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ओल्मेक विशाल सिर किस प्रकार के सामाजिक संकेत दे सकते हैं?

What kind of social signs may Olmec colossal heads give?

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Correct Answer

A. नेतृत्व और सत्ता के प्रतीकSymbols of leadership and power

Step 1

Concept

Olmec colossal heads are linked with symbols of leadership or power. Connect them with Mesoamerican art in exams.

Step 2

Why this answer is correct

The correct answer is A. नेतृत्व और सत्ता के प्रतीक / Symbols of leadership and power. Olmec colossal heads are linked with symbols of leadership or power. Connect them with Mesoamerican art in exams.

Step 3

Exam Tip

ओल्मेक विशाल सिर नेतृत्व या सत्ता प्रतीकों से जोड़े जाते हैं। परीक्षा में इन्हें मेसोअमेरिकी कला से जोड़ें।

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मेसोपोटामिया में कीलाक्षर चिन्ह किस उपकरण से मिट्टी पर बनाए जाते थे?

In Mesopotamia cuneiform signs were made on clay with what tool?

Explanation opens after your attempt
Correct Answer

B. नुकीली लेखनीPointed stylus

Step 1

Concept

Cuneiform signs were made on clay tablets with a pointed stylus. Link cuneiform with administrative records in exams.

Step 2

Why this answer is correct

The correct answer is B. नुकीली लेखनी / Pointed stylus. Cuneiform signs were made on clay tablets with a pointed stylus. Link cuneiform with administrative records in exams.

Step 3

Exam Tip

कीलाक्षर चिन्ह नुकीली लेखनी से मिट्टी की तख्तियों पर बनाए जाते थे। परीक्षा में कीलाक्षर को प्रशासनिक रिकॉर्ड से जोड़ें।

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सिंधु सभ्यता के लोग लिखने के लिए किस प्रकार के चिन्हों का उपयोग करते थे?

What type of signs did the Indus people use for writing?

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Correct Answer

A. चित्रात्मक चिन्हPictographic signs

Step 1

Concept

The Indus script contains small pictographic signs. For exams remember that it has not been fully deciphered.

Step 2

Why this answer is correct

The correct answer is A. चित्रात्मक चिन्ह / Pictographic signs. The Indus script contains small pictographic signs. For exams remember that it has not been fully deciphered.

Step 3

Exam Tip

सिंधु लिपि में छोटे चित्रात्मक चिन्ह मिलते हैं। परीक्षा में यह याद रखें कि यह लिपि अभी पूरी तरह पढ़ी नहीं गई है।

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यदि (x-2+(m-5)x+9=0) की जड़ें बराबर पर विपरीत चिह्न वाली नहीं हैं और समान हैं, तो (m) के मान क्या हैं?

If (x-2+(m-5)x+9=0) has equal roots that are not of opposite signs, what are the values of (m)?

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Correct Answer

A. (11) और (-1)(11) and (-1)

Step 1

Concept

For equal roots, ((m-5)2-36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).

Step 2

Why this answer is correct

The correct answer is A. (11) और (-1) / (11) and (-1). For equal roots, ((m-5)2-36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).

Step 3

Exam Tip

समान जड़ों के लिए ((m-5)2-36=0) होगा। इसलिए \(m-5=\pm6\), अतः (m=11) या (m=-1)।

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समीकरण \(x^2+13x+42=0\) के दोनों मूलों के चिन्ह कैसे होंगे?

What will be the signs of both roots of \(x^2+13x+42=0\)?

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Correct Answer

A. दोनों ऋणात्मकBoth negative

Step 1

Concept

The roots are (-6) and (-7) because ((x+6)(x+7)=0). When the sum is negative and product is positive, both roots are negative.

Step 2

Why this answer is correct

The correct answer is A. दोनों ऋणात्मक / Both negative. The roots are (-6) and (-7) because ((x+6)(x+7)=0). When the sum is negative and product is positive, both roots are negative.

Step 3

Exam Tip

मूल (-6) और (-7) हैं क्योंकि ((x+6)(x+7)=0)। योग ऋणात्मक और गुणनफल धनात्मक होने पर दोनों मूल ऋणात्मक होते हैं।

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समीकरण \(x^2+9x+18=0\) के दोनों मूलों के चिन्ह कैसे होंगे?

What will be the signs of both roots of \(x^2+9x+18=0\)?

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Correct Answer

A. दोनों ऋणात्मकBoth negative

Step 1

Concept

The roots are (-3) and (-6) because ((x+3)(x+6)=0). When the sum is negative and product is positive, both roots are negative.

Step 2

Why this answer is correct

The correct answer is A. दोनों ऋणात्मक / Both negative. The roots are (-3) and (-6) because ((x+3)(x+6)=0). When the sum is negative and product is positive, both roots are negative.

Step 3

Exam Tip

मूल (-3) और (-6) हैं क्योंकि ((x+3)(x+6)=0)। योग ऋणात्मक और गुणनफल धनात्मक होने पर दोनों मूल ऋणात्मक होते हैं।

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समीकरण \(x^2+7x+10=0\) के दोनों मूलों के चिन्ह कैसे होंगे?

What will be the signs of both roots of \(x^2+7x+10=0\)?

Explanation opens after your attempt
Correct Answer

A. दोनों ऋणात्मकBoth negative

Step 1

Concept

The roots are (-5) and (-2) because ((x+5)(x+2)=0). When the sum is negative and product is positive, both roots are negative.

Step 2

Why this answer is correct

The correct answer is A. दोनों ऋणात्मक / Both negative. The roots are (-5) and (-2) because ((x+5)(x+2)=0). When the sum is negative and product is positive, both roots are negative.

Step 3

Exam Tip

मूल (-5) और (-2) हैं क्योंकि ((x+5)(x+2)=0)। योग ऋणात्मक और गुणनफल धनात्मक होने पर दोनों मूल ऋणात्मक होते हैं।

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यदि किसी द्विघात समीकरण के वास्तविक मूलों का गुणनफल ऋणात्मक है तो मूलों के चिन्ह कैसे होंगे?

If the product of real roots of a quadratic equation is negative then how are the signs of the roots?

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Correct Answer

C. एक धनात्मक और एक ऋणात्मकOne positive and one negative

Step 1

Concept

A negative product occurs when one root is positive and the other is negative. \(\alpha\beta<0\) is a quick sign check.

Step 2

Why this answer is correct

The correct answer is C. एक धनात्मक और एक ऋणात्मक / One positive and one negative. A negative product occurs when one root is positive and the other is negative. \(\alpha\beta<0\) is a quick sign check.

Step 3

Exam Tip

ऋणात्मक गुणनफल तभी मिलता है जब एक मूल धनात्मक और दूसरा ऋणात्मक हो। \(\alpha\beta<0\) संकेतों की जांच का छोटा संकेत है।

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चट्टानों की गहरी परतों में पाए गए जीवाश्म सामान्यतः किसके संकेत माने जाते हैं?

Fossils found in deeper layers of rocks are generally considered signs of what?

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Correct Answer

A. अधिक पुराने जीवों केOlder organisms

Step 1

Concept

Rock layers form over time.

Step 2

Why this answer is correct

Lower layers are generally older than upper layers.

Step 3

Exam Tip

Therefore fossils in deeper layers are considered older. चरण 1: चट्टानों की परतें समय के साथ बनती हैं। चरण 2: नीचे की परतें सामान्यतः ऊपर की परतों से पुरानी होती हैं। चरण 3: इसलिए गहरी परतों के जीवाश्म अधिक पुराने माने जाते हैं।

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चित्र आधारित प्रश्न में जर्मेनिया की पहचान करने के लिए कौन सा समूह सबसे सही है?

Which group of signs is most correct for identifying Germania in a picture-based question?

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A. बलूत पत्ते तलवार और काला लाल सुनहरा ध्वजOak leaves sword and black red gold flag

Step 1

Concept

Germania was the female figure of German nationalism.

Step 2

Why this answer is correct

Oak leaves sword and black red gold flag are signs linked with her.

Step 3

Exam Tip

Use such signs to identify the image correctly. चरण 1: जर्मेनिया जर्मन राष्ट्रवाद की नारी आकृति थी। चरण 2: बलूत पत्ते तलवार और काला लाल सुनहरा ध्वज उससे जुड़े संकेत हैं। चरण 3: ऐसे संकेतों को देखकर चित्र की सही पहचान करें।

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जर्मेनिया की छवि में राष्ट्रीय गौरव के साथ सैन्य संकेत क्यों मिलते हैं?

Why do military signs appear along with national pride in Germania's image?

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Correct Answer

A. क्योंकि राष्ट्र की रक्षा और एकीकरण संघर्ष से जुड़े थेBecause defence and unification of the nation were linked with struggle

Step 1

Concept

German nationalism demanded unity.

Step 2

Why this answer is correct

The idea of struggle for unity and defence was also connected with it.

Step 3

Exam Tip

Therefore signs like the sword appear with national pride. चरण 1: जर्मन राष्ट्रवाद में एकता की मांग थी। चरण 2: एकता और रक्षा के लिए संघर्ष की कल्पना भी जुड़ी थी। चरण 3: इसलिए तलवार जैसे संकेत राष्ट्रीय गौरव के साथ दिखाई देते हैं।

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मैरिएन की आंखों पर पट्टी नहीं बल्कि लाल टोपी और स्वतंत्रता से जुड़े चिह्न दिखाए जाते थे। इससे क्या संकेत मिलता है?

Marianne was shown with the red cap and signs of liberty rather than a blindfold. What does this indicate?

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Correct Answer

A. वह गणराज्य और स्वतंत्र नागरिकता की प्रतीक थीShe symbolised republic and free citizenship

Step 1

Concept

Every symbol has its own context.

Step 2

Why this answer is correct

Marianne's signs were linked with the French Revolution and the Republic.

Step 3

Exam Tip

So see her as a national figure of liberty not as a goddess of justice. चरण 1: हर प्रतीक का अपना संदर्भ होता है। चरण 2: मैरिएन के चिह्न फ्रांसीसी क्रांति और गणराज्य से जुड़े थे। चरण 3: इसलिए उसे न्याय की देवी नहीं बल्कि स्वतंत्रता की राष्ट्रीय आकृति समझें।

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फ्रांसीसी क्रांति में नए झंडे और चिन्हों का प्रयोग किस बात का संकेत था?

The use of new flags and signs in the French Revolution indicated what?

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Correct Answer

A. नई राष्ट्रीय पहचानNew national identity

Step 1

Concept

Flags and signs represent identity.

Step 2

Why this answer is correct

New symbols gave the message of a new nation and citizen unity.

Step 3

Exam Tip

In symbol-based questions remember the word identity. चरण 1: झंडे और चिन्ह पहचान को दर्शाते हैं। चरण 2: नए प्रतीकों ने नए राष्ट्र और नागरिक एकता का संदेश दिया। चरण 3: प्रतीक आधारित प्रश्नों में पहचान शब्द याद रखें।

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किस उदाहरण में रासायनिक अभिक्रिया का संकेत गैस और रंग दोनों से मिलता है?

In which example are gas and colour both signs of a chemical reaction?

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A. लेड नाइट्रेट को गर्म करनाHeating lead nitrate

Step 1

Concept

Heating lead nitrate produces brown fumes.

Step 2

Why this answer is correct

Brown fumes show gas formation and colour change.

Step 3

Exam Tip

This is an important example of thermal decomposition. चरण 1: लेड नाइट्रेट को गर्म करने पर भूरे धुएँ निकलते हैं। चरण 2: भूरे धुएँ गैस बनने और रंग परिवर्तन दोनों दिखाते हैं। चरण 3: यह ऊष्मीय वियोजन का महत्वपूर्ण उदाहरण है।

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नीचे में से कौन सा संकेत हमेशा रासायनिक अभिक्रिया का अकेला निश्चित प्रमाण नहीं है?

Which of the following signs alone is not always definite proof of a chemical reaction?

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Correct Answer

A. रंग बदलनाColour change

Step 1

Concept

Colour change can be a sign of reaction.

Step 2

Why this answer is correct

But final conclusion should not be based only on colour.

Step 3

Exam Tip

Other signs and formation of a new substance should also be checked. चरण 1: रंग बदलना अभिक्रिया का संकेत हो सकता है। चरण 2: लेकिन केवल रंग देखकर अंतिम निर्णय नहीं लेना चाहिए। चरण 3: अन्य संकेतों और नए पदार्थ बनने को भी जांचना चाहिए।

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समीकरणों (9x-4y=11) और (3x+4y=25) को हल करने पर (x-y) का मान क्या होगा?

Solving (9x-4y=11) and (3x+4y=25), what is the value of (x-y)?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

Adding gives (12x=36), so (x=3) and (y=4). Hence (x-y=-1); check signs before marking.

Step 2

Why this answer is correct

The correct answer is B. (1). Adding gives (12x=36), so (x=3) and (y=4). Hence (x-y=-1); check signs before marking.

Step 3

Exam Tip

जोड़ने पर (12x=36), इसलिए (x=3) और (y=4)। अतः (x-y=-1), चिन्हों की जांच करें।

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समीकरण (y=15-2x) और (x-y=6) का हल चुनें।

Choose the solution of (y=15-2x) and (x-y=6).

Explanation opens after your attempt
Correct Answer

D. ( (7,1) )

Step 1

Concept

Putting (15-2x) in place of (y) gives (x-(15-2x)=6), so (x=7) and (y=1). Always use brackets with a minus sign.

Step 2

Why this answer is correct

The correct answer is D. ( (7,1) ). Putting (15-2x) in place of (y) gives (x-(15-2x)=6), so (x=7) and (y=1). Always use brackets with a minus sign.

Step 3

Exam Tip

(15-2x) को (y) की जगह रखने पर (x-(15-2x)=6), इसलिए (x=7) और (y=1)। ऋण के साथ कोष्ठक जरूर लगाएँ।

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किस बहुपद के शून्यक (-1) और (4) हैं?

Which polynomial has zeroes (-1) and (4)?

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Correct Answer

A. \(x^2-3x-4\)

Step 1

Concept

The polynomial is ((x+1)(x-4)=x-2-3x-4). Be careful with signs while forming factors.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-4\). The polynomial is ((x+1)(x-4)=x-2-3x-4). Be careful with signs while forming factors.

Step 3

Exam Tip

शून्यकों से बहुपद ((x+1)(x-4)=x-2-3x-4) बनता है। चिन्ह बदलते समय सावधानी रखें।

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यदि (p(x)=2x-3-5x-2+mx+6) को (x+1) से भाग देने पर शेष (0) है, तो (m) क्या है?

If (p(x)=2x-3-5x-2+mx+6) leaves remainder (0) when divided by (x+1), what is (m)?

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Correct Answer

A. (-13)

Step 1

Concept

By remainder theorem (p(-1)=0), so (-2-5-m+6=0), giving (-1-m=0) and (m=-1). Always check signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (-13). By remainder theorem (p(-1)=0), so (-2-5-m+6=0), giving (-1-m=0) and (m=-1). Always check signs carefully.

Step 3

Exam Tip

शेष प्रमेय से (p(-1)=0), इसलिए (-2-5-m+6=0) और (m=-1) नहीं, सही समीकरण (-1-m=0) देता है (m=-1)।

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(p(x)=3x-3-7x-2+2x-11) में \(x^2\) के गुणांक और अचर पद का योग क्या है?

In (p(x)=3x-3-7x-2+2x-11), what is the sum of the coefficient of \(x^2\) and the constant term?

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Correct Answer

A. (-18)

Step 1

Concept

The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.

Step 2

Why this answer is correct

The correct answer is A. (-18). The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.

Step 3

Exam Tip

\(x^2\) का गुणांक (-7) और अचर पद (-11) है, इसलिए योग (-18) है। संकेत सहित जोड़ना न भूलें।

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कौन सा विकल्प \(x^2-5x+6\) को पदों के सही समूह के रूप में दिखाता है?

Which option shows the correct group of terms of \(x^2-5x+6\)?

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Correct Answer

A. \(x^2\), (-5x), (6)

Step 1

Concept

The terms with signs are \(x^2\), (-5x), and (6). Keep the negative sign with the term while identifying terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2\), (-5x), (6). The terms with signs are \(x^2\), (-5x), and (6). Keep the negative sign with the term while identifying terms.

Step 3

Exam Tip

चिह्न सहित पद \(x^2\), (-5x) और (6) हैं। पद पहचानते समय ऋण चिह्न साथ रखें।

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(\left\(-\dfrac{1}{2}\right\)^{-3}) का मान क्या होगा?

What is the value of (\left\(-\dfrac{1}{2}\right\)^{-3})?

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Correct Answer

A. (,-8,)

Step 1

Concept

A negative exponent inverts the fraction, so (\left\(-\dfrac{1}{2}\right\)^{-3}=(-2)3=-8). In exams, keep the sign of a negative base according to the power.

Step 2

Why this answer is correct

The correct answer is A. (,-8,). A negative exponent inverts the fraction, so (\left\(-\dfrac{1}{2}\right\)^{-3}=(-2)3=-8). In exams, keep the sign of a negative base according to the power.

Step 3

Exam Tip

ऋणात्मक घात से भिन्न उलटती है, इसलिए (\left\(-\dfrac{1}{2}\right\)^{-3}=(-2)3=-8)। परीक्षा में negative base का sign power के अनुसार रखें।

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((-2)4-(-2)3) का मान क्या है?

What is the value of ((-2)4-(-2)3)?

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Correct Answer

A. (,24,)

Step 1

Concept

((-2)4=16) and ((-2)3=-8), so (16-(-8)=24). In exams, odd and even powers have different signs.

Step 2

Why this answer is correct

The correct answer is A. (,24,). ((-2)4=16) and ((-2)3=-8), so (16-(-8)=24). In exams, odd and even powers have different signs.

Step 3

Exam Tip

((-2)4=16) और ((-2)3=-8), इसलिए (16-(-8)=24)। परीक्षा में odd और even powers के sign अलग होते हैं।

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((x-7)(x+3)) का विस्तार क्या है?

What is the expansion of ((x-7)(x+3))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-21\)

Step 1

Concept

Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-21\). Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.

Step 3

Exam Tip

गुणा करने पर \(x^2+3x-7x-21=x^2-4x-21\) है। चिह्नों पर ध्यान दें।

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((x-5)(x+2)) का विस्तार क्या है?

What is the expansion of ((x-5)(x+2))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x-10\)

Step 1

Concept

Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-10\). Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.

Step 3

Exam Tip

गुणा करने पर \(x^2+2x-5x-10=x^2-3x-10\) है। चिह्नों पर ध्यान दें।

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((x-4)(x+1)) का विस्तार क्या है?

What is the expansion of ((x-4)(x+1))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x-4\)

Step 1

Concept

Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-4\). Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.

Step 3

Exam Tip

गुणा करने पर \(x^2+x-4x-4=x^2-3x-4\) मिलता है। चिह्नों पर विशेष ध्यान दें।

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द्विघात समीकरण \(7x^2+2x-3=0\) के मूलों की प्रकृति क्या होगी?

What will be the nature of roots of \(7x^2+2x-3=0\)?

Explanation opens after your attempt
Correct Answer

A. दो भिन्न वास्तविक मूलTwo distinct real roots

Step 1

Concept

Here (D=22-4\cdot7\cdot(-3)=88), so (D>0). In exams, when (c) is negative, (D) can often become positive.

Step 2

Why this answer is correct

The correct answer is A. दो भिन्न वास्तविक मूल / Two distinct real roots. Here (D=22-4\cdot7\cdot(-3)=88), so (D>0). In exams, when (c) is negative, (D) can often become positive.

Step 3

Exam Tip

यहां (D=22-4\cdot7\cdot(-3)=88), इसलिए (D>0)। परीक्षा में (c) ऋणात्मक हो तो (D) अक्सर धनात्मक हो सकता है।

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\(x^2-20x+96=0\) में कौनसी संख्या जोड़ी मध्य पद बनाने में मदद करेगी?

Which number pair helps in making the middle term in \(x^2-20x+96=0\)?

Explanation opens after your attempt
Correct Answer

A. (-8) और (-12)(-8) and (-12)

Step 1

Concept

(-8+(-12)=-20) and ((-8)(-12)=96), so this pair is correct. In exams, when (c) is positive and (b) is negative, both numbers are negative.

Step 2

Why this answer is correct

The correct answer is A. (-8) और (-12) / (-8) and (-12). (-8+(-12)=-20) and ((-8)(-12)=96), so this pair is correct. In exams, when (c) is positive and (b) is negative, both numbers are negative.

Step 3

Exam Tip

(-8+(-12)=-20) और ((-8)(-12)=96), इसलिए यह जोड़ी सही है। परीक्षा में (c) धनात्मक और (b) ऋणात्मक हो तो दोनों संख्याएं ऋणात्मक होती हैं।

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\(x^2-4x-32=0\) के लिए सही कथन कौनसा है?

Which statement is correct for \(x^2-4x-32=0\)?

Explanation opens after your attempt
Correct Answer

A. मूल (8) और (-4) हैंThe roots are (8) and (-4)

Step 1

Concept

(x-2-4x-32=(x-8)(x+4)), so the roots are (8) and (-4). In exams, the larger value decides the sign of the middle term.

Step 2

Why this answer is correct

The correct answer is A. मूल (8) और (-4) हैं / The roots are (8) and (-4). (x-2-4x-32=(x-8)(x+4)), so the roots are (8) and (-4). In exams, the larger value decides the sign of the middle term.

Step 3

Exam Tip

(x-2-4x-32=(x-8)(x+4)), इसलिए मूल (8) और (-4) हैं। परीक्षा में बड़ा मान मध्य पद का चिन्ह तय करता है।

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\(4x^2-19x-5=0\) के मूल क्या हैं?

What are the roots of \(4x^2-19x-5=0\)?

Explanation opens after your attempt
Correct Answer

A. \(x=5,-\frac{1}{4}\)

Step 1

Concept

(4x-2-19x-5=(4x+1)(x-5)), so the roots are (5) and \(-\frac{1}{4}\). In exams, reverse the signs from linear factors to write roots.

Step 2

Why this answer is correct

The correct answer is A. \(x=5,-\frac{1}{4}\). (4x-2-19x-5=(4x+1)(x-5)), so the roots are (5) and \(-\frac{1}{4}\). In exams, reverse the signs from linear factors to write roots.

Step 3

Exam Tip

(4x-2-19x-5=(4x+1)(x-5)), इसलिए मूल (5) और \(-\frac{1}{4}\) हैं। परीक्षा में रैखिक गुणनखंडों के चिन्ह उलटकर मूल लिखें।

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\(4x^2-19x-5=0\) में मध्य पद का सही विभाजन कौनसा है?

What is the correct splitting of the middle term in \(4x^2-19x-5=0\)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-20x+x-5=0\)

Step 1

Concept

Here (ac=-20) and (-20+1=-19), so the middle term is (-20x+x). In exams, check the sign of (ac) carefully.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2-20x+x-5=0\). Here (ac=-20) and (-20+1=-19), so the middle term is (-20x+x). In exams, check the sign of (ac) carefully.

Step 3

Exam Tip

यहां (ac=-20) और (-20+1=-19), इसलिए मध्य पद (-20x+x) होगा। परीक्षा में (ac) का संकेत ध्यान से देखें।

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\(x^2-18x+80=0\) में कौनसी संख्या जोड़ी मध्य पद बनाने में मदद करेगी?

Which number pair helps in making the middle term in \(x^2-18x+80=0\)?

Explanation opens after your attempt
Correct Answer

A. (-8) और (-10)(-8) and (-10)

Step 1

Concept

(-8+(-10)=-18) and ((-8)(-10)=80), so this pair is correct. In exams, when (c) is positive and (b) is negative, both numbers are negative.

Step 2

Why this answer is correct

The correct answer is A. (-8) और (-10) / (-8) and (-10). (-8+(-10)=-18) and ((-8)(-10)=80), so this pair is correct. In exams, when (c) is positive and (b) is negative, both numbers are negative.

Step 3

Exam Tip

(-8+(-10)=-18) और ((-8)(-10)=80), इसलिए यह जोड़ी सही है। परीक्षा में (c) धनात्मक और (b) ऋणात्मक हो तो दोनों संख्याएं ऋणात्मक होती हैं।

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\(x^2-x-30=0\) के लिए सही कथन कौनसा है?

Which statement is correct for \(x^2-x-30=0\)?

Explanation opens after your attempt
Correct Answer

A. मूल (6) और (-5) हैंThe roots are (6) and (-5)

Step 1

Concept

(x-2-x-30=(x-6)(x+5)), so the roots are (6) and (-5). In exams, the larger value decides the sign of the middle term.

Step 2

Why this answer is correct

The correct answer is A. मूल (6) और (-5) हैं / The roots are (6) and (-5). (x-2-x-30=(x-6)(x+5)), so the roots are (6) and (-5). In exams, the larger value decides the sign of the middle term.

Step 3

Exam Tip

(x-2-x-30=(x-6)(x+5)), इसलिए मूल (6) और (-5) हैं। परीक्षा में बड़ा मान मध्य पद का चिन्ह तय करता है।

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\(5x^2-13x-6=0\) के मूल क्या हैं?

What are the roots of \(5x^2-13x-6=0\)?

Explanation opens after your attempt
Correct Answer

A. \(x=3,-\frac{2}{5}\)

Step 1

Concept

(5x-2-13x-6=(5x+2)(x-3)), so the roots are (3) and \(-\frac{2}{5}\). In exams, reverse the signs from linear factors to write roots.

Step 2

Why this answer is correct

The correct answer is A. \(x=3,-\frac{2}{5}\). (5x-2-13x-6=(5x+2)(x-3)), so the roots are (3) and \(-\frac{2}{5}\). In exams, reverse the signs from linear factors to write roots.

Step 3

Exam Tip

(5x-2-13x-6=(5x+2)(x-3)), इसलिए मूल (3) और \(-\frac{2}{5}\) हैं। परीक्षा में रैखिक गुणनखंडों के चिन्ह उलटकर मूल लिखें।

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\(5x^2-13x-6=0\) में मध्य पद का सही विभाजन कौनसा है?

What is the correct splitting of the middle term in \(5x^2-13x-6=0\)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2-15x+2x-6=0\)

Step 1

Concept

Here (ac=-30) and (-15+2=-13), so the middle term is (-15x+2x). In exams, check the sign of (ac) carefully.

Step 2

Why this answer is correct

The correct answer is A. \(5x^2-15x+2x-6=0\). Here (ac=-30) and (-15+2=-13), so the middle term is (-15x+2x). In exams, check the sign of (ac) carefully.

Step 3

Exam Tip

यहां (ac=-30) और (-15+2=-13), इसलिए मध्य पद (-15x+2x) होगा। परीक्षा में (ac) का संकेत ध्यान से देखें।

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\(x^2-14x+45=0\) में कौनसी संख्या जोड़ी मध्य पद बनाने में मदद करेगी?

Which number pair helps in making the middle term in \(x^2-14x+45=0\)?

Explanation opens after your attempt
Correct Answer

A. (-5) और (-9)(-5) and (-9)

Step 1

Concept

(-5+(-9)=-14) and ((-5)(-9)=45), so this pair is correct. In exams, if (c) is positive and (b) is negative, both numbers may be negative.

Step 2

Why this answer is correct

The correct answer is A. (-5) और (-9) / (-5) and (-9). (-5+(-9)=-14) and ((-5)(-9)=45), so this pair is correct. In exams, if (c) is positive and (b) is negative, both numbers may be negative.

Step 3

Exam Tip

(-5+(-9)=-14) और ((-5)(-9)=45), इसलिए यह जोड़ी सही है। परीक्षा में (c) धनात्मक और (b) ऋणात्मक हो तो दोनों संख्याएं ऋणात्मक हो सकती हैं।

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\(x^2-3x-10=0\) के लिए निम्न में से कौनसा कथन सही है?

Which statement is correct for \(x^2-3x-10=0\)?

Explanation opens after your attempt
Correct Answer

A. मूल (5) और (-2) हैंThe roots are (5) and (-2)

Step 1

Concept

(x-2-3x-10=(x-5)(x+2)), so the roots are (5) and (-2). In exams, in mixed signs the larger value decides the middle-term sign.

Step 2

Why this answer is correct

The correct answer is A. मूल (5) और (-2) हैं / The roots are (5) and (-2). (x-2-3x-10=(x-5)(x+2)), so the roots are (5) and (-2). In exams, in mixed signs the larger value decides the middle-term sign.

Step 3

Exam Tip

(x-2-3x-10=(x-5)(x+2)), इसलिए मूल (5) और (-2) हैं। परीक्षा में मिश्रित चिन्हों में बड़ा मान मध्य पद का चिन्ह तय करता है।

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\(x^2-2x-15=0\) को हल करने के लिए सही गुणनखंड रूप क्या है?

What is the correct factorised form to solve \(x^2-2x-15=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x-5)(x+3)=0)

Step 1

Concept

(-5+3=-2) and \(-5\times3=-15\), so ((x-5)(x+3)) is correct. In exams, match both product and sum.

Step 2

Why this answer is correct

The correct answer is A. ((x-5)(x+3)=0). (-5+3=-2) and \(-5\times3=-15\), so ((x-5)(x+3)) is correct. In exams, match both product and sum.

Step 3

Exam Tip

(-5+3=-2) और \(-5\times3=-15\), इसलिए ((x-5)(x+3)) सही है। परीक्षा में गुणनफल और योग दोनों मिलाएं।

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\(x^2+6x-55=0\) के मूल क्या हैं?

What are the roots of \(x^2+6x-55=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=5,-11)

Step 1

Concept

((x+11)(x-5)=0), so (x=-11) and (x=5). In exams, the sign changes while finding roots from factors.

Step 2

Why this answer is correct

The correct answer is A. (x=5,-11). ((x+11)(x-5)=0), so (x=-11) and (x=5). In exams, the sign changes while finding roots from factors.

Step 3

Exam Tip

((x+11)(x-5)=0), इसलिए (x=-11) और (x=5) हैं। परीक्षा में गुणनखंड से मूल निकालते समय चिन्ह बदलता है।

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\(x^2+6x-55=0\) के सही गुणनखंड कौनसे हैं?

What are the correct factors of \(x^2+6x-55=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+11)(x-5))

Step 1

Concept

(11+(-5)=6) and \(11\times(-5)=-55\), so ((x+11)(x-5)) is correct. In exams, keep one sign positive and one negative.

Step 2

Why this answer is correct

The correct answer is A. ((x+11)(x-5)). (11+(-5)=6) and \(11\times(-5)=-55\), so ((x+11)(x-5)) is correct. In exams, keep one sign positive and one negative.

Step 3

Exam Tip

(11+(-5)=6) और \(11\times(-5)=-55\), इसलिए ((x+11)(x-5)) सही है। परीक्षा में एक चिन्ह धनात्मक और एक ऋणात्मक रखें।

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\(3x^2-11x+6=0\) में मध्य पद का सही विभाजन क्या है?

What is the correct splitting of the middle term in \(3x^2-11x+6=0\)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-9x-2x+6=0\)

Step 1

Concept

((-9)+(-2)=-11) and ((-9)(-2)=18=ac), so (-9x-2x) is correct. In exams, split the middle term by checking (ac).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-9x-2x+6=0\). ((-9)+(-2)=-11) and ((-9)(-2)=18=ac), so (-9x-2x) is correct. In exams, split the middle term by checking (ac).

Step 3

Exam Tip

((-9)+(-2)=-11) और ((-9)(-2)=18=ac), इसलिए (-9x-2x) सही है। परीक्षा में (ac) देखकर मध्य पद तोड़ें।

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\(x^2+9x+20=0\) के मूल कौनसे हैं?

Which are the roots of \(x^2+9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=-4,-5)

Step 1

Concept

(x-2+9x+20=(x+4)(x+5)), so the roots are (-4) and (-5). In exams, a positive middle term can give negative roots.

Step 2

Why this answer is correct

The correct answer is A. (x=-4,-5). (x-2+9x+20=(x+4)(x+5)), so the roots are (-4) and (-5). In exams, a positive middle term can give negative roots.

Step 3

Exam Tip

(x-2+9x+20=(x+4)(x+5)), इसलिए मूल (-4) और (-5) हैं। परीक्षा में धनात्मक मध्य पद से ऋणात्मक मूल मिल सकते हैं।

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\(x^2-6x-27=0\) के सही गुणनखंड कौनसे हैं?

What are the correct factors of \(x^2-6x-27=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x-9)(x+3))

Step 1

Concept

Since (-9+3=-6) and \(-9\times3=-27\), ((x-9)(x+3)) is correct. In exams, choose mixed signs carefully.

Step 2

Why this answer is correct

The correct answer is A. ((x-9)(x+3)). Since (-9+3=-6) and \(-9\times3=-27\), ((x-9)(x+3)) is correct. In exams, choose mixed signs carefully.

Step 3

Exam Tip

(-9+3=-6) और \(-9\times3=-27\), इसलिए ((x-9)(x+3)) सही है। परीक्षा में मिश्रित चिन्ह वाले गुणनखंड ध्यान से चुनें।

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\(x^2+5x-14=0\) के मूल क्या हैं?

What are the roots of \(x^2+5x-14=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=2,-7)

Step 1

Concept

((x+7)(x-2)=0), so (x=-7) and (x=2). In exams, the sign changes while finding roots from factors.

Step 2

Why this answer is correct

The correct answer is A. (x=2,-7). ((x+7)(x-2)=0), so (x=-7) and (x=2). In exams, the sign changes while finding roots from factors.

Step 3

Exam Tip

((x+7)(x-2)=0), इसलिए (x=-7) और (x=2) हैं। परीक्षा में गुणनखंड से मूल निकालते समय चिन्ह बदलता है।

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\(x^2+5x-14=0\) के सही गुणनखंड कौनसे हैं?

What are the correct factors of \(x^2+5x-14=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+7)(x-2))

Step 1

Concept

(7+(-2)=5) and \(7\times(-2)=-14\), so ((x+7)(x-2)) is correct. In exams, keep one sign positive and one negative.

Step 2

Why this answer is correct

The correct answer is A. ((x+7)(x-2)). (7+(-2)=5) and \(7\times(-2)=-14\), so ((x+7)(x-2)) is correct. In exams, keep one sign positive and one negative.

Step 3

Exam Tip

(7+(-2)=5) और \(7\times(-2)=-14\), इसलिए ((x+7)(x-2)) सही है। परीक्षा में एक चिन्ह धनात्मक और एक ऋणात्मक रखें।

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\(2x^2-7x+5=0\) में मध्य पद का सही विभाजन क्या है?

What is the correct splitting of the middle term in \(2x^2-7x+5=0\)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-2x-5x+5=0\)

Step 1

Concept

((-2)+(-5)=-7) and ((-2)(-5)=10=ac), so (-2x-5x) is correct. In exams, checking (ac) is important while splitting the middle term.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-2x-5x+5=0\). ((-2)+(-5)=-7) and ((-2)(-5)=10=ac), so (-2x-5x) is correct. In exams, checking (ac) is important while splitting the middle term.

Step 3

Exam Tip

((-2)+(-5)=-7) और ((-2)(-5)=10=ac), इसलिए (-2x-5x) सही है। परीक्षा में मध्य पद तोड़ते समय (ac) देखना जरूरी है।

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\(x^2+8x+12=0\) के मूल कौनसे हैं?

Which are the roots of \(x^2+8x+12=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=-2,-6)

Step 1

Concept

(x-2+8x+12=(x+2)(x+6)), so the roots are (-2) and (-6). In exams, a positive middle term can give negative roots.

Step 2

Why this answer is correct

The correct answer is A. (x=-2,-6). (x-2+8x+12=(x+2)(x+6)), so the roots are (-2) and (-6). In exams, a positive middle term can give negative roots.

Step 3

Exam Tip

(x-2+8x+12=(x+2)(x+6)), इसलिए मूल (-2) और (-6) हैं। परीक्षा में धनात्मक मध्य पद से ऋणात्मक मूल मिल सकते हैं।

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\(x^2-4x-21=0\) के सही गुणनखंड कौनसे हैं?

What are the correct factors of \(x^2-4x-21=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x-7)(x+3))

Step 1

Concept

Since (-7+3=-4) and \(-7\times3=-21\), ((x-7)(x+3)) is correct. In exams, choose mixed signs carefully.

Step 2

Why this answer is correct

The correct answer is A. ((x-7)(x+3)). Since (-7+3=-4) and \(-7\times3=-21\), ((x-7)(x+3)) is correct. In exams, choose mixed signs carefully.

Step 3

Exam Tip

(-7+3=-4) और \(-7\times3=-21\), इसलिए ((x-7)(x+3)) सही है। परीक्षा में मिश्रित चिन्ह वाले गुणनखंड ध्यान से चुनें।

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\(x^2+11x+30=0\) को गुणनखंड रूप में कैसे लिखा जाएगा?

How will \(x^2+11x+30=0\) be written in factorised form?

Explanation opens after your attempt
Correct Answer

A. ((x+5)(x+6)=0)

Step 1

Concept

(5+6=11) and \(5\times6=30\), so the correct factors are ((x+5)(x+6)). In exams, positive (c) and positive (b) give both positive signs.

Step 2

Why this answer is correct

The correct answer is A. ((x+5)(x+6)=0). (5+6=11) and \(5\times6=30\), so the correct factors are ((x+5)(x+6)). In exams, positive (c) and positive (b) give both positive signs.

Step 3

Exam Tip

(5+6=11) और \(5\times6=30\), इसलिए सही गुणनखंड ((x+5)(x+6)) हैं। परीक्षा में धनात्मक (c) और धनात्मक (b) पर दोनों चिन्ह धनात्मक होते हैं।

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\(x^2+x-6=0\) के मूल क्या हैं?

What are the roots of \(x^2+x-6=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=2,-3)

Step 1

Concept

((x+3)(x-2)=0), so (x=-3) and (x=2). In exams, the sign changes while finding roots from factors.

Step 2

Why this answer is correct

The correct answer is A. (x=2,-3). ((x+3)(x-2)=0), so (x=-3) and (x=2). In exams, the sign changes while finding roots from factors.

Step 3

Exam Tip

((x+3)(x-2)=0), इसलिए (x=-3) और (x=2) हैं। परीक्षा में गुणनखंड से मूल निकालते समय संकेत बदलता है।

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\(x^2+x-6=0\) के लिए सही गुणनखंड कौनसे हैं?

What are the correct factors for \(x^2+x-6=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+3)(x-2))

Step 1

Concept

(3+(-2)=1) and \(3\times(-2)=-6\), so ((x+3)(x-2)) is correct. In exams, match signs with the product.

Step 2

Why this answer is correct

The correct answer is A. ((x+3)(x-2)). (3+(-2)=1) and \(3\times(-2)=-6\), so ((x+3)(x-2)) is correct. In exams, match signs with the product.

Step 3

Exam Tip

(3+(-2)=1) और \(3\times(-2)=-6\), इसलिए ((x+3)(x-2)) सही है। परीक्षा में चिन्हों को गुणनफल से मिलाएं।

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\(2x^2-5x+3=0\) में मध्य पद का सही विभाजन क्या है?

What is the correct splitting of the middle term in \(2x^2-5x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-2x-3x+3=0\)

Step 1

Concept

((-2)+(-3)=-5) and ((-2)(-3)=6=ac), so the correct split is (-2x-3x). In exams, the product of the two numbers must be (ac).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-2x-3x+3=0\). ((-2)+(-3)=-5) and ((-2)(-3)=6=ac), so the correct split is (-2x-3x). In exams, the product of the two numbers must be (ac).

Step 3

Exam Tip

((-2)+(-3)=-5) और ((-2)(-3)=6=ac), इसलिए सही विभाजन (-2x-3x) है। परीक्षा में दोनों संख्याओं का गुणनफल (ac) होना चाहिए।

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\(x^2-2x-8=0\) के लिए सही गुणनखंड कौनसे हैं?

What are the correct factors for \(x^2-2x-8=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x-4)(x+2))

Step 1

Concept

Since (-4+2=-2) and \(-4\times2=-8\), ((x-4)(x+2)) is correct. In exams, match both product and sum.

Step 2

Why this answer is correct

The correct answer is A. ((x-4)(x+2)). Since (-4+2=-2) and \(-4\times2=-8\), ((x-4)(x+2)) is correct. In exams, match both product and sum.

Step 3

Exam Tip

(-4+2=-2) और \(-4\times2=-8\), इसलिए ((x-4)(x+2)) सही है। परीक्षा में गुणनफल और योग दोनों मिलाएं।

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समीकरण \(x^2+10x+21=0\) के मूल कौन से हैं?

What are the roots of \(x^2+10x+21=0\)?

Explanation opens after your attempt
Correct Answer

A. (-3) और (-7)(-3) and (-7)

Step 1

Concept

(x-2+10x+21=(x+3)(x+7)). Therefore the roots are (-3) and (-7).

Step 2

Why this answer is correct

The correct answer is A. (-3) और (-7) / (-3) and (-7). (x-2+10x+21=(x+3)(x+7)). Therefore the roots are (-3) and (-7).

Step 3

Exam Tip

(x-2+10x+21=(x+3)(x+7)) है। इसलिए मूल (-3) और (-7) हैं।

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समीकरण \(x^2+9x+20=0\) के मूल कौन से हैं?

What are the roots of \(x^2+9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. (-4) और (-5)(-4) and (-5)

Step 1

Concept

(x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).

Step 2

Why this answer is correct

The correct answer is A. (-4) और (-5) / (-4) and (-5). (x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).

Step 3

Exam Tip

(x-2+9x+20=(x+4)(x+5)) है। इसलिए मूल (-4) और (-5) हैं।

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समीकरण \(x^2+5x+6=0\) के मूल कौन से हैं?

What are the roots of \(x^2+5x+6=0\)?

Explanation opens after your attempt
Correct Answer

A. (-2) और (-3)(-2) and (-3)

Step 1

Concept

(x-2+5x+6=(x+2)(x+3)) so the roots are (-2) and (-3). Pay special attention to signs.

Step 2

Why this answer is correct

The correct answer is A. (-2) और (-3) / (-2) and (-3). (x-2+5x+6=(x+2)(x+3)) so the roots are (-2) and (-3). Pay special attention to signs.

Step 3

Exam Tip

(x-2+5x+6=(x+2)(x+3)) इसलिए मूल (-2) और (-3) हैं। चिन्हों पर विशेष ध्यान दें।

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किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?

In which option will the sum of roots be positive and the product of roots be positive?

Explanation opens after your attempt
Correct Answer

A. \(x^2-9x+20=0\)

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-9x+20=0\). In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=9\) और गुणनफल \(\frac{c}{a}=20\) है। इसलिए दोनों धनात्मक हैं।

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किस विकल्प में मूलों का योग ऋणात्मक और गुणनफल ऋणात्मक होगा?

In which option will the sum of roots be negative and the product of roots be negative?

Explanation opens after your attempt
Correct Answer

A. \(x^2+5x-24=0\)

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+5x-24=0\). In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=-5\) और गुणनफल \(\frac{c}{a}=-24\) है। इसलिए दोनों ऋणात्मक हैं।

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किस विकल्प में मूलों का योग धनात्मक और गुणनफल ऋणात्मक होगा?

In which option will the sum of roots be positive and the product of roots be negative?

Explanation opens after your attempt
Correct Answer

A. \(x^2-6x-16=0\)

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=6\) and the product is \(\frac{c}{a}=-16\). So the sum is positive and the product is negative.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-6x-16=0\). In the first option, the sum is \(-\frac{b}{a}=6\) and the product is \(\frac{c}{a}=-16\). So the sum is positive and the product is negative.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=6\) और गुणनफल \(\frac{c}{a}=-16\) है। इसलिए योग धनात्मक और गुणनफल ऋणात्मक है।

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किस विकल्प में मूलों का योग ऋणात्मक और गुणनफल धनात्मक होगा?

In which option will the sum of roots be negative and the product of roots be positive?

Explanation opens after your attempt
Correct Answer

A. \(x^2+7x+12=0\)

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=-7\) and the product is \(\frac{c}{a}=12\). So the sum is negative and the product is positive.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+7x+12=0\). In the first option, the sum is \(-\frac{b}{a}=-7\) and the product is \(\frac{c}{a}=12\). So the sum is negative and the product is positive.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=-7\) और गुणनफल \(\frac{c}{a}=12\) है। इसलिए योग ऋणात्मक और गुणनफल धनात्मक है।

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किस विकल्प में मूलों का योग और गुणनफल दोनों धनात्मक होंगे?

In which option will both the sum and product of roots be positive?

Explanation opens after your attempt
Correct Answer

A. \(x^2-5x+6=0\)

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=5\) and the product is \(\frac{c}{a}=6\). Both are positive.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-5x+6=0\). In the first option, the sum is \(-\frac{b}{a}=5\) and the product is \(\frac{c}{a}=6\). Both are positive.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=5\) और गुणनफल \(\frac{c}{a}=6\) है। दोनों धनात्मक हैं।

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समीकरण \(6x^2-13x+5=0\) के लिए (2a+b-c) का मान क्या है?

For the equation \(6x^2-13x+5=0\), what is the value of (2a+b-c)?

Explanation opens after your attempt
Correct Answer

A. (-6)

Step 1

Concept

Here (a=6), (b=-13), (c=5). Hence (2a+b-c=12-13-5=-6).

Step 2

Why this answer is correct

The correct answer is A. (-6). Here (a=6), (b=-13), (c=5). Hence (2a+b-c=12-13-5=-6).

Step 3

Exam Tip

यहाँ (a=6), (b=-13), (c=5) हैं। इसलिए (2a+b-c=12-13-5=-6) है।

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समीकरण \(-4x^2+6x-9=0\) के लिए (a-b+c) का मान क्या है?

For the equation \(-4x^2+6x-9=0\), what is the value of (a-b+c)?

Explanation opens after your attempt
Correct Answer

B. (-19)

Step 1

Concept

Here (a=-4), (b=6), (c=-9). Hence (a-b+c=-4-6-9=-19).

Step 2

Why this answer is correct

The correct answer is B. (-19). Here (a=-4), (b=6), (c=-9). Hence (a-b+c=-4-6-9=-19).

Step 3

Exam Tip

यहाँ (a=-4), (b=6), (c=-9) हैं। इसलिए (a-b+c=-4-6-9=-19) है।

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समीकरण \(5x-2x^2=9\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?

What is the standard form of \(5x-2x^2=9\) with positive coefficient of \(x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-5x+9=0\)

Step 1

Concept

Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-5x+9=0\). Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.

Step 3

Exam Tip

सभी पद एक ओर लाकर \(-2x^2+5x-9=0\) मिलता है और (-1) से गुणा करने पर \(2x^2-5x+9=0\) मिलता है। मानक रूप में चिन्ह सावधानी से बदलें।

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समीकरण \(2x^2-x+8=0\) में (x) का गुणांक क्या है?

What is the coefficient of (x) in \(2x^2-x+8=0\)?

Explanation opens after your attempt
Correct Answer

A. (-1)

Step 1

Concept

The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.

Step 2

Why this answer is correct

The correct answer is A. (-1). The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.

Step 3

Exam Tip

(-x) का गुणांक (-1) होता है। चिन्ह सहित गुणांक लिखना जरूरी है।

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समीकरण \(-x^2+4x-1=0\) में (a,b,c) के सही मान कौन-से हैं?

Which are the correct values of (a,b,c) in \(-x^2+4x-1=0\)?

Explanation opens after your attempt
Correct Answer

A. (a=-1,\ b=4,\ c=-1)

Step 1

Concept

The coefficient of \(x^2\) is (-1), the coefficient of (x) is (4), and the constant term is (-1). Never ignore the negative sign.

Step 2

Why this answer is correct

The correct answer is A. (a=-1,\ b=4,\ c=-1). The coefficient of \(x^2\) is (-1), the coefficient of (x) is (4), and the constant term is (-1). Never ignore the negative sign.

Step 3

Exam Tip

\(x^2\) का गुणांक (-1), (x) का गुणांक (4) और स्थिर पद (-1) है। ऋण चिन्ह को कभी न छोड़ें।

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समीकरण \(x^2=4x+12\) का मानक रूप कौन सा है?

Which is the standard form of \(x^2=4x+12\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-12=0\)

Step 1

Concept

When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-12=0\). When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.

Step 3

Exam Tip

दाईं ओर के पदों को बाईं ओर लाने पर चिन्ह बदलते हैं। इसलिए \(x^2-4x-12=0\) सही है।

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कौन सा विकल्प \(\sqrt{72}-\sqrt{50}+\sqrt{8}\) के बराबर है?

Which option is equal to \(\sqrt{72}-\sqrt{50}+\sqrt{8}\)?

Explanation opens after your attempt
Correct Answer

A. \(3\sqrt{2}\)

Step 1

Concept

\(\sqrt{72}=6\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Hence the value is \(3\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(3\sqrt{2}\). \(\sqrt{72}=6\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Hence the value is \(3\sqrt{2}\).

Step 3

Exam Tip

\(\sqrt{72}=6\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\) है। इसलिए मान \(3\sqrt{2}\) है।

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यदि (p(x)=x-2+2x-1) है, तो इसके शून्यक कौन से हैं?

If (p(x)=x-2+2x-1), what are its zeroes?

Explanation opens after your attempt
Correct Answer

A. \(-1+\sqrt{2}\) और \(-1-\sqrt{2}\)\(-1+\sqrt{2}\) and \(-1-\sqrt{2}\)

Step 1

Concept

By the formula, \(x=\frac{-2\pm\sqrt{4+4}}{2}=-1\pm\sqrt{2}\). Pay special attention to signs.

Step 2

Why this answer is correct

The correct answer is A. \(-1+\sqrt{2}\) और \(-1-\sqrt{2}\) / \(-1+\sqrt{2}\) and \(-1-\sqrt{2}\). By the formula, \(x=\frac{-2\pm\sqrt{4+4}}{2}=-1\pm\sqrt{2}\). Pay special attention to signs.

Step 3

Exam Tip

सूत्र से \(x=\frac{-2\pm\sqrt{4+4}}{2}=-1\pm\sqrt{2}\)। चिह्नों पर विशेष ध्यान दें।

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राष्ट्रवादी प्रतीकों के अध्ययन में स्रोत आधारित प्रश्नों के लिए कौन सा कौशल सबसे आवश्यक है?

Which skill is most necessary for source-based questions on nationalist symbols?

Explanation opens after your attempt
Correct Answer

A. दृश्य संकेतों को ऐतिहासिक विचारों से जोड़नाConnecting visual signs with historical ideas

Step 1

Concept

In source-based questions observe the given signs carefully.

Step 2

Why this answer is correct

Connect them with ideas like liberty republic and unity.

Step 3

Exam Tip

Then write a brief evidence-based answer. चरण 1: स्रोत आधारित प्रश्न में दिए गए संकेतों को ध्यान से देखें। चरण 2: उन्हें स्वतंत्रता गणराज्य और एकता जैसे विचारों से जोड़ें। चरण 3: फिर संक्षिप्त और प्रमाण आधारित उत्तर लिखें।

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किसी अज्ञात अभिक्रिया में रंग बदलता है ऊष्मा निकलती है और गैस बनती है। सबसे उचित निष्कर्ष क्या है?

In an unknown reaction colour changes heat is released and gas forms. What is the most suitable conclusion?

Explanation opens after your attempt
Correct Answer

A. रासायनिक अभिक्रिया होने की प्रबल संभावना हैThere is a strong possibility of a chemical reaction

Step 1

Concept

Colour change gas formation and heat release are signs of reaction.

Step 2

Why this answer is correct

When several signs appear together the possibility of chemical reaction becomes stronger.

Step 3

Exam Tip

Conclusions should be based on observations. चरण 1: रंग परिवर्तन गैस बनना और ऊष्मा निकलना अभिक्रिया के संकेत हैं। चरण 2: कई संकेत साथ मिलें तो रासायनिक अभिक्रिया की संभावना बढ़ती है। चरण 3: निष्कर्ष अवलोकनों के आधार पर निकालना चाहिए।

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रासायनिक अभिक्रिया में नए पदार्थ बनने का सबसे स्पष्ट संकेत क्या हो सकता है?

What can be the clearest sign of formation of new substances in a chemical reaction?

Explanation opens after your attempt
Correct Answer

A. रंग या गैस में परिवर्तनChange in colour or gas

Step 1

Concept

In a chemical reaction the nature of substances changes.

Step 2

Why this answer is correct

Colour change or gas evolution may indicate formation of new substances.

Step 3

Exam Tip

In experiment-based questions observe such signs carefully. चरण 1: रासायनिक अभिक्रिया में पदार्थों की प्रकृति बदलती है। चरण 2: रंग बदलना या गैस निकलना नए पदार्थ बनने का संकेत हो सकता है। चरण 3: प्रयोग आधारित प्रश्नों में ऐसे संकेतों को ध्यान से देखें।

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किसी अभिक्रिया को पहचानने के लिए सबसे अच्छा तरीका क्या है?

What is the best way to identify a reaction?

Explanation opens after your attempt
Correct Answer

A. रंग गैस ताप गंध और अवक्षेप जैसे संकेत देखनाObserving signs like colour gas temperature smell and precipitate

Step 1

Concept

A chemical reaction may show many signs.

Step 2

Why this answer is correct

Colour change gas evolution temperature change smell change and precipitate formation are main signs.

Step 3

Exam Tip

In exams think of all signs together. चरण 1: रासायनिक अभिक्रिया कई संकेत दे सकती है। चरण 2: रंग बदलना गैस निकलना ताप बदलना गंध बदलना और अवक्षेप बनना मुख्य संकेत हैं। चरण 3: परीक्षा में सभी संकेतों को साथ सोचें।

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किसी अभिक्रिया में गैस रंगहीन हो तो क्या केवल रंग न दिखने से अभिक्रिया न होने का निष्कर्ष सही है?

If a gas in a reaction is colourless is it correct to conclude no reaction occurred only because no colour is seen?

Explanation opens after your attempt
Correct Answer

A. नहीं क्योंकि अन्य संकेत भी हो सकते हैंNo because other signs may be present

Step 1

Concept

All gases are not coloured.

Step 2

Why this answer is correct

Signs of reaction may include bubbles temperature smell or precipitate.

Step 3

Exam Tip

So do not decide only by colour. चरण 1: सभी गैसें रंगीन नहीं होतीं। चरण 2: अभिक्रिया के संकेत गैस बुलबुले ताप गंध या अवक्षेप भी हो सकते हैं। चरण 3: इसलिए केवल रंग देखकर निर्णय न करें।

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