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Question Expert Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 12

एक अज्ञात नमूना अम्ल से अभिक्रिया करके गैस देता है जो चूने के पानी को दूधिया करती है। नमूना किस वर्ग का हो सकता है?

An unknown sample reacts with acid to give a gas that turns lime water milky. Which class could the sample belong to?

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Correct Answer

A. कार्बोनेट या हाइड्रोजन कार्बोनेटCarbonate or hydrogen carbonate

Step 1

Concept

Milkiness of lime water indicates carbon dioxide.

Step 2

Why this answer is correct

Carbonates and hydrogen carbonates give carbon dioxide with acids.

Step 3

Exam Tip

So the sample may belong to these classes. चरण 1: चूने के पानी का दूधिया होना कार्बन डाइऑक्साइड का संकेत है। चरण 2: कार्बोनेट और हाइड्रोजन कार्बोनेट अम्ल से कार्बन डाइऑक्साइड देते हैं। चरण 3: इसलिए नमूना इन वर्गों में से हो सकता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 11

किसी नमूने को गर्म करने पर गैस निकली और बचे ठोस का विलयन क्षारीय था। यदि नमूना खाने का सोडा था तो बचा ठोस कौन सा होगा?

A sample is heated, gas is released, and the solution of the remaining solid is basic. If the sample was baking soda, what is the remaining solid?

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Correct Answer

B. सोडियम कार्बोनेटSodium carbonate

Step 1

Concept

Baking soda decomposes on heating.

Step 2

Why this answer is correct

It forms carbon dioxide, water, and sodium carbonate.

Step 3

Exam Tip

Sodium carbonate solution is basic. चरण 1: खाने का सोडा गरम करने पर अपघटित होता है। चरण 2: इससे कार्बन डाइऑक्साइड जल और सोडियम कार्बोनेट बनते हैं। चरण 3: सोडियम कार्बोनेट का विलयन क्षारीय होता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 10

एक नमूना चूने के पानी को दूधिया करने वाली गैस देता है। अधिक गैस देने पर दूधियापन समाप्त हो जाता है। इस पूरी प्रक्रिया में कौन से दो कैल्शियम यौगिक क्रम से बनते हैं?

A sample gives a gas that turns lime water milky. On passing excess gas, the milkiness disappears. Which two calcium compounds form in order?

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Correct Answer

A. कैल्शियम कार्बोनेट फिर कैल्शियम हाइड्रोजन कार्बोनेटCalcium carbonate then calcium hydrogen carbonate

Step 1

Concept

Carbon dioxide forms calcium carbonate with lime water, causing milkiness.

Step 2

Why this answer is correct

Excess carbon dioxide forms calcium hydrogen carbonate.

Step 3

Exam Tip

It is soluble, so the milkiness disappears. चरण 1: कार्बन डाइऑक्साइड चूने के पानी से कैल्शियम कार्बोनेट बनाती है जिससे दूधियापन आता है। चरण 2: अधिक कार्बन डाइऑक्साइड से कैल्शियम हाइड्रोजन कार्बोनेट बनता है। चरण 3: यह घुलनशील होता है इसलिए दूधियापन समाप्त होता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 10

एक नमूना अम्ल से कार्बन डाइऑक्साइड देता है और उसका जलीय विलयन लाल लिटमस को नीला करता है। सबसे संभावित पदार्थ कौन सा है?

A sample gives carbon dioxide with acid and its aqueous solution turns red litmus blue. Which substance is most likely?

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Correct Answer

A. सोडियम कार्बोनेटSodium carbonate

Step 1

Concept

Releasing carbon dioxide with acid indicates a carbonate.

Step 2

Why this answer is correct

Turning red litmus blue shows basic nature.

Step 3

Exam Tip

Sodium carbonate shows both properties. चरण 1: अम्ल से कार्बन डाइऑक्साइड निकलना कार्बोनेट की पहचान है। चरण 2: लाल लिटमस का नीला होना क्षारीय प्रकृति बताता है। चरण 3: सोडियम कार्बोनेट दोनों गुण दिखाता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 9

किसी कार्बोनेट नमूने में अम्ल मिलाने पर निकली गैस को अधिक समय तक चूने के पानी में भेजा गया। अंतिम घोल फिर साफ क्यों हो सकता है?

A gas released from a carbonate sample with acid is passed into lime water for a long time. Why can the final solution become clear again?

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Correct Answer

B. अधिक गैस घुलनशील कैल्शियम हाइड्रोजन कार्बोनेट बनाती हैExcess gas forms soluble calcium hydrogen carbonate

Step 1

Concept

Carbonates release carbon dioxide with acids.

Step 2

Why this answer is correct

The gas first forms calcium carbonate and causes milkiness.

Step 3

Exam Tip

Excess gas forms soluble calcium hydrogen carbonate, making the solution clear. चरण 1: कार्बोनेट अम्ल से कार्बन डाइऑक्साइड गैस देते हैं। चरण 2: पहले यह गैस कैल्शियम कार्बोनेट बनाकर दूधियापन देती है। चरण 3: अधिक गैस घुलनशील कैल्शियम हाइड्रोजन कार्बोनेट बनाती है जिससे घोल साफ दिख सकता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 8

किसी नमूने को गरम करने पर जल की बूंदें दिखीं और रंग बदल गया। यह किस प्रकार के लवण की पहचान हो सकती है?

On heating a sample, water droplets appear and its colour changes. This may identify what kind of salt?

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Correct Answer

A. क्रिस्टलीकरण जल वाला लवणSalt containing water of crystallisation

Step 1

Concept

Some salts contain fixed water in their crystals.

Step 2

Why this answer is correct

This water can come out on heating.

Step 3

Exam Tip

Loss of water can change colour or appearance. चरण 1: कुछ लवण अपने क्रिस्टल में निश्चित जल रखते हैं। चरण 2: गरम करने पर यह जल बाहर निकल सकता है। चरण 3: जल निकलने से रंग या रूप बदल सकता है।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 8

एक नमूना लाल लिटमस को नीला करता है पर अम्ल मिलाने पर कार्बन डाइऑक्साइड नहीं देता। वह क्या हो सकता है?

A sample turns red litmus blue but does not give carbon dioxide when acid is added. What could it be?

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Correct Answer

A. सोडियम हाइड्रॉक्साइडSodium hydroxide

Step 1

Concept

Turning red litmus blue shows basic nature.

Step 2

Why this answer is correct

Carbonates and hydrogen carbonates release carbon dioxide with acids.

Step 3

Exam Tip

Sodium hydroxide is a base but does not release carbon dioxide with acid. चरण 1: लाल लिटमस को नीला करना क्षारीय प्रकृति बताता है। चरण 2: कार्बोनेट और हाइड्रोजन कार्बोनेट अम्ल से कार्बन डाइऑक्साइड देते हैं। चरण 3: सोडियम हाइड्रॉक्साइड क्षार है लेकिन अम्ल से कार्बन डाइऑक्साइड नहीं देता।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 7

किसी नमूने में कार्बोनेट आयन की उपस्थिति की पुष्टि के लिए सबसे उपयुक्त क्रम कौन सा है?

Which is the most suitable sequence to confirm the presence of carbonate ions in a sample?

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Correct Answer

A. पतला अम्ल मिलाएँ और गैस को चूने के पानी में भेजेंAdd dilute acid and pass the gas into lime water

Step 1

Concept

Carbonates react with acids to produce carbon dioxide.

Step 2

Why this answer is correct

Carbon dioxide turns lime water milky.

Step 3

Exam Tip

Therefore this sequence confirms carbonate ions. चरण 1: कार्बोनेट अम्ल से क्रिया करके कार्बन डाइऑक्साइड देते हैं। चरण 2: कार्बन डाइऑक्साइड चूने के पानी को दूधिया करती है। चरण 3: इसलिए यह क्रम कार्बोनेट की पहचान के लिए उचित है।

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Question Expert Science Chemical Substances – Nature and Behaviour Chemical Reactions and Equations Class 10 Level 2

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?

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Correct Answer

A. कैल्शियम ऑक्साइड और कार्बन डाइऑक्साइडCalcium 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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Question Hard Science Chemical Substances – Nature and Behaviour Chemical Reactions and Equations Class 10 Level 3

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?

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Correct Answer

A. नीचे तीर अवक्षेप और ऊपर तीर गैस दिखाता हैDownward 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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Question Hard Science Chemical Substances – Nature and Behaviour Chemical Reactions and Equations Class 10 Level 2

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?

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Correct Answer

A. ऊष्माक्षेपी संयोजनExothermic 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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Question Expert Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 5

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?

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Correct Answer

D. हाइलाइट रूप संरचना पर भारी पड़ रहे हैंHighlights 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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Question Expert Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 5

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?

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Correct Answer

B. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइटClean 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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Question Expert Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 2

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?

Explanation opens after your attempt
Correct Answer

A. हाइलाइट रूप संरचना पर भारी पड़ रहे हैंHighlights 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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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 6

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?

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Correct Answer

A. साफ नकारात्मक स्थान नियंत्रित रंग और स्पष्ट हाइलाइटClean 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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Question Medium Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 8

किसी उत्पाद चित्र में सामग्री पहचानने के लिए बनावट क्यों जरूरी है?

Why is texture important to identify material in a product drawing?

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Correct Answer

D. यह बताती है कि वस्तु लकड़ी धातु कपड़ा या कांच जैसी हैIt 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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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?

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Correct Answer

A. (1)

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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(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)?

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Correct Answer

B. (0)

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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)?

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Correct Answer

A. कोई भी अशून्य वास्तविक संख्याAny 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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)?

Explanation opens after your attempt
Correct Answer

A. (2)

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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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?

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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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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?

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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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(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)?

Explanation opens after your attempt
Correct Answer

B. (0)

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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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

द्विघात बहुपद \(2x^2-7x+3\) के शून्यकों का गुणनफल क्या है?

What is the product of the zeroes of the quadratic polynomial \(2x^2-7x+3\)?

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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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(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)?

Explanation opens after your attempt
Correct Answer

A. (-12)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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)?

Explanation opens after your attempt
Correct Answer

B. (15)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (23)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (18)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (13)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

C. (13)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

C. (12)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

A. (9)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

C. (12)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

C. (44)

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

C. (51)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

D. (39)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

D. (45)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

C. (28)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

C. (31)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

A. (18)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

A. (24)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

A. (21)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

A. (17)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (21)

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

C. (24)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

A. (12)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

A. (25)

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

A. (9)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

A. (19)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

D. (37)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (16)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

D. (32)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

A. (18)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

D. (27)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (20)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

B. (17)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

C. (16)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

C. (17)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

B. (12)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

B. (20)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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?

Explanation opens after your attempt
Correct Answer

B. (12)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

C. (17)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (12)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (13)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (10)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

A. (9)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

C. (12)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (10)

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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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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?

Explanation opens after your attempt
Correct Answer

B. (8)

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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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

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)?

Explanation opens after your attempt
Correct Answer

A. (4)

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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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

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?

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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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

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)?

Explanation opens after your attempt
Correct Answer

A. (3)

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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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

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?

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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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

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)?

Explanation opens after your attempt
Correct Answer

A. (2)

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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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

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?

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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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

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)?

Explanation opens after your attempt
Correct Answer

A. (3)

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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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

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?

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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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

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)?

Explanation opens after your attempt
Correct Answer

A. (2)

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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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

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)?

Explanation opens after your attempt
Correct Answer

A. (6)

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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Question Easy Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

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)?

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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Question Easy Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

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)?

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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Question Easy Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

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)?

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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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

(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)?

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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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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?

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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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

(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)?

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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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

(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?

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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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

\(x^2+2x+c=0\) 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)?

Explanation opens after your attempt
Correct Answer

A. (c<-2)

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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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

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 (\(\beta-2\))?

Explanation opens after your attempt
Correct Answer

A. (8)

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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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि मूलों का योग (6) और उनके वर्गों का योग (52) है तो मूलों का गुणनफल क्या होगा?

If the sum of roots is (6) and the sum of their squares is (52), what is the product of roots?

Explanation opens after your attempt
Correct Answer

A. (-8)

Step 1

Concept

(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). From \(52=36-2\alpha\beta\), we get \(\alpha\beta=-8\).

Step 2

Why this answer is correct

The correct answer is A. (-8). (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). From \(52=36-2\alpha\beta\), we get \(\alpha\beta=-8\).

Step 3

Exam Tip

(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) है। \(52=36-2\alpha\beta\) से \(\alpha\beta=-8\) मिलता है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-6x-16=0\) के मूलों को (2) घटाने पर नए मूलों का गुणनफल क्या होगा?

If each root of \(x^2-6x-16=0\) is decreased by (2), what is the product of the new roots?

Explanation opens after your attempt
Correct Answer

A. (-24)

Step 1

Concept

The old roots are (8) and (-2). The new roots are (6) and (-4), so the product is (-24).

Step 2

Why this answer is correct

The correct answer is A. (-24). The old roots are (8) and (-2). The new roots are (6) and (-4), so the product is (-24).

Step 3

Exam Tip

पुराने मूल (8) और (-2) हैं। नए मूल (6) और (-4) होंगे इसलिए गुणनफल (-24) है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2-8x+15=0\) के मूल \(\alpha\) और \(\beta\) हैं तो (\(\alpha-1\)) और (\(\beta-1\)) का गुणनफल क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-8x+15=0\), what is the product of (\(\alpha-1\)) and (\(\beta-1\))?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). (\(\alpha-1\)\(\beta-1\)=15-8+1=8).

Step 2

Why this answer is correct

The correct answer is A. (8). Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). (\(\alpha-1\)\(\beta-1\)=15-8+1=8).

Step 3

Exam Tip

यहां \(\alpha+\beta=8\) और \(\alpha\beta=15\) है। (\(\alpha-1\)\(\beta-1\)=15-8+1=8) है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि मूलों का योग (4) और उनके वर्गों का योग (20) है तो मूलों का गुणनफल क्या होगा?

If the sum of roots is (4) and the sum of their squares is (20), what is the product of roots?

Explanation opens after your attempt
Correct Answer

A. (-2)

Step 1

Concept

(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). From \(20=16-2\alpha\beta\), we get \(\alpha\beta=-2\).

Step 2

Why this answer is correct

The correct answer is A. (-2). (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). From \(20=16-2\alpha\beta\), we get \(\alpha\beta=-2\).

Step 3

Exam Tip

(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) है। \(20=16-2\alpha\beta\) से \(\alpha\beta=-2\) मिलता है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

समीकरण \(x^2-4x-12=0\) के मूलों को (1) घटाने पर नए मूलों का गुणनफल क्या होगा?

If each root of \(x^2-4x-12=0\) is decreased by (1), what is the product of the new roots?

Explanation opens after your attempt
Correct Answer

A. (-15)

Step 1

Concept

The old roots are (6) and (-2). The new roots are (5) and (-3), so the product is (-15).

Step 2

Why this answer is correct

The correct answer is A. (-15). The old roots are (6) and (-2). The new roots are (5) and (-3), so the product is (-15).

Step 3

Exam Tip

पुराने मूल (6) और (-2) हैं। नए मूल (5) और (-3) होंगे इसलिए गुणनफल (-15) है।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि किसी द्विघात समीकरण के मूल (r) और (r) हैं तो उनके गुणनफल का मान क्या होगा?

If the roots of a quadratic equation are (r) and (r), what will be their product?

Explanation opens after your attempt
Correct Answer

C. \(r^2\)

Step 1

Concept

The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).

Step 2

Why this answer is correct

The correct answer is C. \(r^2\). The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).

Step 3

Exam Tip

(r) और (r) का गुणनफल \(r^2\) होता है। बराबर मूलों में योग (2r) और गुणनफल \(r^2\) याद रखें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि एक मूल (6) है और मूलों का गुणनफल (48) है तो दूसरा मूल क्या होगा?

If one root is (6) and the product of roots is (48), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (8)

Step 1

Concept

The other root is \(\frac{48}{6}=8\). Divide the product by the given root.

Step 2

Why this answer is correct

The correct answer is B. (8). The other root is \(\frac{48}{6}=8\). Divide the product by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{48}{6}=8\) होगा। गुणनफल को दिए हुए मूल से भाग करें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि एक मूल (5) है और मूलों का गुणनफल (35) है तो दूसरा मूल क्या होगा?

If one root is (5) and the product of roots is (35), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 2

Why this answer is correct

The correct answer is B. (7). The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि एक मूल (3) है और मूलों का गुणनफल (12) है तो दूसरा मूल क्या होगा?

If one root is (3) and the product of roots is (12) then what is the other root?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.

Step 2

Why this answer is correct

The correct answer is B. (4). The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{12}{3}=4\) होगा। गुणनफल वाले प्रश्न में दिए मूल से भाग दें।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?

Which quadratic equation has sum of roots (0) and product (-169)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-169=0\)

Step 1

Concept

\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2-169=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-169) रखने पर (x^2-169=0) मिलता है\)।

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