x\cdot2=20x\).
The correct answer is A. \(25x^2+20x+4\). Take (a=5x) and (b=2) in ((a+b)2). The middle term is \(2\cdot5x\cdot2=20x\).
((a+b)2) में (a=5x) और (b=2) लें। मध्य पद \(2\cdot5x\cdot2=20x\) है।
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What is the expansion of ((4x-5)2)?
A. \(16x^2-40x+25\)
Use ((a-b)2=a-2-2ab+b-2). Here (a=4x) and (b=5).
The correct answer is A. \(16x^2-40x+25\). Use ((a-b)2=a-2-2ab+b-2). Here (a=4x) and (b=5).
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=4x) और (b=5) हैं।
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What is the expansion of ((4x+3)2)?
A. \(16x^2+24x+9\)
Take (a=4x) and (b=3) in ((a+b)2). The middle term is \(2\cdot4x\cdot3=24x\).
The correct answer is A. \(16x^2+24x+9\). Take (a=4x) and (b=3) in ((a+b)2). The middle term is \(2\cdot4x\cdot3=24x\).
((a+b)2) में (a=4x) और (b=3) लें। मध्य पद \(2\cdot4x\cdot3=24x\) है।
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What is the expansion of ((3x-4)2)?
A. \(9x^2-24x+16\)
Use ((a-b)2=a-2-2ab+b-2). Here (a=3x) and (b=4).
The correct answer is A. \(9x^2-24x+16\). Use ((a-b)2=a-2-2ab+b-2). Here (a=3x) and (b=4).
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=3x) और (b=4) हैं।
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What is the expansion of ((3x+2)2)?
A. \(9x^2+12x+4\)
Take (a=3x) and (b=2) in ((a+b)2). The middle term is \(2\cdot3x\cdot2=12x\).
The correct answer is A. \(9x^2+12x+4\). Take (a=3x) and (b=2) in ((a+b)2). The middle term is \(2\cdot3x\cdot2=12x\).
((a+b)2) में (a=3x) और (b=2) लें। मध्य पद \(2\cdot3x\cdot2=12x\) है।
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What is the expansion of ((2x-3)2)?
A. \(4x^2-12x+9\)
Use ((a-b)2=a-2-2ab+b-2). Here (a=2x) and (b=3).
The correct answer is A. \(4x^2-12x+9\). Use ((a-b)2=a-2-2ab+b-2). Here (a=2x) and (b=3).
((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=2x) और (b=3) हैं।
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What is the expanded form of ((2x+1)(x-4)=0)?
A. \(2x^2-7x-4=0\)
Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
The correct answer is A. \(2x^2-7x-4=0\). Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
विस्तार करने पर \(2x^2-8x+x-4=0\) मिलता है। समान पद जोड़कर \(2x^2-7x-4=0\) बनता है।
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What is the expanded form of ((x+4)(x+5)=0)?
A. \(x^2+9x+20=0\)
Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
The correct answer is A. \(x^2+9x+20=0\). Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
विस्तार करने पर \(x^2+5x+4x+20=0\) मिलता है। समान पद जोड़कर \(x^2+9x+20=0\) बनता है।
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What is the expanded form of ((x+2)(x+3)=0)?
A. \(x^2+5x+6=0\)
Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
The correct answer is A. \(x^2+5x+6=0\). Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
विस्तार से \(x^2+3x+2x+6=0\) मिलता है। समान पद जोड़कर \(x^2+5x+6=0\) बनता है।
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