A. क्योंकि नोक पर ऑक्सिन बनता है/Because auxin is produced at the tip
Step 1
Concept
Auxin is produced in the growing tip of a plant.
Step 2
Why this answer is correct
Auxin helps cells elongate.
Step 3
Exam Tip
If the tip is removed the auxin effect may reduce and bending may become weak. चरण 1: पौधे की बढ़ती नोक में ऑक्सिन बनता है। चरण 2: ऑक्सिन कोशिकाओं की लंबाई बढ़ाने में सहायक है। चरण 3: नोक हटाने पर ऑक्सिन का प्रभाव कम हो सकता है इसलिए मुड़ना कमजोर हो सकता है।
A. व्यवहार नियम और दंड स्पष्ट करने के लिए/To clarify rules of conduct and punishments
Step 1
Concept
In complex societies written rules clarified disputes and punishments. Remember Hammurabi and the Twelve Tables.
Step 2
Why this answer is correct
The correct answer is A. व्यवहार नियम और दंड स्पष्ट करने के लिए / To clarify rules of conduct and punishments. In complex societies written rules clarified disputes and punishments. Remember Hammurabi and the Twelve Tables.
Step 3
Exam Tip
जटिल समाजों में लिखित नियम विवाद और दंड को स्पष्ट करते थे। परीक्षा में हम्मुराबी और बारह पट्टिकाएं याद रखें।
A. नियम टूटने के बावजूद उद्देश्य सफल है/The intention is successful despite rule breaking
Step 1
Concept
Expert evaluation considers context and effect. Exam tip: write relation of rule and purpose.
Step 2
Why this answer is correct
The correct answer is A. नियम टूटने के बावजूद उद्देश्य सफल है / The intention is successful despite rule breaking. Expert evaluation considers context and effect. Exam tip: write relation of rule and purpose.
Step 3
Exam Tip
विशेषज्ञ मूल्यांकन संदर्भ और प्रभाव देखता है। परीक्षा में rule and purpose का संबंध लिखें।
A. क्योंकि यह व्यवहारिक जरूरतों से विकसित हुआ/Because it developed from practical needs
Step 1
Concept
Peacekeeping developed from practical UN needs for peace. Exam tip: treat it as a practical interpretation of the Charter.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि यह व्यवहारिक जरूरतों से विकसित हुआ / Because it developed from practical needs. Peacekeeping developed from practical UN needs for peace. Exam tip: treat it as a practical interpretation of the Charter.
Step 3
Exam Tip
शांति स्थापना संयुक्त राष्ट्र की व्यवहारिक शांति जरूरतों से विकसित हुई। परीक्षा में इसे चार्टर की व्यावहारिक व्याख्या मानें।
A. क्योंकि शांति स्थापना बाद में व्यवहार से विकसित हुई/Because peacekeeping developed later through practice
Step 1
Concept
Peacekeeping developed through UN practice and needs. Exam tip: treat it as a practical arrangement emerging from the Charter.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि शांति स्थापना बाद में व्यवहार से विकसित हुई / Because peacekeeping developed later through practice. Peacekeeping developed through UN practice and needs. Exam tip: treat it as a practical arrangement emerging from the Charter.
Step 3
Exam Tip
शांति स्थापना संयुक्त राष्ट्र के व्यवहार और जरूरतों से विकसित हुई। परीक्षा में इसे चार्टर से निकली व्यावहारिक व्यवस्था मानें।
B. सत्ता समाज अर्थव्यवस्था और विचारों पर प्रभाव बताकर/By explaining effects on power society economy and ideas
Step 1
Concept
Long-term impact appears in many areas. For exams write effects in four categories.
Step 2
Why this answer is correct
The correct answer is B. सत्ता समाज अर्थव्यवस्था और विचारों पर प्रभाव बताकर / By explaining effects on power society economy and ideas. Long-term impact appears in many areas. For exams write effects in four categories.
Step 3
Exam Tip
दीर्घकालीन प्रभाव कई क्षेत्रों में दिखाई देता है। परीक्षा में चार श्रेणियों में प्रभाव लिखें।
C. उसने नए गणतांत्रिक शासन को संस्थागत रूप दिया/It institutionalized the new republican government
Step 1
Concept
The constitution gave a stable form to the new state's government. For exams look at institutional changes after revolution.
Step 2
Why this answer is correct
The correct answer is C. उसने नए गणतांत्रिक शासन को संस्थागत रूप दिया / It institutionalized the new republican government. The constitution gave a stable form to the new state's government. For exams look at institutional changes after revolution.
Step 3
Exam Tip
संविधान ने नए राज्य की शासन व्यवस्था को स्थिर रूप दिया। परीक्षा में क्रांति के बाद संस्थागत बदलाव देखें।
A. दोनों मिलकर अधिक संतुलित समझ देते हैं/Together they give a more balanced understanding
Step 1
Concept
One source may be incomplete so comparing many evidences is necessary. Remember limits and uses of sources.
Step 2
Why this answer is correct
The correct answer is A. दोनों मिलकर अधिक संतुलित समझ देते हैं / Together they give a more balanced understanding. One source may be incomplete so comparing many evidences is necessary. Remember limits and uses of sources.
Step 3
Exam Tip
एक स्रोत अधूरा हो सकता है इसलिए अनेक प्रमाणों की तुलना जरूरी है। परीक्षा में स्रोतों की सीमा और उपयोग याद रखें।
A. सिंधु लिपि अभी पूरी तरह पढ़ी नहीं गई है/The Indus script is not fully deciphered
Step 1
Concept
The Indus script has not been fully deciphered. Remember it as an undeciphered ancient script in exams.
Step 2
Why this answer is correct
The correct answer is A. सिंधु लिपि अभी पूरी तरह पढ़ी नहीं गई है / The Indus script is not fully deciphered. The Indus script has not been fully deciphered. Remember it as an undeciphered ancient script in exams.
Step 3
Exam Tip
सिंधु लिपि अभी पूरी तरह पढ़ी नहीं जा सकी है। परीक्षा में इसे प्राचीन अनसुलझी लिपि के रूप में याद रखें।
The Twelve Tables were an early written form of Roman law. In exams, connect them with rights and law.
Step 2
Why this answer is correct
The correct answer is A. रोमन कानून / Roman law. The Twelve Tables were an early written form of Roman law. In exams, connect them with rights and law.
Step 3
Exam Tip
बारह पट्टिकाएं रोमन कानून का प्रारंभिक लिखित रूप थीं। परीक्षा में इन्हें नागरिक अधिकार और कानून से जोड़ें।
Cuneiform writing was written on clay tablets. Link it with administration and trade records in exams.
Step 2
Why this answer is correct
The correct answer is B. मिट्टी की तख्तियों पर / Clay tablets. Cuneiform writing was written on clay tablets. Link it with administration and trade records in exams.
Step 3
Exam Tip
कीलाक्षर लेखन मिट्टी की तख्तियों पर लिखा जाता था। परीक्षा में इसे प्रशासन और व्यापारिक रिकॉर्ड से जोड़ें।
Gulbadan Begum wrote the Humayun Nama. It is an important example of women's writing in the Mughal period.
Step 2
Why this answer is correct
The correct answer is A. हुमायूननामा / Humayun Nama. Gulbadan Begum wrote the Humayun Nama. It is an important example of women's writing in the Mughal period.
Step 3
Exam Tip
गुलबदन बेगम ने हुमायूननामा लिखा था। मुगल काल में महिला लेखन का यह महत्वपूर्ण उदाहरण है।
Harshacharita was written by Banabhatta and is an important literary source for Harshavardhana. For exams match court writers with rulers.
Step 2
Why this answer is correct
The correct answer is B. बाणभट्ट / Banabhatta. Harshacharita was written by Banabhatta and is an important literary source for Harshavardhana. For exams match court writers with rulers.
Step 3
Exam Tip
हर्षचरित बाणभट्ट की रचना है और यह हर्षवर्धन के लिए महत्वपूर्ण साहित्यिक स्रोत है। परीक्षा में राजदरबारी लेखकों को शासकों से मिलाकर याद करें।
Baburnama was originally written in Chagatai Turkish. Remember Babur as the founder of the Mughal Empire in exams.
Step 2
Why this answer is correct
The correct answer is A. तुर्की चगताई / Chagatai Turkish. Baburnama was originally written in Chagatai Turkish. Remember Babur as the founder of the Mughal Empire in exams.
Step 3
Exam Tip
बाबरनामा मूल रूप से चगताई तुर्की में लिखा गया था। परीक्षा में बाबर को मुगल साम्राज्य के संस्थापक के रूप में याद रखें।
Fatawa-i-Jahandari presents Barani's political ideas. Exam tip: remember authors with their texts carefully.
Step 2
Why this answer is correct
The correct answer is A. फतवा-ए-जहांदारी / Fatawa-i-Jahandari. Fatawa-i-Jahandari presents Barani's political ideas. Exam tip: remember authors with their texts carefully.
Step 3
Exam Tip
फतवा-ए-जहांदारी बरनी की राजनीतिक विचारों वाली रचना है। परीक्षा में लेखक और ग्रंथ का मेल ध्यान से याद रखें।
Baburnama was originally written in Turkish. Exam tip: do not confuse it with its later Persian translation.
Step 2
Why this answer is correct
The correct answer is C. तुर्की / Turkish. Baburnama was originally written in Turkish. Exam tip: do not confuse it with its later Persian translation.
Step 3
Exam Tip
बाबरनामा मूल रूप से तुर्की भाषा में लिखा गया था। परीक्षा में बाद के फारसी अनुवाद से भ्रमित न हों।
Most Indian inscriptions of Ashoka are in Brahmi script. For exams, also remember the use of Kharosthi in the north-west.
Step 2
Why this answer is correct
The correct answer is C. ब्राह्मी / Brahmi. Most Indian inscriptions of Ashoka are in Brahmi script. For exams, also remember the use of Kharosthi in the north-west.
Step 3
Exam Tip
अशोक के अधिकतर भारतीय अभिलेख ब्राह्मी लिपि में हैं। परीक्षा में उत्तर पश्चिम में खरोष्ठी का प्रयोग भी याद रखें।
B. क्योंकि लिपि पढ़ी नहीं जा सकी है/Because the script has not been deciphered
Step 1
Concept
Since the Indus script is undeciphered, historians rely more on archaeological evidence. For exams, understand source limitations.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि लिपि पढ़ी नहीं जा सकी है / Because the script has not been deciphered. Since the Indus script is undeciphered, historians rely more on archaeological evidence. For exams, understand source limitations.
Step 3
Exam Tip
सिंधु लिपि अपठित होने से इतिहासकारों को पुरातात्त्विक साक्ष्यों पर अधिक निर्भर रहना पड़ता है। परीक्षा में स्रोत की सीमा समझें।
Ratnavali is a play associated with Harshavardhana. For exams, remember Harsha as both ruler and writer.
Step 2
Why this answer is correct
The correct answer is A. रत्नावली / Ratnavali. Ratnavali is a play associated with Harshavardhana. For exams, remember Harsha as both ruler and writer.
Step 3
Exam Tip
रत्नावली हर्षवर्धन से जुड़ी नाट्य रचना है। परीक्षा में हर्ष को शासक और साहित्यकार दोनों रूपों में याद रखें।
Most of Ashoka's inscriptions are in the Brahmi script. For exams, also remember the use of Kharosthi in the north-west region.
Step 2
Why this answer is correct
The correct answer is D. ब्राह्मी / Brahmi. Most of Ashoka's inscriptions are in the Brahmi script. For exams, also remember the use of Kharosthi in the north-west region.
Step 3
Exam Tip
अशोक के अधिकांश अभिलेख ब्राह्मी लिपि्मी लिपि में हैं। परीक्षा में उत्तर-पश्चिम क्षेत्र में खरोष्ठी का प्रयोग भी याद रखें।
Most of Ashoka's inscriptions were in the Brahmi script. Remember the link between inscriptions and scripts for exams.
Step 2
Why this answer is correct
The correct answer is D. ब्राह्मी / Brahmi. Most of Ashoka's inscriptions were in the Brahmi script. Remember the link between inscriptions and scripts for exams.
Step 3
Exam Tip
अशोक के अधिकांश अभिलेख ब्राह्मी लिपि में थे। परीक्षा में अभिलेख और लिपि का संबंध याद रखें।
Many Ashokan inscriptions were written in Brahmi script. For exams, remember Brahmi as an important ancient Indian script.
Step 2
Why this answer is correct
The correct answer is A. ब्राह्मी / Brahmi. Many Ashokan inscriptions were written in Brahmi script. For exams, remember Brahmi as an important ancient Indian script.
Step 3
Exam Tip
अशोक के अनेक अभिलेख ब्राह्मी लिपि में लिखे गए। परीक्षा में ब्राह्मी को प्राचीन भारत की महत्वपूर्ण लिपि मानकर याद करें।
The original (d=5), but in reverse order \(18,13,8,3,\ldots\), (d=-5). Reversing the order changes the sign.
Step 2
Why this answer is correct
The correct answer is C. ऋणात्मक हो जाएगा / It becomes negative. The original (d=5), but in reverse order \(18,13,8,3,\ldots\), (d=-5). Reversing the order changes the sign.
Step 3
Exam Tip
मूल (d=5) है, पर उलटे क्रम \(18,13,8,3,\ldots\) में (d=-5) होगा। क्रम उलटने पर चिह्न बदलता है।
The original (d=7), and in reverse order \(23,16,9,2,\ldots\), (d=-7). Reversing the order changes the sign of the common difference.
Step 2
Why this answer is correct
The correct answer is C. वह ऋणात्मक हो जाएगा / It will become negative. The original (d=7), and in reverse order \(23,16,9,2,\ldots\), (d=-7). Reversing the order changes the sign of the common difference.
Step 3
Exam Tip
मूल (d=7) है और उलटा क्रम \(23,16,9,2,\ldots\) में (d=-7) होगा। क्रम उलटने पर सार्व अंतर का चिह्न बदल जाता है।
The reverse order is \(24,18,12,6,\ldots\), and (d=18-24=-6). When the order is reversed, the sign of the common difference changes.
Step 2
Why this answer is correct
The correct answer is B. (-6). The reverse order is \(24,18,12,6,\ldots\), and (d=18-24=-6). When the order is reversed, the sign of the common difference changes.
Step 3
Exam Tip
उलटा क्रम \(24,18,12,6,\ldots\) होगा और (d=18-24=-6) है। क्रम उलटने पर सार्व अंतर का चिह्न बदल जाता है।
\(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{9}{2},\frac{3}{2}\right\)). \(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(4.5=\frac{9}{2}\) और \(1.5=\frac{3}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
\(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{7}{2},\frac{5}{2}\right\) ). \(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(3.5=\frac{7}{2}\) और \(2.5=\frac{5}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.
Step 2
Why this answer is correct
The correct answer is B. \(x^3+2x+5\). In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.
Step 3
Exam Tip
मानक रूप में पद बड़ी घात से छोटी घात की ओर लिखे जाते हैं। \(x^3+2x+5\) इसी क्रम में है।
(\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6}). In exams, identify (a,b) from (a+b) and \(2\sqrt{ab}\).
Step 2
Why this answer is correct
The correct answer is A. \((\sqrt{3}-\sqrt{2})^{2}\). (\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6}). In exams, identify (a,b) from (a+b) and \(2\sqrt{ab}\).
Step 3
Exam Tip
(\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6})। परीक्षा में (a+b) और \(2\sqrt{ab}\) से (a,b) पहचानें।
Since (17=\(\sqrt{17}\)2) and the middle term is \(-2\sqrt{17}x\), it is (\(x-\sqrt{17}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x-\sqrt{17}\)2=0). Since (17=\(\sqrt{17}\)2) and the middle term is \(-2\sqrt{17}x\), it is (\(x-\sqrt{17}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (17=\(\sqrt{17}\)2) और मध्य पद \(-2\sqrt{17}x\) है, इसलिए यह (\(x-\sqrt{17}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
Since (13=\(\sqrt{13}\)2) and the middle term is \(2\sqrt{13}x\), it is (\(x+\sqrt{13}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x+\sqrt{13}\)2=0). Since (13=\(\sqrt{13}\)2) and the middle term is \(2\sqrt{13}x\), it is (\(x+\sqrt{13}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (13=\(\sqrt{13}\)2) और मध्य पद \(2\sqrt{13}x\) है, इसलिए यह (\(x+\sqrt{13}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
Since (11=\(\sqrt{11}\)2) and the middle term is \(-2\sqrt{11}x\), it is (\(x-\sqrt{11}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x-\sqrt{11}\)2=0). Since (11=\(\sqrt{11}\)2) and the middle term is \(-2\sqrt{11}x\), it is (\(x-\sqrt{11}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (11=\(\sqrt{11}\)2) और मध्य पद \(-2\sqrt{11}x\) है, इसलिए यह (\(x-\sqrt{11}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
Since (7=\(\sqrt{7}\)2) and the middle term is \(2\sqrt{7}x\), it is (\(x+\sqrt{7}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x+\sqrt{7}\)2=0). Since (7=\(\sqrt{7}\)2) and the middle term is \(2\sqrt{7}x\), it is (\(x+\sqrt{7}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (7=\(\sqrt{7}\)2) और मध्य पद \(2\sqrt{7}x\) है, इसलिए यह (\(x+\sqrt{7}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
Since (5=\(\sqrt{5}\)2) and the middle term is \(-2\sqrt{5}x\), it is (\(x-\sqrt{5}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x-\sqrt{5}\)2=0). Since (5=\(\sqrt{5}\)2) and the middle term is \(-2\sqrt{5}x\), it is (\(x-\sqrt{5}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (5=\(\sqrt{5}\)2) और मध्य पद \(-2\sqrt{5}x\) है, इसलिए यह (\(x-\sqrt{5}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
Since (3=\(\sqrt{3}\)2) and the middle term is \(2\sqrt{3}x\), it is (\(x+\sqrt{3}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 2
Why this answer is correct
The correct answer is A. (\(x+\sqrt{3}\)2=0). Since (3=\(\sqrt{3}\)2) and the middle term is \(2\sqrt{3}x\), it is (\(x+\sqrt{3}\)2). In exams, identify perfect squares even with irrational coefficients.
Step 3
Exam Tip
क्योंकि (3=\(\sqrt{3}\)2) और मध्य पद \(2\sqrt{3}x\) है, इसलिए यह (\(x+\sqrt{3}\)2) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।
(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।
Because (3+4=7) and \(3\times4=12\), the correct factors are ((x+3)(x+4)). In exams, pay close attention to signs.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)(x+4)=0). Because (3+4=7) and \(3\times4=12\), the correct factors are ((x+3)(x+4)). In exams, pay close attention to signs.
Step 3
Exam Tip
क्योंकि (3+4=7) और \(3\times4=12\), इसलिए सही गुणनखंड ((x+3)(x+4)) हैं। परीक्षा में संकेतों पर विशेष ध्यान दें।
Multiplying the whole equation by (5) gives \(x^2+10x-35=0\). To remove fractions, multiply the whole equation.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x-35=0\). Multiplying the whole equation by (5) gives \(x^2+10x-35=0\). To remove fractions, multiply the whole equation.
Step 3
Exam Tip
पूरे समीकरण को (5) से गुणा करने पर \(x^2+10x-35=0\) मिलता है। भिन्न हटाने के लिए पूरे समीकरण पर गुणा करें।
Multiplying the whole equation by (4) gives \(x^2-4x+12=0\). To remove fractions, multiply the whole equation.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+12=0\). Multiplying the whole equation by (4) gives \(x^2-4x+12=0\). To remove fractions, multiply the whole equation.
Step 3
Exam Tip
पूरे समीकरण को (4) से गुणा करने पर \(x^2-4x+12=0\) मिलता है। भिन्न हटाने के लिए पूरे समीकरण पर गुणा करें।
Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-10=0\). Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 3
Exam Tip
पूरे समीकरण को (2) से गुणा करने पर \(x^2+6x-10=0\) मिलता है। भिन्न हटाने के लिए हर से गुणा करें।
\(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^2=5x-4\). \(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 3
Exam Tip
\(x^2=5x-4\) को \(x^2-5x+4=0\) बनाया जा सकता है, इसलिए यह द्विघात है। मानक रूप में दायां पक्ष (0) होना चाहिए।
After cancelling \(385=5\cdot7\cdot11\), only \(2^3\) remains in the denominator. In exams always check the denominator in lowest form.
Step 2
Why this answer is correct
The correct answer is A. समाप्त दशमलव / Terminating decimal. After cancelling \(385=5\cdot7\cdot11\), only \(2^3\) remains in the denominator. In exams always check the denominator in lowest form.
Step 3
Exam Tip
\(385=5\cdot7\cdot11\) कटने के बाद हर में केवल \(2^3\) बचता है। परीक्षा में हमेशा सरलतम रूप के हर को देखें।
After cancelling \(231=3\cdot7\cdot11\), the denominator left is \(2\cdot5^2\). Therefore the decimal terminates.
Step 2
Why this answer is correct
The correct answer is A. समाप्त / Terminating. After cancelling \(231=3\cdot7\cdot11\), the denominator left is \(2\cdot5^2\). Therefore the decimal terminates.
Step 3
Exam Tip
\(231=3\cdot7\cdot11\) कटने के बाद हर में \(2\cdot5^2\) बचता है। इसलिए दशमलव समाप्त होगा।
\(154=2\cdot7\cdot11\), so after cancellation only \(5^2\) remains in the denominator. In exams decide from the denominator in lowest form.
Step 2
Why this answer is correct
The correct answer is A. समाप्त दशमलव / Terminating decimal. \(154=2\cdot7\cdot11\), so after cancellation only \(5^2\) remains in the denominator. In exams decide from the denominator in lowest form.
Step 3
Exam Tip
\(154=2\cdot7\cdot11\), इसलिए कटने के बाद हर में केवल \(5^2\) बचता है। परीक्षा में निर्णय हमेशा सरलतम रूप के हर से करें।
After simplification, (7) remains in the denominator, so the decimal is non-terminating recurring. In exams do not decide only from the original denominator.
Step 2
Why this answer is correct
The correct answer is A. अनवसानी आवर्ती / Non-terminating recurring. After simplification, (7) remains in the denominator, so the decimal is non-terminating recurring. In exams do not decide only from the original denominator.
Step 3
Exam Tip
सरलीकरण के बाद हर में (7) बचता है, इसलिए दशमलव अनवसानी आवर्ती होगा। परीक्षा में केवल मूल हर देखकर निर्णय न लें।
A. (p) और (q) दोनों (3) से विभाज्य हो जाते हैं/Both (p) and (q) become divisible by (3)
Step 1
Concept
From \(\sqrt{3}=\frac{p}{q}\), we get \(p^2=3q^2\), so both (p) and (q) become divisible by (3). In exams use the coprime condition at the end.
Step 2
Why this answer is correct
The correct answer is A. (p) और (q) दोनों (3) से विभाज्य हो जाते हैं / Both (p) and (q) become divisible by (3). From \(\sqrt{3}=\frac{p}{q}\), we get \(p^2=3q^2\), so both (p) and (q) become divisible by (3). In exams use the coprime condition at the end.
Step 3
Exam Tip
\(\sqrt{3}=\frac{p}{q}\) से \(p^2=3q^2\) मिलता है, इसलिए (p) और (q) दोनों (3) से विभाज्य हो जाते हैं। परीक्षा में सहअभाज्य शर्त को अंत में उपयोग करें।
\(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{14}\). \(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.
Step 3
Exam Tip
\(\sqrt{14}\) अपरिमेय है क्योंकि (14) पूर्ण वर्ग नहीं है। बाकी विकल्प परिमेय रूप में लिखे जा सकते हैं।
Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-11) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-7) और (2) हैं। टिप: समान (x)-मान को एक बार गिनें।
The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-5) / (2) and (-5). The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 3
Exam Tip
दोहराया (2) अलग शून्यक में एक बार गिना जाता है। टिप: अलग शून्यक में समान मान पुनः न लिखें।
The same (x)-value (4) is repeated, so there is one distinct zero. Tip: do not count repetition for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The same (x)-value (4) is repeated, so there is one distinct zero. Tip: do not count repetition for distinct zeroes.
Step 3
Exam Tip
एक ही (x)-मान (4) दोहराया गया है इसलिए अलग शून्यक एक है। टिप: अलग शून्यक में दोहराव न गिनें।
\(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\). For a purely recurring decimal, first use a denominator of (9)'s and then reduce fully.
Step 2
Why this answer is correct
The correct answer is A. (37). \(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\). For a purely recurring decimal, first use a denominator of (9)'s and then reduce fully.
Step 3
Exam Tip
\(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\) है। पूर्ण आवर्ती दशमलव में पहले (9) वाला हर बनाएं और फिर पूरा सरल करें।
