100 results found for "product of irrationals" in Class 10.
किस विकल्प में दो अपरिमेय संख्याओं का गुणनफल परिमेय लेकिन योग अपरिमेय है?
In which option do two irrational numbers have a rational product but an irrational sum?
#product of irrationals
#sum of irrationals
#class 10
A \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
B \(\sqrt{5}\) और \(-\sqrt{5}\) / \(\sqrt{5}\) and \(-\sqrt{5}\)
C \(\sqrt{2}\) और \(\sqrt{8}\) / \(\sqrt{2}\) and \(\sqrt{8}\)
D \(\sqrt{7}\) और \(\sqrt{28}\) / \(\sqrt{7}\) and \(\sqrt{28}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{3}\) are both irrational.
Step 2
Why this answer is correct
Their product is \(\sqrt{36}=6\), which is rational, and their sum is \(3\sqrt{3}\), which is irrational.
Step 3
Exam Tip
Check the nature of the sum and product separately. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। चरण 2: उनका गुणन \(\sqrt{36}=6\) परिमेय है, और योग \(3\sqrt{3}\) अपरिमेय है। चरण 3: योग और गुणन की प्रकृति अलग-अलग जाँचें।
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यदि (p(x)=x-2 -18), तो शून्यकों का गुणनफल और योग क्या हैं?
If (p(x)=x-2 -18), what are the product and sum of its zeroes?
#opposite-irrationals
#sum-product
#zeroes
A गुणनफल (-18), योग (0) / Product (-18), sum (0)
B गुणनफल (18), योग (0) / Product (18), sum (0)
C गुणनफल (-18), योग \(6\sqrt{2}\) / Product (-18), sum \(6\sqrt{2}\)
D गुणनफल (0), योग (-18) / Product (0), sum (-18)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-18), योग (0) / Product (-18), sum (0)
Step 1
Concept
The zeroes are \(3\sqrt{2}\) and \(-3\sqrt{2}\). Therefore the sum is (0) and the product is (-18).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-18), योग (0) / Product (-18), sum (0). The zeroes are \(3\sqrt{2}\) and \(-3\sqrt{2}\). Therefore the sum is (0) and the product is (-18).
Step 3
Exam Tip
शून्यक \(3\sqrt{2}\) और \(-3\sqrt{2}\) हैं। इसलिए योग (0) और गुणनफल (-18) है।
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कौन सा उदाहरण दिखाता है कि दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है?
Which example shows that the product of two irrational numbers can be rational?
#product of irrationals
#examples
#class 10
A \(\sqrt{2}\cdot \sqrt{3}\)
B \(\sqrt{5}\cdot \sqrt{5}\)
C \(\sqrt{7}\cdot 2\)
D \(\sqrt{11}\cdot \sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5}\cdot \sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
\(\sqrt{5}\cdot \sqrt{5}=5\) which is rational.
Step 3
Exam Tip
The product of two identical irrational square roots becomes the number inside. चरण 1: \(\sqrt{5}\) अपरिमेय है। चरण 2: \(\sqrt{5}\cdot \sqrt{5}=5\) परिमेय है। चरण 3: दो समान अपरिमेय वर्गमूलों का गुणनफल भीतर की संख्या बन जाता है।
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निम्न में से कौन-सा उदाहरण सिद्ध करता है कि दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है?
Which example proves that the product of two irrational numbers can be rational?
#counterexample
#product of irrationals
#class 10
A \(\sqrt{2}\times\sqrt{2}=2\)
B \(\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
C \(\sqrt{2}\times2=2\sqrt{2}\)
D \(\sqrt{2}+2=2+\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\times\sqrt{2}=2\)
Step 1
Concept
\(\sqrt{2}\) is irrational.
Step 2
Why this answer is correct
Multiplying the two irrational numbers gives \(\sqrt{2}\times\sqrt{2}=2\), which is rational.
Step 3
Exam Tip
One valid counterexample is enough to disprove a universal statement. चरण 1: \(\sqrt{2}\) एक अपरिमेय संख्या है। चरण 2: दो समान अपरिमेय संख्याओं का गुणन \(\sqrt{2}\times\sqrt{2}=2\) देता है, जो परिमेय है। चरण 3: किसी सामान्य कथन को गलत दिखाने के लिए एक सही उदाहरण काफी होता है।
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किस विकल्प में दी गई दोनों संख्याएँ अपरिमेय हैं, पर उनका गुणनफल परिमेय है?
In which option are both numbers irrational but their product is rational?
#product of irrationals
#surds
#real numbers
#class 10
A \(\sqrt{2},\sqrt{3}\)
B \(\sqrt{5},\sqrt{20}\)
C \(\sqrt{6},\sqrt{10}\)
D \(\sqrt{7},\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5},\sqrt{20}\)
Step 1
Concept
Both numbers are individually irrational.
Step 2
Why this answer is correct
\(\sqrt{5}\times\sqrt{20}=\sqrt{100}=10\), which is rational.
Step 3
Exam Tip
Check whether the product inside the square root becomes a perfect square. चरण 1: दोनों संख्याएँ अलग-अलग अपरिमेय हैं। चरण 2: \(\sqrt{5}\times\sqrt{20}=\sqrt{100}=10\), जो परिमेय है। चरण 3: ऐसे प्रश्नों में गुणन के बाद मूल के अंदर की संख्या पूर्ण वर्ग बन रही है या नहीं, यह देखें।
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कौन-सा विकल्प \(3+\sqrt{2}\) और \(3-\sqrt{2}\) के बारे में सही है?
Which option is correct about \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?
#conjugate irrationals
#rational product
#class 10
A दोनों अपरिमेय हैं और उनका गुणनफल परिमेय है / Both are irrational and their product is rational
B दोनों परिमेय हैं और उनका योग अपरिमेय है / Both are rational and their sum is irrational
C एक परिमेय है और एक अपरिमेय है / One is rational and one is irrational
D दोनों का गुणनफल अपरिमेय है / Their product is irrational
Explanation opens after your attempt
Correct Answer
A. दोनों अपरिमेय हैं और उनका गुणनफल परिमेय है / Both are irrational and their product is rational
Step 1
Concept
\(3+\sqrt{2}\) and \(3-\sqrt{2}\) both contain an irrational part, so both are irrational.
Step 2
Why this answer is correct
Their product is (9-2=7), which is rational.
Step 3
Exam Tip
Conjugate irrational numbers can have a rational product. चरण 1: \(3+\sqrt{2}\) और \(3-\sqrt{2}\) दोनों में अपरिमेय भाग है, इसलिए दोनों अपरिमेय हैं। चरण 2: उनका गुणनफल (9-2=7) परिमेय है। चरण 3: संयुग्मी अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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यदि \(\sqrt{2}\) और \(\sqrt{3}\) के बीच एक अपरिमेय संख्या चुननी हो, तो कौन सा विकल्प निश्चित रूप से सही है?
If an irrational number is to be chosen between \(\sqrt{2}\) and \(\sqrt{3}\), which option is definitely correct?
#between-irrationals
#comparison
#number-system
A \(\sqrt{\frac{5}{2}}\)
B \(\frac{3}{2}\)
C \(\sqrt{4}\)
D \(\frac{\sqrt{2}+\sqrt{3}}{0}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{\frac{5}{2}}\)
Step 1
Concept
Since \(2<\frac{5}{2}<3\), \(\sqrt{2}<\sqrt{\frac{5}{2}}<\sqrt{3}\), and it is irrational. In exams compare by squaring.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{\frac{5}{2}}\). Since \(2<\frac{5}{2}<3\), \(\sqrt{2}<\sqrt{\frac{5}{2}}<\sqrt{3}\), and it is irrational. In exams compare by squaring.
Step 3
Exam Tip
क्योंकि \(2<\frac{5}{2}<3\), इसलिए \(\sqrt{2}<\sqrt{\frac{5}{2}}<\sqrt{3}\) और यह अपरिमेय है। परीक्षा में वर्ग करके तुलना करें।
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यदि \(\alpha=4+\sqrt{15}\) और \(\beta=4-\sqrt{15}\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?
If \(\alpha=4+\sqrt{15}\) and \(\beta=4-\sqrt{15}\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?
#conjugate-irrationals
#zeroes-expression
#expert
A (62)
B (64)
C (30)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=1\), so \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{64-2}{1}=62\). In such questions, first find the sum and product.
Step 2
Why this answer is correct
The correct answer is A. (62). Here \(\alpha+\beta=8\) and \(\alpha\beta=1\), so \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{64-2}{1}=62\). In such questions, first find the sum and product.
Step 3
Exam Tip
\(\alpha+\beta=8\) और \(\alpha\beta=1\), इसलिए \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{64-2}{1}=62\)। ऐसे प्रश्नों में पहले योग और गुणनफल निकालें।
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यदि किसी द्विघात बहुपद के शून्यक \(3+\sqrt{5}\) और \(3-\sqrt{5}\) हैं, तो उनके योग का प्रकार क्या है?
If the zeroes of a quadratic polynomial are \(3+\sqrt{5}\) and \(3-\sqrt{5}\), what is the type of their sum?
#conjugate-irrationals
#zeroes
#sum
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अवास्तविक संख्या / Non-real number
D ऋणात्मक अपरिमेय संख्या / Negative irrational number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.
Step 3
Exam Tip
योग \(3+\sqrt{5}+3-\sqrt{5}=6\) है, जो परिमेय है। संयुग्मी अपरिमेय संख्याओं का योग अक्सर परिमेय होता है।
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यदि \(x=\sqrt{3}-\sqrt{2}\) है तो (x) के बारे में सही कथन कौन सा है?
If \(x=\sqrt{3}-\sqrt{2}\) then which statement about (x) is correct?
#difference of irrationals
#proof
#class 10
A (x) परिमेय है / (x) is rational
B (x) अपरिमेय है / (x) is irrational
C (x=1) है / (x=1)
D (x=0) है / (x=0)
Explanation opens after your attempt
Correct Answer
B. (x) अपरिमेय है / (x) is irrational
Step 1
Concept
Suppose \(\sqrt{3}-\sqrt{2}\) is rational.
Step 2
Why this answer is correct
Squaring gives \(5-2\sqrt{6}\), forcing \(\sqrt{6}\) to be rational which is false.
Step 3
Exam Tip
The difference of unlike radicals is not directly an integer. चरण 1: मान लें \(\sqrt{3}-\sqrt{2}\) परिमेय है। चरण 2: वर्ग करने पर \(5-2\sqrt{6}\) से \(\sqrt{6}\) परिमेय होना पड़ेगा जो गलत है। चरण 3: अलग-अलग वर्गमूलों का अंतर सीधे पूर्णांक नहीं माना जाता।
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कौन-सा विकल्प \(\sqrt{3}+\sqrt{6}\) और \(\sqrt{12}\) के बीच सही तुलना देता है?
Which option gives the correct comparison between \(\sqrt{3}+\sqrt{6}\) and \(\sqrt{12}\)?
#comparison of irrationals
#surds
#class 10
A \(\sqrt{3}+\sqrt{6}>\sqrt{12}\)
B \(\sqrt{3}+\sqrt{6}<\sqrt{12}\)
C दोनों बराबर हैं / Both are equal
D दोनों परिमेय हैं / Both are rational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}+\sqrt{6}>\sqrt{12}\)
Step 1
Concept
All terms are positive and \(\sqrt{6}>0\).
Step 2
Why this answer is correct
Since \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{6}>\sqrt{3}\), the sum \(\sqrt{3}+\sqrt{6}\) is greater than \(2\sqrt{3}\).
Step 3
Exam Tip
For comparison, convert what you can and use positivity. चरण 1: सभी पद धनात्मक हैं और \(\sqrt{6}>0\)। चरण 2: \(\sqrt{3}+\sqrt{6}\), \(\sqrt{3}\) से बड़ा है और \(\sqrt{12}=2\sqrt{3}\) है; संख्यात्मक रूप से \(\sqrt{6}>\sqrt{3}\), इसलिए योग \(2\sqrt{3}\) से बड़ा है। चरण 3: तुलना में समान मूल में बदलना और धनात्मकता देखना मदद करता है।
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कौन-सी संख्या (1) और (2) के बीच एक अपरिमेय संख्या है, पर \(\sqrt{2}\) से बड़ी है?
Which number is an irrational number between (1) and (2), but greater than \(\sqrt{2}\)?
#number line
#comparison of irrationals
#class 10
A \(\sqrt{3}\)
B \(\sqrt{2}\)
C \(\frac{3}{2}\)
D \(\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) is about (1.732), so it lies between (1) and (2).
Step 2
Why this answer is correct
Since (3>2), \(\sqrt{3}>\sqrt{2}\).
Step 3
Exam Tip
For positive square roots, compare the numbers inside the roots. चरण 1: \(\sqrt{3}\) लगभग (1.732) है, इसलिए यह (1) और (2) के बीच है। चरण 2: (3>2), इसलिए \(\sqrt{3}>\sqrt{2}\)। चरण 3: धनात्मक वर्गमूलों की तुलना में अंदर की संख्याओं की तुलना कर सकते हैं।
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कौन-सा विकल्प दो अपरिमेय संख्याओं के योग को परिमेय बनाता है?
Which option makes the sum of two irrational numbers rational?
#sum of irrationals
#counterexample
#class 10
A (\(2+\sqrt{5}\)+\(\sqrt{5}-2\))
B (\(4+\sqrt{7}\)+\(4-\sqrt{7}\))
C (\(\sqrt{3}+1\)+\(\sqrt{3}-1\))
D (\(\sqrt{2}+\sqrt{3}\)+\(\sqrt{2}-\sqrt{3}\))
Explanation opens after your attempt
Correct Answer
B. (\(4+\sqrt{7}\)+\(4-\sqrt{7}\))
Step 1
Concept
\(4+\sqrt{7}\) and \(4-\sqrt{7}\) are both irrational.
Step 2
Why this answer is correct
Their sum is (8), which is rational.
Step 3
Exam Tip
In such examples, equal irrational parts cancel with opposite signs. चरण 1: \(4+\sqrt{7}\) और \(4-\sqrt{7}\) दोनों अपरिमेय हैं। चरण 2: उनका योग (8) है, जो परिमेय है। चरण 3: ऐसे उदाहरणों में समान अपरिमेय पद विपरीत चिह्न के साथ कटते हैं।
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किस विकल्प में (x+y) परिमेय है, जबकि (x) और (y) दोनों अपरिमेय हैं?
In which option is (x+y) rational while both (x) and (y) are irrational?
#sum of irrationals
#rational result
#class 10
A \(x=\sqrt{8},y=-2\sqrt{2}\)
B \(x=\sqrt{3},y=\sqrt{12}\)
C \(x=\sqrt{5},y=\sqrt{20}\)
D \(x=\sqrt{6},y=\sqrt{24}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\sqrt{8},y=-2\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), so (x) and \(y=-2\sqrt{2}\) are both irrational.
Step 2
Why this answer is correct
Their sum is \(2\sqrt{2}-2\sqrt{2}=0\), which is rational.
Step 3
Exam Tip
Opposite irrational terms can give a rational sum. चरण 1: \(\sqrt{8}=2\sqrt{2}\), इसलिए (x) और \(y=-2\sqrt{2}\) दोनों अपरिमेय हैं। चरण 2: उनका योग \(2\sqrt{2}-2\sqrt{2}=0\), जो परिमेय है। चरण 3: विपरीत अपरिमेय पदों के योग से परिमेय उत्तर मिल सकता है।
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किस विकल्प में दोनों संख्याएँ अपरिमेय हैं और उनका योग भी अपरिमेय है?
In which option are both numbers irrational and their sum is also irrational?
#sum of irrationals
#like surds
#class 10
A \(\sqrt{2}\) और \(-\sqrt{2}\) / \(\sqrt{2}\) and \(-\sqrt{2}\)
B \(\sqrt{3}\) और \(2\sqrt{3}\) / \(\sqrt{3}\) and \(2\sqrt{3}\)
C \(\sqrt{5}\) और \(-\sqrt{5}\) / \(\sqrt{5}\) and \(-\sqrt{5}\)
D \(\sqrt{7}\) और \(1-\sqrt{7}\) / \(\sqrt{7}\) and \(1-\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}\) और \(2\sqrt{3}\) / \(\sqrt{3}\) and \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) and \(2\sqrt{3}\) are both irrational.
Step 2
Why this answer is correct
Their sum is \(3\sqrt{3}\), which is irrational.
Step 3
Exam Tip
In sum questions, identify whether like surds cancel or combine. चरण 1: \(\sqrt{3}\) और \(2\sqrt{3}\) दोनों अपरिमेय हैं। चरण 2: उनका योग \(3\sqrt{3}\) है, जो अपरिमेय है। चरण 3: योग वाले प्रश्नों में कटने वाले और जुड़ने वाले समान मूल अलग-अलग पहचानें।
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कौन-सा युग्म दिखाता है कि दो अपरिमेय संख्याओं का भागफल परिमेय हो सकता है?
Which pair shows that the quotient of two irrational numbers can be rational?
#quotient of irrationals
#rational result
#class 10
A \(\sqrt{6}\) और \(\sqrt{3}\) / \(\sqrt{6}\) and \(\sqrt{3}\)
B \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
C \(\sqrt{10}\) और \(\sqrt{2}\) / \(\sqrt{10}\) and \(\sqrt{2}\)
D \(\sqrt{7}\) और \(\sqrt{5}\) / \(\sqrt{7}\) and \(\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{3}\) are both irrational.
Step 2
Why this answer is correct
\(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\), which is rational.
Step 3
Exam Tip
In quotients, check whether the value inside the root becomes a perfect square. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। चरण 2: \(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\), जो परिमेय है। चरण 3: भागफल में मूल के अंदर का भाग पूर्ण वर्ग बन रहा है या नहीं, यह देखें।
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कौन-सा विकल्प दो अलग-अलग अपरिमेय संख्याओं का उदाहरण है जिनका भागफल परिमेय है?
Which option is an example of two different irrational numbers whose quotient is rational?
#quotient of irrationals
#counterexample
#class 10
A \(\frac{\sqrt{2}}{\sqrt{3}}\)
B \(\frac{\sqrt{12}}{\sqrt{3}}\)
C \(\frac{\sqrt{5}}{\sqrt{20}}\)
D \(\frac{\sqrt{7}}{2}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{\sqrt{5}}{\sqrt{20}}\)
Step 1
Concept
\(\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\) are both irrational and different.
Step 2
Why this answer is correct
\(\frac{\sqrt{5}}{\sqrt{20}}=\frac{\sqrt{5}}{2\sqrt{5}}=\frac{1}{2}\), which is rational.
Step 3
Exam Tip
A common irrational factor can cancel in a quotient. चरण 1: \(\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\) दोनों अपरिमेय हैं और अलग-अलग हैं। चरण 2: \(\frac{\sqrt{5}}{\sqrt{20}}=\frac{\sqrt{5}}{2\sqrt{5}}=\frac{1}{2}\), जो परिमेय है। चरण 3: भागफल में समान अपरिमेय गुणनखंड कट सकता है।
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निम्न में से कौन-सा युग्म दिखाता है कि दो अपरिमेय संख्याओं का योग परिमेय हो सकता है?
Which pair shows that the sum of two irrational numbers can be rational?
#counterexample
#sum of irrationals
#class 10
A \(\sqrt{2},\sqrt{3}\)
B \(\sqrt{5},-\sqrt{5}\)
C \(\sqrt{7},\sqrt{7}\)
D \(\sqrt{11},1\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5},-\sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\) and \(-\sqrt{5}\) are both irrational.
Step 2
Why this answer is correct
Their sum is (0), which is rational.
Step 3
Exam Tip
Before applying a general rule for two irrationals, test possible counterexamples. चरण 1: \(\sqrt{5}\) और \(-\sqrt{5}\) दोनों अपरिमेय हैं। चरण 2: उनका योग (0) है, जो परिमेय संख्या है। चरण 3: दो अपरिमेय संख्याओं के योग पर सामान्य नियम लगाने से पहले उदाहरण जाँचें।
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कैल्शियम कार्बोनेट के गर्म होने पर ठोस उत्पाद और गैसीय उत्पाद का सही युग्म कौन सा है?
What is the correct pair of solid product and gaseous product when calcium carbonate is heated?
#science
#class10
#expert
#calcium-carbonate
#thermal-decomposition
A कैल्शियम ऑक्साइड और कार्बन डाइऑक्साइड / Calcium oxide and carbon dioxide
B कैल्शियम हाइड्रॉक्साइड और हाइड्रोजन / Calcium hydroxide and hydrogen
C कैल्शियम सल्फेट और ऑक्सीजन / Calcium sulphate and oxygen
D कैल्शियम क्लोराइड और नाइट्रोजन / Calcium chloride and nitrogen
Explanation opens after your attempt
Correct Answer
A. कैल्शियम ऑक्साइड और कार्बन डाइऑक्साइड / Calcium oxide and carbon dioxide
Step 1
Concept
Calcium carbonate decomposes by heat.
Step 2
Why this answer is correct
Calcium oxide remains as the solid.
Step 3
Exam Tip
Carbon dioxide evolves as the gas. चरण 1: कैल्शियम कार्बोनेट ऊष्मा से टूटता है। चरण 2: ठोस के रूप में कैल्शियम ऑक्साइड बचता है। चरण 3: गैस के रूप में कार्बन डाइऑक्साइड निकलती है।
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नीचे की ओर तीर वाले उत्पाद और ऊपर की ओर तीर वाले उत्पाद में सही अंतर क्या है?
What is the correct difference between a product with a downward arrow and a product with an upward arrow?
#science
#class10
#hard
#arrow-symbols
#gas
#precipitate
A नीचे तीर अवक्षेप और ऊपर तीर गैस दिखाता है / Downward arrow shows precipitate and upward arrow shows gas
B नीचे तीर गैस और ऊपर तीर अवक्षेप दिखाता है / Downward arrow shows gas and upward arrow shows precipitate
C दोनों केवल ऊष्मा दिखाते हैं / Both show only heat
D दोनों केवल द्रव दिखाते हैं / Both show only liquid
Explanation opens after your attempt
Correct Answer
A. नीचे तीर अवक्षेप और ऊपर तीर गैस दिखाता है / Downward arrow shows precipitate and upward arrow shows gas
Step 1
Concept
Downward arrow shows an insoluble solid.
Step 2
Why this answer is correct
Upward arrow shows evolution of gas.
Step 3
Exam Tip
Identify both symbols separately while reading equations. चरण 1: नीचे की ओर तीर अघुलनशील ठोस को दिखाता है। चरण 2: ऊपर की ओर तीर गैस निकलने को दिखाता है। चरण 3: समीकरण पढ़ते समय दोनों संकेतों को अलग पहचानें।
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यदि किसी अभिक्रिया में ऊष्मा उत्पादों की ओर लिखी है और केवल एक उत्पाद बनता है तो कौन सा वर्गीकरण संभव है?
If heat is written on the product side and only one product forms which classification is possible?
#science
#class10
#hard
#exothermic
#combination
A ऊष्माक्षेपी संयोजन / Exothermic combination
B ऊष्माशोषी वियोजन / Endothermic decomposition
C वैद्युत वियोजन / Electrolytic decomposition
D प्रकाशीय वियोजन / Photolytic decomposition
Explanation opens after your attempt
Correct Answer
A. ऊष्माक्षेपी संयोजन / Exothermic combination
Step 1
Concept
Heat on the product side shows heat release.
Step 2
Why this answer is correct
Formation of only one product can indicate combination.
Step 3
Exam Tip
Therefore it can be exothermic combination. चरण 1: उत्पादों की ओर ऊष्मा लिखना ऊष्मा निकलने को दिखाता है। चरण 2: केवल एक उत्पाद बनना संयोजन की पहचान हो सकती है। चरण 3: इसलिए यह ऊष्माक्षेपी संयोजन हो सकता है।
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यदि उत्पाद चित्र में चमक बहुत अधिक है और रूप दब गया है तो सर्वोत्तम आलोचना क्या होगी?
If shine is excessive in a product drawing and form is suppressed what is the best criticism?
#product drawing
#highlight
#form
A चमक हमेशा पर्याप्त है / Shine is always enough
B रूप का उत्पाद से संबंध नहीं / Form has no relation to product
C रंग की जरूरत नहीं / Colour is not needed
D हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure
Explanation opens after your attempt
Correct Answer
D. हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure
Step 1
Concept
Highlight should clarify form. Exam tip: keep balance between shine and form.
Step 2
Why this answer is correct
The correct answer is D. हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure. Highlight should clarify form. Exam tip: keep balance between shine and form.
Step 3
Exam Tip
हाइलाइट को रूप स्पष्ट करना चाहिए। परीक्षा में shine और form का संतुलन रखें।
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यदि किसी विज्ञापन में उत्पाद प्रीमियम दिखाना है तो कौन सा संयोजन सबसे परिपक्व होगा?
If a product has to look premium in an advertisement which combination will be most mature?
#product design
#premium
#space
A भीड़भाड़ पृष्ठभूमि और हर जगह तीखे रंग / Crowded background and sharp colours everywhere
B साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlight
C असंगठित रेखाएं और कम विरोध / Disorganized lines and low contrast
D मुख्य उत्पाद को पृष्ठभूमि में छिपाना / Hide main product in background
Explanation opens after your attempt
Correct Answer
B. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlight
Step 1
Concept
Premium visuals need clarity control and space. Exam tip: observe space and focus in product design.
Step 2
Why this answer is correct
The correct answer is B. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlight. Premium visuals need clarity control and space. Exam tip: observe space and focus in product design.
Step 3
Exam Tip
प्रीमियम दृश्य में स्पष्टता नियंत्रण और स्थान महत्वपूर्ण हैं। परीक्षा में product design में space and focus देखें।
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किसी उत्पाद चित्र में चमक बहुत अधिक है और रूप अस्पष्ट है तो सर्वोत्तम आलोचना क्या है?
In a product drawing if shine is too much and form is unclear what is the best criticism?
#product drawing
#highlight
#form
A हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure
B चमक हमेशा पर्याप्त है / Shine is always enough
C रूप का उत्पाद से संबंध नहीं / Form has no relation to product
D मान की जरूरत नहीं / Value is not needed
Explanation opens after your attempt
Correct Answer
A. हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure
Step 1
Concept
Highlights should clarify form not suppress it. Exam tip: observe balance of shine and form.
Step 2
Why this answer is correct
The correct answer is A. हाइलाइट रूप संरचना पर भारी पड़ रहे हैं / Highlights are overpowering form structure. Highlights should clarify form not suppress it. Exam tip: observe balance of shine and form.
Step 3
Exam Tip
हाइलाइट को रूप स्पष्ट करना चाहिए न कि उसे दबाना। परीक्षा में shine और form balance देखें।
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यदि विज्ञापन में उत्पाद को प्रीमियम दिखाना है तो कौन सा तत्व संयोजन उपयोगी होगा?
If a product has to look premium in an advertisement which element combination is useful?
#product design
#premium
#negative space
A साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlights
B भीड़भाड़ वाली पृष्ठभूमि और अनेक टकराते रंग / Crowded background and many clashing colours
C हर जगह समान बनावट / Same texture everywhere
D धुंधला केंद्र बिंदु / Blurred focal point
Explanation opens after your attempt
Correct Answer
A. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlights
Step 1
Concept
Clarity and controlled elements help premium effect. Exam tip: observe space and focus in product design.
Step 2
Why this answer is correct
The correct answer is A. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइट / Clean negative space controlled colour and clear highlights. Clarity and controlled elements help premium effect. Exam tip: observe space and focus in product design.
Step 3
Exam Tip
प्रीमियम प्रभाव के लिए स्पष्टता और नियंत्रित तत्व उपयोगी हैं। परीक्षा में product design में space और focus देखें।
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किसी उत्पाद चित्र में सामग्री पहचानने के लिए बनावट क्यों जरूरी है?
Why is texture important to identify material in a product drawing?
#texture
#material identity
#product drawing
A यह रंगत्व को मिटाती है / It erases hue
B यह स्थान खत्म करती है / It ends space
C यह केवल सजावट है / It is only decoration
D यह बताती है कि वस्तु लकड़ी धातु कपड़ा या कांच जैसी है / It tells whether object is like wood metal cloth or glass
Explanation opens after your attempt
Correct Answer
D. यह बताती है कि वस्तु लकड़ी धातु कपड़ा या कांच जैसी है / It tells whether object is like wood metal cloth or glass
Step 1
Concept
Texture helps identify material surface. Exam tip: connect material identity with texture.
Step 2
Why this answer is correct
The correct answer is D. यह बताती है कि वस्तु लकड़ी धातु कपड़ा या कांच जैसी है / It tells whether object is like wood metal cloth or glass. Texture helps identify material surface. Exam tip: connect material identity with texture.
Step 3
Exam Tip
बनावट सामग्री की सतह पहचानने में मदद करती है। परीक्षा में material identity को texture से जोड़ें।
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यदि (p(x)=2x-2 -7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?
If (p(x)=2x-2 -7x+5), what is the difference between the sum and product of its zeroes?
#sum-product
#quadratic
#zeroes
A (1)
B (2)
C \(\frac{1}{2}\)
D (3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 3
Exam Tip
योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है।
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(p(x)=x-3 -3x-2 -4x+12) में (p(2)) और (p(-2)) का गुणनफल क्या है?
What is the product of (p(2)) and (p(-2)) for (p(x)=x-3 -3x-2 -4x+12)?
#evaluation
#product
#cubic
A (-32)
B (0)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). (p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 3
Exam Tip
(p(2)=8-12-8+12=0), इसलिए गुणनफल (0) होगा। एक मान (0) हो तो पूरा गुणनफल (0) होता है।
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यदि (p(x)=x-2 -ax+a) के शून्यकों का गुणनफल और योग बराबर हैं, तो \(a\neq0\) होने पर (a) क्या है?
If the sum and product of zeroes of (p(x)=x-2 -ax+a) are equal, and \(a\neq0\), what is (a)?
#sum-product
#parameter
#conceptual
A कोई भी अशून्य वास्तविक संख्या / Any non-zero real number
B सिर्फ (1) / Only (1)
C सिर्फ (-1) / Only (-1)
D सिर्फ (2) / Only (2)
Explanation opens after your attempt
Correct Answer
A. कोई भी अशून्य वास्तविक संख्या / Any non-zero real number
Step 1
Concept
The sum is (a) and the product is also (a). Therefore every non-zero (a) works.
Step 2
Why this answer is correct
The correct answer is A. कोई भी अशून्य वास्तविक संख्या / Any non-zero real number. The sum is (a) and the product is also (a). Therefore every non-zero (a) works.
Step 3
Exam Tip
योग (a) और गुणनफल (a) दोनों समान हैं। इसलिए \(a\neq0\) के लिए हर अशून्य (a) काम करता है।
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यदि (p(x)=kx-2 -6x+4) के शून्यकों का गुणनफल (2) है, तो (k) क्या है?
If the product of zeroes of (p(x)=kx-2 -6x+4) is (2), what is (k)?
#product-zeroes
#parameter
#quadratic
A (2)
B (4)
C (1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{4}{k}\), so \(\frac{4}{k}=2\) and (k=2). Product equals constant term divided by leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). The product is \(\frac{4}{k}\), so \(\frac{4}{k}=2\) and (k=2). Product equals constant term divided by leading coefficient.
Step 3
Exam Tip
गुणनफल \(\frac{4}{k}\) है, इसलिए \(\frac{4}{k}=2\) और (k=2)। गुणनफल में स्थिर पद को प्रमुख गुणांक से भाग देते हैं।
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यदि शून्यकों का योग (-4) और गुणनफल (7) है, तो मोनिक द्विघात बहुपद कौन-सा है?
If the sum of zeroes is (-4) and product is (7), which is the monic quadratic polynomial?
#sum-product
#construct-polynomial
#quadratic
A \(x^2+4x+7\)
B \(x^2-4x+7\)
C \(x^2+7x-4\)
D \(x^2-7x+4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+7\)
Step 1
Concept
\(A monic quadratic is (x^2-(\)sum)x+product\(). Hence (x^2-(-4)x+7=x^2+4x+7).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+4x+7). A monic quadratic is (x^2-(\)sum)x+product\(). Hence (x^2-(-4)x+7=x^2+4x+7).\)
Step 3
Exam Tip
\(मोनिक द्विघात (x^2-(\)योग)x+गुणनफल) होता है। \(इसलिए (x^2-(-4)x+7=x^2+4x+7) है\)।
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यदि (p(x)=5x-2 +2x-8), तो शून्यकों का गुणनफल क्या है?
If (p(x)=5x-2 +2x-8), what is the product of its zeroes?
#product-zeroes
#quadratic
#formula
A -\(\frac{8}{5}\)
B \(\frac{8}{5}\)
C -\(\frac{2}{5}\)
D \(\frac{2}{5}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{8}{5}\)
Step 1
Concept
For \(ax^2+bx+c\), the product of zeroes is \(\frac{c}{a}\). Here \(\frac{-8}{5}=-\frac{8}{5}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{8}{5}\). For \(ax^2+bx+c\), the product of zeroes is \(\frac{c}{a}\). Here \(\frac{-8}{5}=-\frac{8}{5}\).
Step 3
Exam Tip
द्विघात \(ax^2+bx+c\) में शून्यकों का गुणनफल \(\frac{c}{a}\) होता है। यहाँ \(\frac{-8}{5}=-\frac{8}{5}\) है।
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(p(x)=x-3 -2x-2 -3x+4) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=x-3 -2x-2 -3x+4)?
#evaluation
#product
#cubic
A (-4)
B (0)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 3
Exam Tip
(p(1)=1-2-3+4=0) और (p(-1)=-1-2+3+4=4), इसलिए गुणनफल (0) है। पहले दोनों मान निकालें।
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द्विघात बहुपद \(2x^2-7x+3\) के शून्यकों का गुणनफल क्या है?
What is the product of the zeroes of the quadratic polynomial \(2x^2-7x+3\)?
#polynomials
#zeroes
#product
#hard
A (3)
B \(\frac{3}{2}\)
C \(-\frac{7}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{2}\)
Step 1
Concept
For \(ax^2+bx+c\), the product is \(\frac{c}{a}\). Here, \(\frac{3}{2}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{2}\). For \(ax^2+bx+c\), the product is \(\frac{c}{a}\). Here, \(\frac{3}{2}\) is correct.
Step 3
Exam Tip
द्विघात \(ax^2+bx+c\) में गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{3}{2}\) सही है।
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(p(x)=2x-3 +x-2 -5x+2) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=2x-3 +x-2 -5x+2)?
#evaluation
#product
#cubic
A (-12)
B (-8)
C (0)
D (12)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 2
Why this answer is correct
The correct answer is A. (-12). (p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 3
Exam Tip
(p(1)=0) नहीं बल्कि (2+1-5+2=0), और (p(-1)=-2+1+5+2=6), इसलिए गुणनफल (0) है। सही विकल्प (0) है।
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किस धनात्मक संख्या में (7) जोड़ने पर प्राप्त संख्या और मूल संख्या का गुणनफल (330) होता है?
For which positive number does the product of the number and the number increased by (7) equal (330)?
#quadratic equations
#number problem
#product
A (12)
B (15)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).
Step 2
Why this answer is correct
The correct answer is B. (15). Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).
Step 3
Exam Tip
संख्या (x) हो तो (x(x+7)=330)। \(x^2+7x-330=0\) से धनात्मक हल (x=15) है।
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दो क्रमागत विषम धनात्मक पूर्णांकों का गुणनफल (483) है। बड़ी संख्या क्या है?
The product of two consecutive positive odd integers is (483). What is the larger integer?
#quadratic equations
#consecutive odd integers
#product
A (21)
B (23)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).
Step 2
Why this answer is correct
The correct answer is B. (23). The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).
Step 3
Exam Tip
संख्याएँ (x) और (x+2) हैं। (x(x+2)=483) से (x=21) मिलता है इसलिए बड़ी संख्या (23) है।
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दो क्रमागत सम धनात्मक पूर्णांकों का गुणनफल (360) है। छोटी संख्या क्या है?
The product of two consecutive positive even integers is (360). What is the smaller integer?
#quadratic equations
#consecutive even integers
#product
A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).
Step 2
Why this answer is correct
The correct answer is B. (18). Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).
Step 3
Exam Tip
संख्याएँ (x) और (x+2) मानें। (x(x+2)=360) से \(x^2+2x-360=0\) और (x=18) मिलता है।
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दो संख्याओं का योग (31) और गुणनफल (234) है। छोटी संख्या क्या है?
The sum of two numbers is (31) and their product is (234). What is the smaller number?
#quadratic equations
#sum and product
#numbers
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (31-x). From (x(31-x)=234), the numbers are (13) and (18).
Step 2
Why this answer is correct
The correct answer is B. (13). If one number is (x), the other is (31-x). From (x(31-x)=234), the numbers are (13) and (18).
Step 3
Exam Tip
यदि एक संख्या (x) है तो दूसरी (31-x) होगी। (x(31-x)=234) से संख्याएँ (13) और (18) मिलती हैं।
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दो व्यक्तियों की आयुओं का योग (30) वर्ष और गुणनफल (216) है। उनकी आयु क्या है?
The sum of the ages of two people is (30) years and their product is (216). What are their ages?
#quadratic equations
#age sum product
#application
A (10) वर्ष और (20) वर्ष / (10) years and (20) years
B (11) वर्ष और (19) वर्ष / (11) years and (19) years
C (12) वर्ष और (18) वर्ष / (12) years and (18) years
D (13) वर्ष और (17) वर्ष / (13) years and (17) years
Explanation opens after your attempt
Correct Answer
C. (12) वर्ष और (18) वर्ष / (12) years and (18) years
Step 1
Concept
If one age is (x), the other is (30-x). From (x(30-x)=216), we get (12) and (18).
Step 2
Why this answer is correct
The correct answer is C. (12) वर्ष और (18) वर्ष / (12) years and (18) years. If one age is (x), the other is (30-x). From (x(30-x)=216), we get (12) and (18).
Step 3
Exam Tip
यदि एक आयु (x) है तो दूसरी (30-x) है। (x(30-x)=216) से (12) और (18) मिलते हैं।
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एक संख्या और उससे (4) अधिक संख्या का गुणनफल (221) है। छोटी संख्या क्या है?
The product of a number and the number (4) more than it is (221). What is the smaller number?
#quadratic equations
#number application
#product
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(x+4)=221). The positive solution is (x=13).
Step 2
Why this answer is correct
The correct answer is C. (13). The equation is (x(x+4)=221). The positive solution is (x=13).
Step 3
Exam Tip
समीकरण (x(x+4)=221) है। धनात्मक हल (x=13) है।
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दो धनात्मक संख्याओं का योग (19) और गुणनफल (84) है। वे संख्याएँ कौन सी हैं?
The sum of two positive numbers is (19) and their product is (84). Which numbers are they?
#quadratic equations
#sum product
#number problem
A (6) और (13) / (6) and (13)
B (7) और (12) / (7) and (12)
C (8) और (11) / (8) and (11)
D (9) और (10) / (9) and (10)
Explanation opens after your attempt
Correct Answer
B. (7) और (12) / (7) and (12)
Step 1
Concept
If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).
Step 2
Why this answer is correct
The correct answer is B. (7) और (12) / (7) and (12). If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है तो दूसरी (19-x) है। (x(19-x)=84) से (7) और (12) मिलते हैं।
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दो धनात्मक संख्याओं में अंतर (6) है और उनका गुणनफल (216) है। छोटी संख्या क्या है?
Two positive numbers differ by (6) and their product is (216). What is the smaller number?
#quadratic equations
#number problem
#product
A (10)
B (11)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), then (x(x+6)=216). The positive solution is (x=12).
Step 2
Why this answer is correct
The correct answer is C. (12). If the smaller number is (x), then (x(x+6)=216). The positive solution is (x=12).
Step 3
Exam Tip
छोटी संख्या (x) हो तो (x(x+6)=216)। धनात्मक हल (x=12) है।
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एक संख्या में (6) जोड़कर प्राप्त संख्या और मूल संख्या का गुणनफल (135) है। धनात्मक मूल संख्या क्या है?
The product of a number and the number obtained by adding (6) to it is (135). What is the positive original number?
#quadratic equations
#number product
#application
A (9)
B (10)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then (x(x+6)=135). This gives \(x^2+6x-135=0\), so (x=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Let the number be (x), then (x(x+6)=135). This gives \(x^2+6x-135=0\), so (x=9).
Step 3
Exam Tip
संख्या (x) हो, तो (x(x+6)=135)। इससे \(x^2+6x-135=0\), इसलिए (x=9)।
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दो धनात्मक संख्याओं का योग (21) है और उनका गुणनफल (108) है। बड़ी संख्या क्या है?
The sum of two positive numbers is (21), and their product is (108). What is the larger number?
#quadratic equations
#sum product
#number problem
A (9)
B (10)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).
Step 3
Exam Tip
संख्याएँ (x) और (21-x) हों, तो (x(21-x)=108)। मूल (9) और (12) हैं, इसलिए बड़ी संख्या (12) है।
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एक संख्या के (11) कम और (20) अधिक मानों का गुणनफल (2112) है। धनात्मक मूल संख्या क्या है?
The product of (11) less and (20) more than a number is (2112). What is the positive original number?
#quadratic equations
#number product
#application
A (33)
B (40)
C (44)
D (64)
Explanation opens after your attempt
Step 1
Concept
((x-11)(x+20)=2112) gives (x=44). Use signs for less and more carefully.
Step 2
Why this answer is correct
The correct answer is C. (44). ((x-11)(x+20)=2112) gives (x=44). Use signs for less and more carefully.
Step 3
Exam Tip
((x-11)(x+20)=2112) से (x=44) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।
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दो धनात्मक संख्याओं का अंतर (19) है और उनका गुणनफल (1632) है। बड़ी संख्या क्या है?
The difference between two positive numbers is (19) and their product is (1632). What is the larger number?
#quadratic equations
#difference product
#number problem
A (32)
B (45)
C (51)
D (57)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x) and the larger is (x+19), then (x(x+19)=1632). This gives smaller number (32) and larger number (51).
Step 2
Why this answer is correct
The correct answer is C. (51). If the smaller number is (x) and the larger is (x+19), then (x(x+19)=1632). This gives smaller number (32) and larger number (51).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+19) हो तो (x(x+19)=1632) बनता है। इससे छोटी संख्या (32) और बड़ी संख्या (51) मिलती है।
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एक संख्या के (9) कम और (16) अधिक मानों का गुणनफल (1110) है। धनात्मक मूल संख्या क्या है?
The product of (9) less and (16) more than a number is (1110). What is the positive original number?
#quadratic equations
#number product
#application
A (30)
B (32)
C (34)
D (39)
Explanation opens after your attempt
Step 1
Concept
((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.
Step 2
Why this answer is correct
The correct answer is D. (39). ((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.
Step 3
Exam Tip
((x-9)(x+16)=1110) से (x=39) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।
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दो धनात्मक संख्याओं का अंतर (17) है और उनका गुणनफल (1260) है। बड़ी संख्या क्या है?
The difference between two positive numbers is (17) and their product is (1260). What is the larger number?
#quadratic equations
#difference product
#number problem
A (28)
B (35)
C (42)
D (45)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).
Step 2
Why this answer is correct
The correct answer is D. (45). If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+17) हो तो (x(x+17)=1260) बनता है। इससे छोटी संख्या (28) और बड़ी संख्या (45) मिलती है।
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एक संख्या के (7) कम और (12) अधिक मानों का गुणनफल (756) है। धनात्मक मूल संख्या क्या है?
The product of (7) less and (12) more than a number is (756). What is the positive original number?
#quadratic equations
#number product
#application
A (24)
B (25)
C (28)
D (31)
Explanation opens after your attempt
Step 1
Concept
((x-7)(x+12)=756) gives (x=28). Use signs for less and more carefully.
Step 2
Why this answer is correct
The correct answer is C. (28). ((x-7)(x+12)=756) gives (x=28). Use signs for less and more carefully.
Step 3
Exam Tip
((x-7)(x+12)=756) से (x=28) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।
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दो धनात्मक संख्याओं का अंतर (13) है और उनका गुणनफल (558) है। बड़ी संख्या क्या है?
The difference between two positive numbers is (13) and their product is (558). What is the larger number?
#quadratic equations
#difference product
#number problem
A (18)
B (25)
C (31)
D (36)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x) and the larger is (x+13), then (x(x+13)=558), giving (x=18). The larger number is (31).
Step 2
Why this answer is correct
The correct answer is C. (31). If the smaller number is (x) and the larger is (x+13), then (x(x+13)=558), giving (x=18). The larger number is (31).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+13) हो तो (x(x+13)=558), जिससे (x=18) है। बड़ी संख्या (31) होगी।
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दो धनात्मक संख्याओं का गुणनफल (378) है और बड़ी संख्या छोटी से (3) अधिक है। छोटी संख्या क्या है?
The product of two positive numbers is (378) and the larger number is (3) more than the smaller. What is the smaller number?
#quadratic-equations
#word-problems
#product-difference
A (18)
B (21)
C (15)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+3). From (x(x+3)=378), (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller number is (x), the larger is (x+3). From (x(x+3)=378), (x=18).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+3) है। (x(x+3)=378) से (x=18) मिलता है।
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दो मित्रों की आयु का योग (44) है और उनके आयुओं का गुणनफल (480) है। बड़े मित्र की आयु क्या है?
The sum of ages of two friends is (44) and the product of their ages is (480). What is the age of the older friend?
#quadratic-equations
#word-problems
#ages-product
A (24)
B (20)
C (22)
D (28)
Explanation opens after your attempt
Step 1
Concept
If one age is (x), the other is (44-x). From (x(44-x)=480), the ages are (24) and (20).
Step 2
Why this answer is correct
The correct answer is A. (24). If one age is (x), the other is (44-x). From (x(44-x)=480), the ages are (24) and (20).
Step 3
Exam Tip
यदि एक आयु (x) है, तो दूसरी (44-x) है। (x(44-x)=480) से आयु (24) और (20) मिलती हैं।
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दो संख्याओं का अंतर (8) है और गुणनफल (273) है। बड़ी संख्या क्या है?
The difference of two numbers is (8) and their product is (273). What is the larger number?
#quadratic-equations
#word-problems
#difference-product
A (21)
B (13)
C (19)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+8). From (x(x+8)=273), (x=13), so the larger number is (21).
Step 2
Why this answer is correct
The correct answer is A. (21). If the smaller number is (x), the larger is (x+8). From (x(x+8)=273), (x=13), so the larger number is (21).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+8) होगी। (x(x+8)=273) से (x=13), इसलिए बड़ी संख्या (21) है।
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दो संख्याओं का योग (29) है और गुणनफल (204) है। बड़ी संख्या क्या है?
The sum of two numbers is (29) and their product is (204). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (17)
B (12)
C (15)
D (29)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 2
Why this answer is correct
The correct answer is A. (17). If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (29-x) होगी। (x(29-x)=204) से संख्याएँ (17) और (12) मिलती हैं।
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एक संख्या के (5) कम और (8) अधिक मानों का गुणनफल (464) है। धनात्मक मूल संख्या क्या है?
The product of (5) less and (8) more than a number is (464). What is the positive original number?
#quadratic equations
#number product
#application
A (20)
B (21)
C (24)
D (29)
Explanation opens after your attempt
Step 1
Concept
((x-5)(x+8)=464) gives (x=21). Use signs for less and more carefully.
Step 2
Why this answer is correct
The correct answer is B. (21). ((x-5)(x+8)=464) gives (x=21). Use signs for less and more carefully.
Step 3
Exam Tip
((x-5)(x+8)=464) से (x=21) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।
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दो धनात्मक संख्याओं का अंतर (5) है और उनका गुणनफल (456) है। बड़ी संख्या क्या है?
The difference between two positive numbers is (5) and their product is (456). What is the larger number?
#quadratic equations
#difference product
#number problem
A (19)
B (21)
C (24)
D (27)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x) and the larger is (x+5), then (x(x+5)=456), giving (x=19). The larger number is (24).
Step 2
Why this answer is correct
The correct answer is C. (24). If the smaller number is (x) and the larger is (x+5), then (x(x+5)=456), giving (x=19). The larger number is (24).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+5) हो तो (x(x+5)=456), जिससे (x=19) है। बड़ी संख्या (24) होगी।
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दो धनात्मक संख्याओं का गुणनफल (216) है और बड़ी संख्या छोटी से (6) अधिक है। छोटी संख्या क्या है?
The product of two positive numbers is (216) and the larger number is (6) more than the smaller. What is the smaller number?
#quadratic-equations
#word-problems
#product-difference
A (12)
B (18)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+6). From (x(x+6)=216), (x=12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the smaller number is (x), the larger is (x+6). From (x(x+6)=216), (x=12).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+6) है। (x(x+6)=216) से (x=12) मिलता है।
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दो मित्रों की आयु का योग (40) है और उनके आयुओं का गुणनफल (375) है। बड़े मित्र की आयु क्या है?
The sum of ages of two friends is (40) and the product of their ages is (375). What is the age of the older friend?
#quadratic-equations
#word-problems
#ages-product
A (25)
B (15)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
If one age is (x), the other is (40-x). From (x(40-x)=375), the ages are (25) and (15).
Step 2
Why this answer is correct
The correct answer is A. (25). If one age is (x), the other is (40-x). From (x(40-x)=375), the ages are (25) and (15).
Step 3
Exam Tip
यदि एक आयु (x) है, तो दूसरी (40-x) है। (x(40-x)=375) से आयु (25) और (15) मिलती हैं।
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दो संख्याओं का योग (15) है और गुणनफल (54) है। बड़ी संख्या क्या है?
The sum of two numbers is (15) and their product is (54). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (9)
B (6)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 2
Why this answer is correct
The correct answer is A. (9). If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (15-x) होगी। (x(15-x)=54) से संख्याएँ (9) और (6) मिलती हैं।
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एक संख्या के (4) कम मान और (5) अधिक मान का गुणनफल (420) है। धनात्मक मूल संख्या क्या है?
The product of (4) less than a number and (5) more than the number is (420). What is the positive original number?
#quadratic equations
#number product
#application
A (19)
B (20)
C (21)
D (24)
Explanation opens after your attempt
Step 1
Concept
((x-4)(x+5)=420) gives (x=19). Write less and more with correct signs.
Step 2
Why this answer is correct
The correct answer is A. (19). ((x-4)(x+5)=420) gives (x=19). Write less and more with correct signs.
Step 3
Exam Tip
((x-4)(x+5)=420) से (x=19) मिलता है। कम और अधिक दोनों को सही चिन्ह से लिखें।
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एक संख्या और उसके (18) अधिक मान का गुणनफल (703) है। बड़ी संख्या क्या है?
A number and (18) more than it have product (703). What is the larger number?
#quadratic equations
#number product
#application
A (19)
B (25)
C (31)
D (37)
Explanation opens after your attempt
Step 1
Concept
From (x(x+18)=703), (x=19). Therefore, the larger number is (37).
Step 2
Why this answer is correct
The correct answer is D. (37). From (x(x+18)=703), (x=19). Therefore, the larger number is (37).
Step 3
Exam Tip
(x(x+18)=703) से (x=19) है। इसलिए बड़ी संख्या (37) होगी।
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एक संख्या और उसके (14) अधिक मान का गुणनफल (560) है। छोटी संख्या क्या है?
A number and (14) more than it have product (560). What is the smaller number?
#quadratic equations
#number product
#word problem
A (14)
B (16)
C (20)
D (28)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(x+14)=560). This gives (x=16), and the other value is (30).
Step 2
Why this answer is correct
The correct answer is B. (16). The equation is (x(x+14)=560). This gives (x=16), and the other value is (30).
Step 3
Exam Tip
समीकरण (x(x+14)=560) है। इससे (x=16) मिलता है और दूसरा मान (30) है।
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दो संख्याओं का अंतर (11) है और गुणनफल (672) है। बड़ी संख्या क्या है?
The difference between two numbers is (11) and their product is (672). What is the larger number?
#quadratic equations
#difference product
#application
A (21)
B (24)
C (28)
D (32)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+11). From (x(x+11)=672), (x=21), so the larger number is (32).
Step 2
Why this answer is correct
The correct answer is D. (32). If the smaller number is (x), the larger is (x+11). From (x(x+11)=672), (x=21), so the larger number is (32).
Step 3
Exam Tip
छोटी संख्या (x) हो तो बड़ी (x+11) है। (x(x+11)=672) से (x=21), इसलिए बड़ी संख्या (32) है।
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दो संख्याओं का अंतर (9) है और गुणनफल (486) है। छोटी संख्या क्या है?
The difference between two numbers is (9) and their product is (486). What is the smaller number?
#quadratic equations
#difference product
#word problem
A (18)
B (21)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x) and larger is (x+9), then (x(x+9)=486), giving (x=18). Keep the difference between larger and smaller correct.
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller number is (x) and larger is (x+9), then (x(x+9)=486), giving (x=18). Keep the difference between larger and smaller correct.
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+9) हो तो (x(x+9)=486), जिससे (x=18) है। अंतर को बड़े और छोटे में सही रखें।
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दो संख्याओं का योग (47) है और गुणनफल (540) है। बड़ी संख्या क्या है?
The sum of two numbers is (47) and their product is (540). What is the larger number?
#quadratic equations
#sum product
#application
A (20)
B (22)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (47-x), then (x(47-x)=540). The solutions are (20) and (27), so the larger number is (27).
Step 2
Why this answer is correct
The correct answer is D. (27). If the numbers are (x) and (47-x), then (x(47-x)=540). The solutions are (20) and (27), so the larger number is (27).
Step 3
Exam Tip
संख्याएँ (x) और (47-x) हों तो (x(47-x)=540) है। हल (20) और (27) हैं, इसलिए बड़ी संख्या (27) है।
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दो संख्याओं का योग (43) है और गुणनफल (460) है। छोटी संख्या क्या है?
The sum of two numbers is (43) and their product is (460). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (18)
B (20)
C (23)
D (25)
Explanation opens after your attempt
Step 1
Concept
Take the numbers as (x) and (43-x). From (x(43-x)=460), the numbers are (20) and (23), so the smaller number is (20).
Step 2
Why this answer is correct
The correct answer is B. (20). Take the numbers as (x) and (43-x). From (x(43-x)=460), the numbers are (20) and (23), so the smaller number is (20).
Step 3
Exam Tip
संख्याएँ (x) और (43-x) लें। (x(43-x)=460) से (20) और (23) मिलते हैं, इसलिए छोटी संख्या (20) है।
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दो संख्याओं का अंतर (8) है और गुणनफल (425) है। छोटी संख्या क्या है?
The difference between two numbers is (8) and their product is (425). What is the smaller number?
#quadratic equations
#difference product
#application
A (15)
B (17)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
Put the smaller number as (x) and the larger as (x+8), then (x(x+8)=425) gives (x=17). Add the difference in the correct form.
Step 2
Why this answer is correct
The correct answer is B. (17). Put the smaller number as (x) and the larger as (x+8), then (x(x+8)=425) gives (x=17). Add the difference in the correct form.
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+8) रखें, तब (x(x+8)=425) से (x=17) है। अंतर को सही रूप में जोड़ें।
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दो संख्याओं का अंतर (6) है और गुणनफल (160) है। बड़ी संख्या क्या है?
The difference between two numbers is (6) and their product is (160). What is the larger number?
#quadratic equations
#difference product
#word problem
A (10)
B (14)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
Let the smaller number be (x) and the larger be (x+6), then (x(x+6)=160) gives (10) and (16). The larger number is (16).
Step 2
Why this answer is correct
The correct answer is C. (16). Let the smaller number be (x) and the larger be (x+6), then (x(x+6)=160) gives (10) and (16). The larger number is (16).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+6) हो, तब (x(x+6)=160) से (10) और (16) मिलते हैं। बड़ी संख्या (16) है।
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दो संख्याओं का योग (31) है और गुणनफल (238) है। बड़ी संख्या क्या है?
The sum of two numbers is (31) and their product is (238). What is the larger number?
#quadratic equations
#sum product
#application
A (13)
B (14)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
(x(31-x)=238) gives the numbers (14) and (17). Hence the larger number is (17).
Step 2
Why this answer is correct
The correct answer is C. (17). (x(31-x)=238) gives the numbers (14) and (17). Hence the larger number is (17).
Step 3
Exam Tip
(x(31-x)=238) से संख्याएँ (14) और (17) हैं। इसलिए बड़ी संख्या (17) है।
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दो संख्याओं का योग (29) है और गुणनफल (204) है। छोटी संख्या क्या है?
The sum of two numbers is (29) and their product is (204). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (10)
B (12)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (29-x), then (x(29-x)=204) gives (12) and (17). The smaller number is (12).
Step 2
Why this answer is correct
The correct answer is B. (12). If the numbers are (x) and (29-x), then (x(29-x)=204) gives (12) and (17). The smaller number is (12).
Step 3
Exam Tip
संख्याएँ (x) और (29-x) हों, तब (x(29-x)=204) से (12) और (17) मिलते हैं। छोटी संख्या (12) है।
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एक संख्या और उसके (9) अधिक मान का गुणनफल (340) है। बड़ी संख्या क्या है?
A number and (9) more than it have product (340). What is the larger number?
#quadratic equations
#number product
#application
A (17)
B (20)
C (24)
D (29)
Explanation opens after your attempt
Step 1
Concept
(x(x+9)=340) gives (x=11), so the larger number is (20). Check the product of both numbers at the end.
Step 2
Why this answer is correct
The correct answer is B. (20). (x(x+9)=340) gives (x=11), so the larger number is (20). Check the product of both numbers at the end.
Step 3
Exam Tip
(x(x+9)=340) से (x=11) है, इसलिए बड़ी संख्या (20) है। अंत में दोनों संख्याओं का गुणनफल जाँचें।
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एक संख्या और उसके (8) अधिक मान का गुणनफल (240) है। छोटी संख्या क्या है?
A number and (8) more than it have product (240). What is the smaller number?
#quadratic equations
#number product
#word problem
A (10)
B (12)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(x+8)=240), which gives (x=12). The greater value should be written as (x+8).
Step 2
Why this answer is correct
The correct answer is B. (12). The equation is (x(x+8)=240), which gives (x=12). The greater value should be written as (x+8).
Step 3
Exam Tip
समीकरण (x(x+8)=240) है, जिससे (x=12) मिलता है। अधिक मान को (x+8) लिखना चाहिए।
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एक धनात्मक संख्या और उसके (5) अधिक मान का गुणनफल (204) है। बड़ी संख्या क्या है?
A positive number and (5) more than it have product (204). What is the larger number?
#quadratic equations
#number product
#word problem
A (12)
B (15)
C (17)
D (20)
Explanation opens after your attempt
Step 1
Concept
(x(x+5)=204) gives (x=12), so the larger number is (17). While answering, write only the value asked.
Step 2
Why this answer is correct
The correct answer is C. (17). (x(x+5)=204) gives (x=12), so the larger number is (17). While answering, write only the value asked.
Step 3
Exam Tip
(x(x+5)=204) से (x=12) है, इसलिए बड़ी संख्या (17) है। उत्तर देते समय पूछा गया मान ही लिखें।
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एक धनात्मक संख्या और उसके (3) अधिक मान का गुणनफल (180) है। छोटी संख्या क्या है?
A positive number and (3) more than it have product (180). What is the smaller number?
#quadratic equations
#number product
#application
A (10)
B (12)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
(x(x+3)=180) gives (x=12). The number (3) more than it will be (15).
Step 2
Why this answer is correct
The correct answer is B. (12). (x(x+3)=180) gives (x=12). The number (3) more than it will be (15).
Step 3
Exam Tip
(x(x+3)=180) से (x=12) मिलता है। (3) अधिक वाला मान (15) होगा।
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दो संख्याओं का योग (25) है और गुणनफल (156) है। बड़ी संख्या क्या है?
The sum of two numbers is (25) and their product is (156). What is the larger number?
#quadratic equations
#sum product
#number problem
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
(x(25-x)=156) gives the numbers (12) and (13). Therefore, the larger number is (13).
Step 2
Why this answer is correct
The correct answer is B. (13). (x(25-x)=156) gives the numbers (12) and (13). Therefore, the larger number is (13).
Step 3
Exam Tip
(x(25-x)=156) से संख्याएँ (12) और (13) हैं। इसलिए बड़ी संख्या (13) है।
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दो संख्याओं का योग (21) है और गुणनफल (110) है। छोटी संख्या क्या है?
The sum of two numbers is (21) and their product is (110). What is the smaller number?
#quadratic equations
#sum product
#application
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (21-x), then (x(21-x)=110) gives (10) and (11). The smaller number is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). If the numbers are (x) and (21-x), then (x(21-x)=110) gives (10) and (11). The smaller number is (10).
Step 3
Exam Tip
संख्याएँ (x) और (21-x) हों, तब (x(21-x)=110) से (10) और (11) मिलते हैं। छोटी संख्या (10) है।
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दो संख्याओं का अंतर (3) है और गुणनफल (108) है। छोटी संख्या क्या है?
The difference between two numbers is (3) and their product is (108). What is the smaller number?
#quadratic equations
#difference product
#application
A (9)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
Putting the smaller number as (x) and larger as (x+3), (x(x+3)=108), giving (x=9). Write the difference in the correct direction.
Step 2
Why this answer is correct
The correct answer is A. (9). Putting the smaller number as (x) and larger as (x+3), (x(x+3)=108), giving (x=9). Write the difference in the correct direction.
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+3) रखने पर (x(x+3)=108) है, जिससे (x=9) है। अंतर को सही दिशा में लिखें।
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दो संख्याओं का अंतर (5) है और गुणनफल (84) है। बड़ी संख्या क्या है?
The difference between two numbers is (5) and their product is (84). What is the larger number?
#quadratic equations
#difference product
#word problem
A (7)
B (9)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
Let the smaller number be (x) and the larger be (x+5), then (x(x+5)=84) gives (7) and (12). The larger number is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Let the smaller number be (x) and the larger be (x+5), then (x(x+5)=84) gives (7) and (12). The larger number is (12).
Step 3
Exam Tip
छोटी संख्या (x) और बड़ी (x+5) हो, तब (x(x+5)=84) से संख्याएँ (7) और (12) हैं। बड़ी संख्या (12) है।
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दो संख्याओं का योग (19) है और गुणनफल (90) है। बड़ी संख्या क्या है?
The sum of two numbers is (19) and their product is (90). What is the larger number?
#quadratic equations
#sum product
#application
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting the numbers as (x) and (19-x), (x(19-x)=90). The solutions are (9) and (10), so the larger number is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). Putting the numbers as (x) and (19-x), (x(19-x)=90). The solutions are (9) and (10), so the larger number is (10).
Step 3
Exam Tip
संख्याएँ (x) और (19-x) रखने पर (x(19-x)=90) बनता है। हल (9) और (10) हैं, इसलिए बड़ी संख्या (10) है।
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दो संख्याओं का योग (17) है और गुणनफल (72) है। छोटी संख्या क्या है?
The sum of two numbers is (17) and their product is (72). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (6)
B (8)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Take the numbers as (x) and (17-x), then (x(17-x)=72) gives (8) and (9). The smaller number is (8).
Step 2
Why this answer is correct
The correct answer is B. (8). Take the numbers as (x) and (17-x), then (x(17-x)=72) gives (8) and (9). The smaller number is (8).
Step 3
Exam Tip
संख्याएँ (x) और (17-x) लें, तब (x(17-x)=72) से संख्याएँ (8) और (9) हैं। छोटी संख्या (8) है।
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यदि \(10x^2-23x+p=0\) के मूलों का गुणनफल \(\frac{2}{5}\) है, तो (p) क्या होगा?
If the product of roots of \(10x^2-23x+p=0\) is \(\frac{2}{5}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (4)
B (10)
C \( \frac{1}{25}\)
D \( \frac{23}{5}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{10}\), so \(\frac{p}{10}=\frac{2}{5}\) gives (p=4). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (4). The product of roots is \(\frac{p}{10}\), so \(\frac{p}{10}=\frac{2}{5}\) gives (p=4). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{10}\) है, इसलिए \(\frac{p}{10}=\frac{2}{5}\) से (p=4) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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यदि ((x-6)(x-13)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-6)(x-13)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=6,13)
B (x=-6,-13)
C (x=0,19)
D (x=1,78)
Explanation opens after your attempt
Correct Answer
A. (x=6,13)
Step 1
Concept
((x-6)=0) or ((x-13)=0), so (x=6) or (x=13). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=6,13). ((x-6)=0) or ((x-13)=0), so (x=6) or (x=13). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-6)=0) या ((x-13)=0), इसलिए (x=6) या (x=13) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि \(9x^2-20x+p=0\) के मूलों का गुणनफल \(\frac{1}{3}\) है, तो (p) क्या होगा?
If the product of roots of \(9x^2-20x+p=0\) is \(\frac{1}{3}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (3)
B (9)
C \( \frac{1}{27}\)
D \( \frac{20}{3}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{9}\), so \(\frac{p}{9}=\frac{1}{3}\) gives (p=3). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (3). The product of roots is \(\frac{p}{9}\), so \(\frac{p}{9}=\frac{1}{3}\) gives (p=3). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{9}\) है, इसलिए \(\frac{p}{9}=\frac{1}{3}\) से (p=3) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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यदि ((x-5)(x-11)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-5)(x-11)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=5,11)
B (x=-5,-11)
C (x=0,16)
D (x=1,55)
Explanation opens after your attempt
Correct Answer
A. (x=5,11)
Step 1
Concept
((x-5)=0) or ((x-11)=0), so (x=5) or (x=11). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=5,11). ((x-5)=0) or ((x-11)=0), so (x=5) or (x=11). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-5)=0) या ((x-11)=0), इसलिए (x=5) या (x=11) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि \(7x^2-15x+p=0\) के मूलों का गुणनफल \(\frac{2}{7}\) है, तो (p) क्या होगा?
If the product of roots of \(7x^2-15x+p=0\) is \(\frac{2}{7}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (2)
B (7)
C \( \frac{2}{49}\)
D \( \frac{15}{7}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{7}\), so \(\frac{p}{7}=\frac{2}{7}\) gives (p=2). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (2). The product of roots is \(\frac{p}{7}\), so \(\frac{p}{7}=\frac{2}{7}\) gives (p=2). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{7}\) है, इसलिए \(\frac{p}{7}=\frac{2}{7}\) से (p=2) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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यदि ((x-4)(x-9)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-4)(x-9)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=4,9)
B (x=-4,-9)
C (x=0,13)
D (x=1,36)
Explanation opens after your attempt
Correct Answer
A. (x=4,9)
Step 1
Concept
((x-4)=0) or ((x-9)=0), so (x=4) or (x=9). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=4,9). ((x-4)=0) or ((x-9)=0), so (x=4) or (x=9). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-4)=0) या ((x-9)=0), इसलिए (x=4) या (x=9) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि \(6x^2-13x+p=0\) के मूलों का गुणनफल \(\frac{1}{2}\) है, तो (p) क्या होगा?
If the product of roots of \(6x^2-13x+p=0\) is \(\frac{1}{2}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (3)
B (6)
C \( \frac{1}{12}\)
D \( \frac{13}{2}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{6}\), so \(\frac{p}{6}=\frac{1}{2}\) gives (p=3). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (3). The product of roots is \(\frac{p}{6}\), so \(\frac{p}{6}=\frac{1}{2}\) gives (p=3). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{6}\) है, इसलिए \(\frac{p}{6}=\frac{1}{2}\) से (p=3) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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यदि ((x-3)(x-7)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-3)(x-7)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=3,7)
B (x=-3,-7)
C (x=0,10)
D (x=1,21)
Explanation opens after your attempt
Correct Answer
A. (x=3,7)
Step 1
Concept
((x-3)=0) or ((x-7)=0), so (x=3) or (x=7). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=3,7). ((x-3)=0) or ((x-7)=0), so (x=3) or (x=7). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-3)=0) या ((x-7)=0), इसलिए (x=3) या (x=7) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि \(5x^2-11x+p=0\) के मूलों का गुणनफल \(\frac{2}{5}\) है, तो (p) क्या होगा?
If the product of roots of \(5x^2-11x+p=0\) is \(\frac{2}{5}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (2)
B (5)
C \( \frac{2}{25}\)
D \( \frac{11}{5}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{5}\), so \(\frac{p}{5}=\frac{2}{5}\) gives (p=2). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (2). The product of roots is \(\frac{p}{5}\), so \(\frac{p}{5}=\frac{2}{5}\) gives (p=2). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{5}\) है, इसलिए \(\frac{p}{5}=\frac{2}{5}\) से (p=2) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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यदि \(4x^2-7x+p=0\) के मूलों का गुणनफल \(\frac{3}{2}\) है, तो (p) क्या होगा?
If the product of roots of \(4x^2-7x+p=0\) is \(\frac{3}{2}\), what is (p)?
#quadratic
#product-of-roots
#parameter
A (6)
B (3)
C \( \frac{3}{8}\)
D \( \frac{7}{2}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{p}{4}\), so \(\frac{p}{4}=\frac{3}{2}\) gives (p=6). In exams, use the product formula \(\frac{c}{a}\).
Step 2
Why this answer is correct
The correct answer is A. (6). The product of roots is \(\frac{p}{4}\), so \(\frac{p}{4}=\frac{3}{2}\) gives (p=6). In exams, use the product formula \(\frac{c}{a}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{p}{4}\) है, इसलिए \(\frac{p}{4}=\frac{3}{2}\) से (p=6) है। परीक्षा में गुणनफल का सूत्र \(\frac{c}{a}\) लगाएं।
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शून्य गुणनफल नियम से ((x-9)(x+2)=0) के मूल क्या हैं?
Using zero product rule, what are the roots of ((x-9)(x+2)=0)?
#quadratic
#zero-product-rule
#roots
A (x=9,-2)
B (x=-9,2)
C (x=9,2)
D (x=-9,-2)
Explanation opens after your attempt
Correct Answer
A. (x=9,-2)
Step 1
Concept
((x-9)=0) or ((x+2)=0), so (x=9) or (x=-2). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=9,-2). ((x-9)=0) or ((x+2)=0), so (x=9) or (x=-2). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-9)=0) या ((x+2)=0), इसलिए (x=9) या (x=-2) है। परीक्षा में हर गुणनखंड को अलग-अलग शून्य रखें।
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शून्य गुणनफल नियम से ((x-7)(x+1)=0) के मूल क्या हैं?
Using zero product rule, what are the roots of ((x-7)(x+1)=0)?
#quadratic
#zero-product-rule
#roots
A (x=7,-1)
B (x=-7,1)
C (x=7,1)
D (x=-7,-1)
Explanation opens after your attempt
Correct Answer
A. (x=7,-1)
Step 1
Concept
((x-7)=0) or ((x+1)=0), so (x=7) or (x=-1). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=7,-1). ((x-7)=0) or ((x+1)=0), so (x=7) or (x=-1). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-7)=0) या ((x+1)=0), इसलिए (x=7) या (x=-1) है। परीक्षा में हर गुणनखंड को अलग से शून्य रखें।
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शून्य गुणनफल नियम से (x(x-4)=0) के हल क्या हैं?
Using zero product rule, what are the solutions of (x(x-4)=0)?
#quadratic
#zero-product-rule
#factorisation
A (x=0,4)
B (x=0,-4)
C (x=4,8)
D (x=1,4)
Explanation opens after your attempt
Correct Answer
A. (x=0,4)
Step 1
Concept
If (x(x-4)=0), then (x=0) or (x-4=0). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=0,4). If (x(x-4)=0), then (x=0) or (x-4=0). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
यदि (x(x-4)=0), तो (x=0) या (x-4=0) होगा। परीक्षा में हर गुणनखंड को अलग-अलग शून्य के बराबर रखें।
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(x-2 -2(a-3)x+a-2 -16=0) की जड़ों का गुणनफल (0) हो, तो (a) के मान क्या हैं?
If the product of roots of (x-2 -2(a-3)x+a-2 -16=0) is (0), what are the values of (a)?
#quadratic-roots
#zero-product
#parameter
A (4) और (-4) / (4) and (-4)
B (3) और (-3) / (3) and (-3)
C (8) और (-8) / (8) and (-8)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
A. (4) और (-4) / (4) and (-4)
Step 1
Concept
The product of roots is \(a^2-16\). Setting it equal to (0) gives \(a^2=16\), so (a=4) or (a=-4).
Step 2
Why this answer is correct
The correct answer is A. (4) और (-4) / (4) and (-4). The product of roots is \(a^2-16\). Setting it equal to (0) gives \(a^2=16\), so (a=4) or (a=-4).
Step 3
Exam Tip
जड़ों का गुणनफल \(a^2-16\) है। इसे (0) रखने पर \(a^2=16\), इसलिए (a=4) या (a=-4)।
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यदि किसी द्विघात समीकरण की जड़ों का योग (7) और गुणनफल (10) है, तो समीकरण कौन-सा है?
If the sum of roots of a quadratic equation is (7) and the product is (10), which is the equation?
#quadratic-roots
#forming-equation
#sum-product
A \(x^2+7x+10=0\)
B \(x^2-10x+7=0\)
C \(x^2-7x+10=0\)
D \(x^2+10x-7=0\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-7x+10=0\)
Step 1
Concept
\(The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is C. (x^2-7x+10=0). The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(जड़ों का समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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(x-2 -2(a-2)x+a-2 -9=0) की जड़ों का गुणनफल (0) हो, तो (a) के मान क्या हैं?
If the product of the roots of (x-2 -2(a-2)x+a-2 -9=0) is (0), what are the values of (a)?
#quadratic-roots
#zero-product
#parameter
A (0) और (9) / (0) and (9)
B (3) और (-3) / (3) and (-3)
C (2) और (-2) / (2) and (-2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
B. (3) और (-3) / (3) and (-3)
Step 1
Concept
The product of roots is \(a^2-9\). Setting it equal to (0) gives \(a^2=9\), so (a=3) or (a=-3).
Step 2
Why this answer is correct
The correct answer is B. (3) और (-3) / (3) and (-3). The product of roots is \(a^2-9\). Setting it equal to (0) gives \(a^2=9\), so (a=3) or (a=-3).
Step 3
Exam Tip
जड़ों का गुणनफल \(a^2-9\) है। इसे (0) रखने पर \(a^2=9\), इसलिए (a=3) या (a=-3)।
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(x-2 -2(a+1)x+a-2 -1=0) की जड़ों का गुणनफल (0) हो, तो (a) का कौन-सा मान संभव है?
If the product of the roots of (x-2 -2(a+1)x+a-2 -1=0) is (0), which value of (a) is possible?
#quadratic-roots
#zero-product
#parameter
A (1) या (-1) / (1) or (-1)
B (0) केवल / (0) only
C (2) या (-2) / (2) or (-2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
A. (1) या (-1) / (1) or (-1)
Step 1
Concept
The product of roots is \(a^2-1\). Setting it equal to (0) gives \(a^2=1\), so (a=1) or (a=-1).
Step 2
Why this answer is correct
The correct answer is A. (1) या (-1) / (1) or (-1). The product of roots is \(a^2-1\). Setting it equal to (0) gives \(a^2=1\), so (a=1) or (a=-1).
Step 3
Exam Tip
जड़ों का गुणनफल \(a^2-1\) है। इसे (0) रखने पर \(a^2=1\), इसलिए (a=1) या (a=-1)।
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\(x^2+2x+c=0\) की जड़ें वास्तविक हैं और जड़ों का गुणनफल उनके योग से कम है, तो (c) पर सही शर्त क्या है?
For \(x^2+2x+c=0\), the roots are real and their product is less than their sum. What is the correct condition on (c)?
#quadratic-roots
#product-sum
#inequality
A (c<-2)
B \(c\le1\)
C (c> -2)
D \(-2<c\le1\)
Explanation opens after your attempt
Step 1
Concept
The sum is (-2) and the product is (c), so (c<-2) is needed. This condition also satisfies (D=4-4c>0).
Step 2
Why this answer is correct
The correct answer is A. (c<-2). The sum is (-2) and the product is (c), so (c<-2) is needed. This condition also satisfies (D=4-4c>0).
Step 3
Exam Tip
योग (-2) और गुणनफल (c) है, इसलिए (c<-2) चाहिए। यह शर्त (D=4-4c>0) को भी पूरा करती है।
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यदि \(x^2-10x+24=0\) के मूल \(\alpha\) और \(\beta\) हैं तो (\(\alpha-2\)) और (\(\beta-2\)) का गुणनफल क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-10x+24=0\), what is the product of (\(\alpha-2\)) and (\(\beta-2\))?
#roots
#transformed_expression
#product
A (8)
B (24)
C (14)
D (4)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=10\) and \(\alpha\beta=24\). (\(\alpha-2\)\(\beta-2\)=24-20+4=8).
Step 2
Why this answer is correct
The correct answer is A. (8). Here \(\alpha+\beta=10\) and \(\alpha\beta=24\). (\(\alpha-2\)\(\beta-2\)=24-20+4=8).
Step 3
Exam Tip
यहां \(\alpha+\beta=10\) और \(\alpha\beta=24\) है। (\(\alpha-2\)\(\beta-2\)=24-20+4=8) है।
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