100 results found for "cubic inequality" in Class 10.
यदि (x-a), (x-b) और (x-c) किसी घन बहुपद के गुणनखंड हैं, तो उसका एक संभावित बहुपद कौन सा है?
If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?
#polynomials
#cubic
#factors
#hard
A (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
B (x-3 +(a+b+c)x-2 +(ab+bc+ca)x+abc)
C (x-3 -(ab+bc+ca)x-2 +(a+b+c)x-abc)
D (x-3 +abcx-2 -(a+b+c)x+ab+bc+ca)
Explanation opens after your attempt
Correct Answer
A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
Step 1
Concept
Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 2
Why this answer is correct
The correct answer is A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc). Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 3
Exam Tip
((x-a)(x-b)(x-c)) फैलाने पर पहला रूप मिलता है। शून्यकों और गुणनखंडों का संबंध याद रखें।
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निम्न में से त्रिघात बहुपद कौन सा है?
Which of the following is a cubic polynomial?
#cubic-polynomial
#degree
A \(x^3-4x+2\)
B \(x^2+9\)
C (6x-1)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(x^3-4x+2\)
Step 1
Concept
A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-4x+2\). A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 3
Exam Tip
त्रिघात बहुपद की घात (3) होती है। \(x^3-4x+2\) में सबसे बड़ी घात (3) है।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को (-1) पर काटता है और (2) पर छूता है तो अलग-अलग वास्तविक शून्यक कितने हैं?
If the graph of a cubic polynomial crosses the (x)-axis at (-1) and touches it at (2), how many distinct real zeroes are there?
#cubic
#distinct-zeroes
#graph
A दो / Two
B तीन / Three
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 3
Exam Tip
अलग-अलग शून्यक केवल (-1) और (2) हैं। छूने वाला शून्यक दोहराया हो सकता है पर अलग मान एक ही गिना जाता है।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर छूता और काटता है, तो अलग वास्तविक शून्यक कितने होंगे?
If the graph of a cubic polynomial touches or crosses the (x)-axis at two distinct points, how many distinct real zeroes will it have?
#cubic
#distinct zeroes
#graph reading
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 3
Exam Tip
अलग शून्यक अलग (x)-अक्ष मिलने वाले बिंदुओं की संख्या से मिलते हैं। टिप: घात से अधिकतम संख्या मिलती है, वास्तविक गिनती ग्राफ से पढ़ें।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो वास्तविक शून्यकों की संख्या क्या मानी जाएगी?
If the graph of a cubic polynomial cuts the (x)-axis only once, what is the number of real zeroes?
#cubic graph
#real zero
#count
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 2
Why this answer is correct
The correct answer is A. एक / One. There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 3
Exam Tip
कटान केवल एक है इसलिए एक वास्तविक शून्यक है। टिप: घन बहुपद में अधिकतम तीन वास्तविक शून्यक हो सकते हैं, जरूरी नहीं कि तीन हों।
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किसी घन बहुपद का आलेख (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a cubic polynomial cuts the (x)-axis at three distinct points. What is the number of real zeroes?
#cubic graph zeroes
A तीन / Three
B दो / Two
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 3
Exam Tip
तीन कटान बिंदु तीन वास्तविक शून्यक बताते हैं। टिप: प्रत्येक अलग (x)-अक्ष कटान को गिनें।
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कौन-सा बहुपद घन बहुपद है?
Which polynomial is a cubic polynomial?
#cubic_polynomial
#degree
#classification
A \(x^3-2x+1\)
B \(x^2+4\)
C (7x-9)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(x^3-2x+1\)
Step 1
Concept
A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-2x+1\). A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).
Step 3
Exam Tip
घन बहुपद की घात (3) होती है। \(x^3-2x+1\) की सबसे बड़ी घात (3) है।
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भाषा नीति में औपनिवेशिक भाषा की प्रतिष्ठा किस प्रकार सामाजिक असमानता बना सकती थी?
How could prestige of colonial language create social inequality in language policy?
#language-policy
#colonial-language
#social-inequality
A औपनिवेशिक भाषा जानने वालों को नौकरी शिक्षा और प्रशासन में लाभ मिलना / Those knowing the colonial language getting advantages in jobs education and administration
B स्थानीय भाषाओं को सभी पदों पर समान लाभ मिलना / Local languages getting equal advantage in all posts
C भाषा का रोजगार से कोई संबंध न होना / Language having no relation with employment
D औपनिवेशिक भाषा का तुरंत अंत होना / Immediate end of colonial language
Explanation opens after your attempt
Correct Answer
A. औपनिवेशिक भाषा जानने वालों को नौकरी शिक्षा और प्रशासन में लाभ मिलना / Those knowing the colonial language getting advantages in jobs education and administration
Step 1
Concept
Language could link with opportunity and power. For exams connect language policy with social hierarchy.
Step 2
Why this answer is correct
The correct answer is A. औपनिवेशिक भाषा जानने वालों को नौकरी शिक्षा और प्रशासन में लाभ मिलना / Those knowing the colonial language getting advantages in jobs education and administration. Language could link with opportunity and power. For exams connect language policy with social hierarchy.
Step 3
Exam Tip
भाषा अवसर और शक्ति से जुड़ सकती थी। परीक्षा में भाषा नीति को सामाजिक पदानुक्रम से जोड़ें।
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मूल निवासी संधियों की व्याख्या में शक्ति असमानता क्यों ध्यान में रखनी चाहिए?
Why should power inequality be considered while interpreting indigenous treaties?
#indigenous-treaties
#power-inequality
#land
A क्योंकि सभी संधियां हमेशा बराबर पक्षों में होती थीं / Because all treaties were always between equal sides
B क्योंकि भाषा भूमि समझ और सैन्य दबाव में असमानता हो सकती थी / Because inequality could exist in language land understanding and military pressure
C क्योंकि संधियों का भूमि से कोई संबंध नहीं था / Because treaties had no relation with land
D क्योंकि संधियां इतिहास का स्रोत नहीं होतीं / Because treaties are not historical sources
Explanation opens after your attempt
Correct Answer
B. क्योंकि भाषा भूमि समझ और सैन्य दबाव में असमानता हो सकती थी / Because inequality could exist in language land understanding and military pressure
Step 1
Concept
Treaties should be read not only as legal texts but in power relations. For exams use source criticism.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि भाषा भूमि समझ और सैन्य दबाव में असमानता हो सकती थी / Because inequality could exist in language land understanding and military pressure. Treaties should be read not only as legal texts but in power relations. For exams use source criticism.
Step 3
Exam Tip
संधियों को केवल कानूनी पाठ नहीं बल्कि शक्ति संबंध में पढ़ना चाहिए। परीक्षा में स्रोत आलोचना करें।
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औपनिवेशिक कानून की भाषा में समानता और व्यवहार में असमानता का विरोधाभास कैसे दिखता था?
How was the contradiction between equality in colonial legal language and inequality in practice visible?
#colonial-law
#equality
#legal-inequality
A कानून व्यवस्था घोषित होती थी पर अधिकार और दंड में नस्ली या प्रशासनिक भेद रह सकता था / Rule of law was declared but rights and punishments could remain racially or administratively unequal
B सभी उपनिवेशों में पूर्ण समान नागरिकता थी / All colonies had complete equal citizenship
C औपनिवेशिक कानून कभी लिखा नहीं गया / Colonial law was never written
D कानून का शासन से कोई संबंध नहीं था / Law had no relation with rule
Explanation opens after your attempt
Correct Answer
A. कानून व्यवस्था घोषित होती थी पर अधिकार और दंड में नस्ली या प्रशासनिक भेद रह सकता था / Rule of law was declared but rights and punishments could remain racially or administratively unequal
Step 1
Concept
Colonial law was a tool of both control and legitimacy. For exams understand the difference between law and justice.
Step 2
Why this answer is correct
The correct answer is A. कानून व्यवस्था घोषित होती थी पर अधिकार और दंड में नस्ली या प्रशासनिक भेद रह सकता था / Rule of law was declared but rights and punishments could remain racially or administratively unequal. Colonial law was a tool of both control and legitimacy. For exams understand the difference between law and justice.
Step 3
Exam Tip
औपनिवेशिक कानून नियंत्रण और वैधता दोनों का साधन था। परीक्षा में कानून और न्याय का अंतर समझें।
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लैटिन अमेरिकी स्वतंत्रता के बाद सामाजिक असमानता क्यों बनी रह सकती थी?
Why could social inequality remain after Latin American independence?
#latin-america
#social-inequality
#creole
A क्योंकि राजनीतिक सत्ता परिवर्तन ने हमेशा भूमि जाति और वर्ग संबंध नहीं बदले / Because political power change did not always change land race and class relations
B क्योंकि स्पेन ने सभी को बराबर भूमि दी / Because Spain gave equal land to all
C क्योंकि कोई औपनिवेशिक समाज नहीं था / Because there was no colonial society
D क्योंकि स्वतंत्रता कभी मिली ही नहीं / Because independence never came
Explanation opens after your attempt
Correct Answer
A. क्योंकि राजनीतिक सत्ता परिवर्तन ने हमेशा भूमि जाति और वर्ग संबंध नहीं बदले / Because political power change did not always change land race and class relations
Step 1
Concept
Political independence was not a guarantee of social equality. For exams separate Creole leadership and social questions.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि राजनीतिक सत्ता परिवर्तन ने हमेशा भूमि जाति और वर्ग संबंध नहीं बदले / Because political power change did not always change land race and class relations. Political independence was not a guarantee of social equality. For exams separate Creole leadership and social questions.
Step 3
Exam Tip
राजनीतिक स्वतंत्रता सामाजिक समानता की गारंटी नहीं थी। परीक्षा में क्रिओल नेतृत्व और सामाजिक प्रश्न अलग रखें।
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ग्रीन क्रांति में खाद्यान्न सुरक्षा और असमानता दोनों की चर्चा क्यों होती है?
Why are both food security and inequality discussed in the Green Revolution?
#world history
#revolutions
#green revolution
#food security inequality
A क्योंकि उत्पादन बढ़ा पर लाभ सभी क्षेत्रों और किसानों तक समान नहीं पहुंचा / Because production rose but benefits did not reach all regions and farmers equally
B क्योंकि उत्पादन घटा और लाभ बराबर मिला / Because production fell and benefits were equal
C क्योंकि यह केवल राजशाही क्रांति थी / Because it was only a monarchical revolution
D क्योंकि यह दास विद्रोह था / Because it was a slave revolt
Explanation opens after your attempt
Correct Answer
A. क्योंकि उत्पादन बढ़ा पर लाभ सभी क्षेत्रों और किसानों तक समान नहीं पहुंचा / Because production rose but benefits did not reach all regions and farmers equally
Step 1
Concept
The achievements of the Green Revolution should be understood with its limits. For exams give a balanced answer.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि उत्पादन बढ़ा पर लाभ सभी क्षेत्रों और किसानों तक समान नहीं पहुंचा / Because production rose but benefits did not reach all regions and farmers equally. The achievements of the Green Revolution should be understood with its limits. For exams give a balanced answer.
Step 3
Exam Tip
ग्रीन क्रांति की उपलब्धि के साथ उसकी सीमाएं भी समझनी चाहिए। परीक्षा में संतुलित उत्तर दें।
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यूरोप में राष्ट्रवाद के उदय से पहले समाज में कौन सी असमानता स्पष्ट थी?
Which inequality was clear in society before the rise of nationalism in Europe?
#social inequality
#aristocracy
#common people
A अभिजातों और आम लोगों के बीच असमानता / Inequality between aristocrats and common people
B सभी नागरिकों की पूर्ण समानता / Complete equality of all citizens
C सभी वर्गों की समान आय / Equal income of all classes
D सभी क्षेत्रों में समान कानून / Same law in all regions
Explanation opens after your attempt
Correct Answer
A. अभिजातों और आम लोगों के बीच असमानता / Inequality between aristocrats and common people
Step 1
Concept
Look at the structure of old society.
Step 2
Why this answer is correct
Aristocrats had more rights and prestige.
Step 3
Exam Tip
Nationalist and liberal ideas challenged such inequality. चरण 1: पुराने समाज की संरचना देखें। चरण 2: अभिजातों को अधिक अधिकार और प्रतिष्ठा मिली थी। चरण 3: राष्ट्रवादी और उदार विचारों ने ऐसी असमानता को चुनौती दी।
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अतिरिक्त क्षेत्राधिकार की व्यवस्था औपनिवेशिक असमानता कैसे बनाती थी?
How did extraterritoriality create colonial inequality?
#extraterritoriality
#unequal-treaties
#sovereignty
A विदेशियों को स्थानीय कानून से छूट या विशेष कानूनी संरक्षण मिल सकता था / Foreigners could get exemption from local law or special legal protection
B स्थानीय नागरिकों को विदेशी संसद में सीट मिलती थी / Local citizens got seats in foreign parliament
C सभी कानून समान रूप से लागू होते थे / All laws applied equally
D यह केवल कृषि नीति थी / It was only agricultural policy
Explanation opens after your attempt
Correct Answer
A. विदेशियों को स्थानीय कानून से छूट या विशेष कानूनी संरक्षण मिल सकता था / Foreigners could get exemption from local law or special legal protection
Step 1
Concept
Extraterritoriality could weaken sovereignty. For exams connect it with unequal treaties.
Step 2
Why this answer is correct
The correct answer is A. विदेशियों को स्थानीय कानून से छूट या विशेष कानूनी संरक्षण मिल सकता था / Foreigners could get exemption from local law or special legal protection. Extraterritoriality could weaken sovereignty. For exams connect it with unequal treaties.
Step 3
Exam Tip
अतिरिक्त क्षेत्राधिकार संप्रभुता को कमजोर कर सकता था। परीक्षा में असमान संधियों से जोड़ें।
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नवपाषाण क्रांति के बाद सामाजिक असमानता बढ़ने का एक कारण क्या था?
What was one reason for the rise of social inequality after the Neolithic Revolution?
#world_history
#important_events
#neolithic_revolution
A अधिशेष उत्पादन और संपत्ति संचय / Surplus production and accumulation of property
B चंद्रमा यात्रा / Moon travel
C नाटो की स्थापना / Formation of NATO
D संयुक्त राष्ट्र सुरक्षा परिषद / United Nations Security Council
Explanation opens after your attempt
Correct Answer
A. अधिशेष उत्पादन और संपत्ति संचय / Surplus production and accumulation of property
Step 1
Concept
Surplus production increased property and division of labor. Exam tip: connect agriculture not only with food but with social change.
Step 2
Why this answer is correct
The correct answer is A. अधिशेष उत्पादन और संपत्ति संचय / Surplus production and accumulation of property. Surplus production increased property and division of labor. Exam tip: connect agriculture not only with food but with social change.
Step 3
Exam Tip
अधिशेष उत्पादन से संपत्ति और श्रम विभाजन बढ़ा। परीक्षा में कृषि को केवल भोजन नहीं बल्कि समाज परिवर्तन से जोड़ें।
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सुरक्षा परिषद में वीटो शक्ति किस तरह की असमानता को दिखाती है?
What type of inequality is shown by veto power in the Security Council?
#veto
#security council
#un reform
A खेल असमानता / Sports inequality
B भाषाई असमानता / Linguistic inequality
C कृषि असमानता / Agricultural inequality
D स्थायी और अस्थायी सदस्यों की शक्ति असमानता / Power inequality between permanent and non-permanent members
Explanation opens after your attempt
Correct Answer
D. स्थायी और अस्थायी सदस्यों की शक्ति असमानता / Power inequality between permanent and non-permanent members
Step 1
Concept
Veto power belongs only to permanent members so it shows power inequality. Exam tip: connect it with UN reform debates.
Step 2
Why this answer is correct
The correct answer is D. स्थायी और अस्थायी सदस्यों की शक्ति असमानता / Power inequality between permanent and non-permanent members. Veto power belongs only to permanent members so it shows power inequality. Exam tip: connect it with UN reform debates.
Step 3
Exam Tip
वीटो शक्ति केवल स्थायी सदस्यों को मिलती है इसलिए शक्ति असमानता दिखती है। परीक्षा में इसे संयुक्त राष्ट्र सुधार बहस से जोड़ें।
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फ्रांस की क्रांति से पहले पुराने शासन की कर व्यवस्था में सबसे बड़ी असमानता क्या थी?
What was the greatest inequality in the tax system of the Old Regime before the French Revolution?
#world-history
#revolutions
#french-revolution
A पहले और दूसरे एस्टेट को कई कर विशेषाधिकार मिलते थे / First and Second Estates enjoyed many tax privileges
B तीसरा एस्टेट सभी करों से मुक्त था / Third Estate was free from all taxes
C राजा केवल कुलीनों से कर लेता था / The king taxed only nobles
D चर्च ने कर वसूली पूरी तरह रोक दी थी / The Church fully stopped tax collection
Explanation opens after your attempt
Correct Answer
A. पहले और दूसरे एस्टेट को कई कर विशेषाधिकार मिलते थे / First and Second Estates enjoyed many tax privileges
Step 1
Concept
In the Old Regime the tax burden mainly fell on the Third Estate. For exams treat tax inequality as a major cause of the French Revolution.
Step 2
Why this answer is correct
The correct answer is A. पहले और दूसरे एस्टेट को कई कर विशेषाधिकार मिलते थे / First and Second Estates enjoyed many tax privileges. In the Old Regime the tax burden mainly fell on the Third Estate. For exams treat tax inequality as a major cause of the French Revolution.
Step 3
Exam Tip
पुराने शासन में कर भार मुख्यतः तीसरे एस्टेट पर था। परीक्षा में कर असमानता को फ्रांसीसी क्रांति का प्रमुख कारण मानें।
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उर की राजसी कब्रें किस सभ्यता की सामाजिक असमानता समझने में सहायक हैं?
The royal tombs of Ur help us understand social inequality in which civilization?
#world history
#ancient civilizations
#sumer
#ur
A मिस्र / Egypt
B माया / Maya
C शांग / Shang
D सुमेर / Sumer
Explanation opens after your attempt
Correct Answer
D. सुमेर / Sumer
Step 1
Concept
The tombs of Ur indicate wealth and social ranks. For exams treat grave goods as social evidence.
Step 2
Why this answer is correct
The correct answer is D. सुमेर / Sumer. The tombs of Ur indicate wealth and social ranks. For exams treat grave goods as social evidence.
Step 3
Exam Tip
उर की कब्रें संपत्ति और सामाजिक स्तरों का संकेत देती हैं। परीक्षा में कब्र सामग्री को सामाजिक प्रमाण मानें।
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यदि (p(x)=x-3 -1), तो निम्न में से कौन-सा रैखिक गुणनखंड है?
If (p(x)=x-3 -1), which of the following is a linear factor?
#identity
#cubic
#factorisation
A (x-1)
B (x+1)
C (x-3)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(x-3 -1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.
Step 2
Why this answer is correct
The correct answer is A. (x-1). (x-3 -1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.
Step 3
Exam Tip
(x-3 -1=(x-1)\(x^2+x+1\)) है। इसलिए (x-1) रैखिक गुणनखंड है।
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यदि (p(x)=x-3 -3x-2 -4x+12), तो पूर्ण गुणनखंड रूप क्या है?
If (p(x)=x-3 -3x-2 -4x+12), what is the complete factor form?
#factorisation
#grouping
#cubic
A ((x-3)(x-2)(x+2))
B ((x+3)(x-2)(x+2))
C ((x-3)(x+2)2 )
D ((x+3)(x-2)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-3)(x-2)(x+2))
Step 1
Concept
By grouping, (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).
Step 2
Why this answer is correct
The correct answer is A. ((x-3)(x-2)(x+2)). By grouping, (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).
Step 3
Exam Tip
समूहीकरण से (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)) मिलता है। इसलिए गुणनखंड ((x-3)(x-2)(x+2)) हैं।
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यदि (p(x)=x-3 +px-2 +qx+15) के शून्यक (-1,3,-5) हैं, तो (p+q) क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx+15) are (-1,3,-5), what is (p+q)?
#cubic-zeroes
#coefficients
#trap
A (0)
B (2)
C -(2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).
Step 2
Why this answer is correct
The correct answer is B. (2). The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).
Step 3
Exam Tip
शून्यकों का योग (-3) है, इसलिए (p=3)। युग्म गुणनफलों का योग (-3+5-15=-13), इसलिए (q=-13) और (p+q=-10)।
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यदि (x=2) पर (p(x)=x-3 +mx-10) का मान (0) है, तो (m) क्या है?
If the value of (p(x)=x-3 +mx-10) at (x=2) is (0), what is (m)?
#evaluation
#parameter
#cubic
A (1)
B -(1)
C (2)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8+2m-10=0). This gives (2m=2) and (m=1).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=8+2m-10=0). This gives (2m=2) and (m=1).
Step 3
Exam Tip
(p(2)=8+2m-10=0) है। इससे (2m=2) और (m=1) मिलता है।
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यदि (p(x)=x-3 -9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?
If (p(x)=x-3 -9x), how many distinct real zeroes does it have?
#distinct-zeroes
#cubic
#factorisation
A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
(x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (3). (x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 3
Exam Tip
(x-3 -9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं।
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यदि (p(x)=x-3 +ax-2 +bx-12) के शून्यक (1,3,-4) हैं, तो (a+b) क्या है?
If the zeroes of (p(x)=x-3 +ax-2 +bx-12) are (1,3,-4), what is (a+b)?
#cubic-zeroes
#coefficients
#expert
A -(9)
B (9)
C -(7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).
Step 2
Why this answer is correct
The correct answer is A. -(9). The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).
Step 3
Exam Tip
योग (1+3-4=0) है, इसलिए (a=0)। युग्म गुणनफलों का योग (3-4-12=-13), इसलिए (b=-13) और (a+b=-13)।
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यदि (p(x)=x-3 -6x-2 +12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?
If (p(x)=x-3 -6x-2 +12x-8), what is the zero of (p(x)) with its multiplicity?
#multiplicity
#cubic
#identity
A (2) गुणनता (3) / (2) with multiplicity (3)
B (3) गुणनता (2) / (3) with multiplicity (2)
C -(2) गुणनता (3) / (-2) with multiplicity (3)
D (1) गुणनता (3) / (1) with multiplicity (3)
Explanation opens after your attempt
Correct Answer
A. (2) गुणनता (3) / (2) with multiplicity (3)
Step 1
Concept
This is (p(x)=(x-2)3 ), so (2) is a zero three times. Recognizing cube identities is useful.
Step 2
Why this answer is correct
The correct answer is A. (2) गुणनता (3) / (2) with multiplicity (3). This is (p(x)=(x-2)3 ), so (2) is a zero three times. Recognizing cube identities is useful.
Step 3
Exam Tip
यह (p(x)=(x-2)3 ) है, इसलिए (2) तीन बार शून्यक है। घन पूर्ण पहचान को पहचानना उपयोगी है।
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यदि (p(x)=x-3 -4x-2 -7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?
If (p(x)=x-3 -4x-2 -7x+10) and (x-1) is a factor, what is the remaining quadratic factor?
#division
#factorisation
#cubic
A \(x^2-3x-10\)
B \(x^2+3x-10\)
C \(x^2-5x+10\)
D \(x^2-4x-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10\)
Step 1
Concept
Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10\). Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 3
Exam Tip
(p(x)) को (x-1) से भाग देने पर \(x^2-3x-10\) मिलता है। गुणा करके जाँचें कि ((x-1)\(x^2-3x-10\)=p(x))।
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यदि (p(x)=x-3 -2x-2 -13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -2x-2 -13x-10), which of the following is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (5)
B (2)
C -(1)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 2
Why this answer is correct
The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 3
Exam Tip
(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।
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यदि (p(x)=x-3 +ax-2 +bx+20), (p(1)=0) और (p(-4)=0), तो (a-b) का मान क्या है?
If (p(x)=x-3 +ax-2 +bx+20), (p(1)=0), and (p(-4)=0), what is the value of (a-b)?
#parameter
#zeros
#cubic polynomial
A (13)
B (15)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=-21) and (4a-b=11), so (a=-2), (b=-19), and (a-b=17). When two zeros are given, form two equations.
Step 2
Why this answer is correct
The correct answer is C. (17). The conditions give (a+b=-21) and (4a-b=11), so (a=-2), (b=-19), and (a-b=17). When two zeros are given, form two equations.
Step 3
Exam Tip
शर्तों से (a+b=-21) और (4a-b=11) मिलते हैं, इसलिए (a=-2), (b=-19) और (a-b=17)। दो शून्य दिए हों तो दो समीकरण बनाएं।
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(p(x)=x-3 -x-2 -4x+4) में (p(2)-p(-2)) क्या है?
For (p(x)=x-3 -x-2 -4x+4), what is (p(2)-p(-2))?
#evaluation
#difference
#cubic
A (0)
B (8)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
(p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 2
Why this answer is correct
The correct answer is C. (16). (p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 3
Exam Tip
(p(2)=0) और (p(-2)=-16), इसलिए (p(2)-p(-2)=16)। घटाते समय दूसरे मान का संकेत बदलता है।
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(p(x)=x-3 -3x-2 -4x+12) में (p(2)) और (p(-2)) का गुणनफल क्या है?
What is the product of (p(2)) and (p(-2)) for (p(x)=x-3 -3x-2 -4x+12)?
#evaluation
#product
#cubic
A (-32)
B (0)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). (p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 3
Exam Tip
(p(2)=8-12-8+12=0), इसलिए गुणनफल (0) होगा। एक मान (0) हो तो पूरा गुणनफल (0) होता है।
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यदि (p(x)=x-3 -6x-2 +12x-8), तो (p(5)) क्या है?
If (p(x)=x-3 -6x-2 +12x-8), what is (p(5))?
#identity
#cubic
#evaluation
A (8)
B (18)
C (27)
D (32)
Explanation opens after your attempt
Step 1
Concept
It is ((x-2)3 ), so (p(5)=(5-2)3 =27). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is C. (27). It is ((x-2)3 ), so (p(5)=(5-2)3 =27). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x-2)3 ) है, इसलिए (p(5)=(5-2)3 =27)। पहचान पहचानने से गणना कम होती है।
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यदि (p(x)=3x-3 -12x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=3x-3 -12x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-24)
B (0)
C (24)
D (48)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 3
Exam Tip
(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। विपरीत मानों पर संकेतों को सावधानी से रखें।
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यदि (p(x)=x-3 +ax-2 +bx-10) में (x=1) और (x=5) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=5) are both zeros of (p(x)=x-3 +ax-2 +bx-10), what is (a)?
#zeros
#cubic
#parameter
A (-7)
B (-6)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(p(1)=0) gives (a+b=9) and (p(5)=0) gives (5a+b=-23), so (a=-8). None of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is B. (-6). (p(1)=0) gives (a+b=9) and (p(5)=0) gives (5a+b=-23), so (a=-8). None of the listed choices is correct.
Step 3
Exam Tip
(p(1)=0) से (a+b=9) और (p(5)=0) से (5a+b=-23), इसलिए (a=-8) नहीं बल्कि (a=-8) आता है। विकल्पों में कोई सही नहीं है।
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यदि (p(x)=x-3 +ax-2 +bx+18) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a+b) क्या है?
If (x=1) and (x=-2) are both zeros of (p(x)=x-3 +ax-2 +bx+18), what is (a+b)?
#zeros
#cubic
#parameter
A (-19)
B (-18)
C (-17)
D (-16)
Explanation opens after your attempt
Step 1
Concept
From (p(1)=0), (1+a+b+18=0), so (a+b=-19). This condition is directly enough for the asked sum.
Step 2
Why this answer is correct
The correct answer is A. (-19). From (p(1)=0), (1+a+b+18=0), so (a+b=-19). This condition is directly enough for the asked sum.
Step 3
Exam Tip
(p(1)=0) से (1+a+b+18=0), इसलिए (a+b=-19)। पूछे गए योग के लिए यह शर्त सीधे पर्याप्त है।
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यदि (p(x)=x-3 +ax+b), (p(1)=6) और (p(-2)=-9), तो (a) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(1)=6), and (p(-2)=-9), what is the value of (a)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=5) and (-2a+b=-1). Subtracting gives (3a=6), so (a=2).
Step 2
Why this answer is correct
The correct answer is C. (3). The conditions give (a+b=5) and (-2a+b=-1). Subtracting gives (3a=6), so (a=2).
Step 3
Exam Tip
शर्तों से (a+b=5) और (-2a+b=-1) मिलते हैं। घटाने पर (3a=6) नहीं बल्कि (3a=6), इसलिए (a=2)।
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यदि (p(x)=x-3 +ax+b), (p(2)=13) और (p(-1)=-7), तो (a+b) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(2)=13), and (p(-1)=-7), what is the value of (a+b)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (2a+b=5) and (-a+b=-6), so \(a=\frac{11}{3}\) and \(b=-\frac{7}{3}\). Hence \(a+b=\frac{4}{3}\), so none of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is B. (2). The conditions give (2a+b=5) and (-a+b=-6), so \(a=\frac{11}{3}\) and \(b=-\frac{7}{3}\). Hence \(a+b=\frac{4}{3}\), so none of the listed choices is correct.
Step 3
Exam Tip
शर्तों से (2a+b=5) और (-a+b=-6) मिलते हैं, इसलिए \(a=\frac{11}{3}\) और \(b=-\frac{7}{3}\)। अतः \(a+b=\frac{4}{3}\) नहीं बल्कि विकल्पों में कोई सही नहीं होता।
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(p(x)=4x-3 -11x-2 +6x+2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=4x-3 -11x-2 +6x+2)?
#evaluation
#cubic
#substitution
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (2). (p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=32-44+12+2=2)। हर पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=kx-3 +2x-2 -7x+5) और (p(-1)=16), तो (k) का मान क्या है?
If (p(x)=kx-3 +2x-2 -7x+5) and (p(-1)=16), what is the value of (k)?
#evaluation
#parameter
#cubic polynomial
A (-2)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-k+2+7+5=14-k), so (14-k=16) and (k=-2). Watch signs carefully when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (-2). (p(-1)=-k+2+7+5=14-k), so (14-k=16) and (k=-2). Watch signs carefully when substituting a negative value.
Step 3
Exam Tip
(p(-1)=-k+2+7+5=14-k), इसलिए (14-k=16) और (k=-2)। ऋणात्मक मान रखने पर संकेतों को ध्यान से देखें।
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यदि (p(x)=x-3 +ax-2 +bx-12), (p(2)=0) और (p(3)=0), तो (a+b) का मान क्या है?
If (p(x)=x-3 +ax-2 +bx-12), (p(2)=0), and (p(3)=0), what is the value of (a+b)?
#parameter
#zeros
#cubic polynomial
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The conditions give (2a+b=2) and (3a+b=-5), so (a=-7), (b=16), and (a+b=9). When two values are given, form two equations.
Step 2
Why this answer is correct
The correct answer is C. (9). The conditions give (2a+b=2) and (3a+b=-5), so (a=-7), (b=16), and (a+b=9). When two values are given, form two equations.
Step 3
Exam Tip
शर्तों से (2a+b=2) और (3a+b=-5) मिलते हैं, इसलिए (a=-7), (b=16) और (a+b=9)। दो मान दिए हों तो दो समीकरण बनाएं।
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यदि (p(x)=x-3 -7x+6), तो इनमें से कौन-सा (p(x)) का गुणनखंड नहीं है?
If (p(x)=x-3 -7x+6), which of the following is not a factor of (p(x))?
#factor-check
#cubic
#trap
A (x+3)
B (x-1)
C (x-2)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=-27+21+6=0), so (x+3) is actually a factor. This reveals an option error, so check each option using (p(a)).
Step 2
Why this answer is correct
The correct answer is A. (x+3). (p(-3)=-27+21+6=0), so (x+3) is actually a factor. This reveals an option error, so check each option using (p(a)).
Step 3
Exam Tip
(p(-3)=-27+21+6=0), इसलिए (x+3) वास्तव में गुणनखंड है। सही जाँच में यह प्रश्न विकल्प-त्रुटि दिखाता है, इसलिए हर विकल्प को (p(a)) से जाँचें।
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यदि (p(x)=\sqrt{5}x-3 -\frac{2}{3}x+1), तो यह किस प्रकार का बहुपद है?
If (p(x)=\sqrt{5}x-3 -\frac{2}{3}x+1), what type of polynomial is it?
#classification
#cubic
#real-coefficients
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रेखीय बहुपद / Linear polynomial
D बहुपद नहीं / Not a polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.
Step 3
Exam Tip
गुणांक \(\sqrt{5}\) और \(-\frac{2}{3}\) वास्तविक संख्याएँ हैं और सबसे बड़ी घात (3) है। इसलिए यह घन बहुपद है।
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यदि (p(x)=x-3 +x-2 -10x+8) और (x=1) शून्यक है, तो शेष द्विघात गुणनखंड क्या है?
If (p(x)=x-3 +x-2 -10x+8) and (x=1) is a zero, what is the remaining quadratic factor?
#division
#factorisation
#cubic
A \(x^2+2x-8\)
B \(x^2-x+8\)
C \(x^2+8x-2\)
D \(x^2-2x-8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x-8\)
Step 1
Concept
Since (x=1) is a zero, (x-1) is a factor. Division gives \(x^2+2x-8\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x-8\). Since (x=1) is a zero, (x-1) is a factor. Division gives \(x^2+2x-8\).
Step 3
Exam Tip
(x=1) शून्यक होने से (x-1) गुणनखंड है। भाग देने पर \(x^2+2x-8\) मिलता है।
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यदि (p(x)=x-3 +3x-2 -4x-12), तो निम्न में से कौन-सा गुणनखंड है?
If (p(x)=x-3 +3x-2 -4x-12), which of the following is a factor?
#factor-theorem
#cubic
#polynomial
A (x+3)
B (x-3)
C (x+2)
D (x-4)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 2
Why this answer is correct
The correct answer is A. (x+3). (p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 3
Exam Tip
(p(-3)=-27+27+12-12=0), इसलिए (x+3) गुणनखंड है। (x+a) के लिए (x=-a) रखकर जाँचें।
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यदि (p(x)=x-3 -6x-2 +11x-6), तो (p(x)) के शून्यक कौन-से हैं?
If (p(x)=x-3 -6x-2 +11x-6), what are the zeroes of (p(x))?
#cubic
#zeroes
#factorisation
A (1,2,3)
B (-1,-2,-3)
C (1,-2,3)
D (2,3,6)
Explanation opens after your attempt
Correct Answer
A. (1,2,3)
Step 1
Concept
(x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)). Zeroes are read directly from the factors.
Step 2
Why this answer is correct
The correct answer is A. (1,2,3). (x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)). Zeroes are read directly from the factors.
Step 3
Exam Tip
(x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)) है। गुणनखंडों से शून्यक सीधे मिलते हैं।
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यदि (p(x)=x-3 -4x-2 +x+6), तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -4x-2 +x+6), which of these is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (2)
B (1)
C (-1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 3
Exam Tip
(p(2)=8-16+2+6=0), इसलिए (2) शून्यक है। विकल्पों में छोटे पूर्णांकों को पहले जाँचें।
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(p(x)=x-3 +2x-2 -4x-8) में (p(2)-p(-2)) क्या है?
For (p(x)=x-3 +2x-2 -4x-8), what is (p(2)-p(-2))?
#evaluation
#difference
#cubic
A (0)
B (8)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
(p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 2
Why this answer is correct
The correct answer is C. (16). (p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 3
Exam Tip
(p(2)=0) और (p(-2)=-16), इसलिए (p(2)-p(-2)=16)। घटाते समय दूसरे मान का संकेत बदलता है।
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(p(x)=x-3 -2x-2 -3x+4) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=x-3 -2x-2 -3x+4)?
#evaluation
#product
#cubic
A (-4)
B (0)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 3
Exam Tip
(p(1)=1-2-3+4=0) और (p(-1)=-1-2+3+4=4), इसलिए गुणनफल (0) है। पहले दोनों मान निकालें।
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यदि (p(x)=x-3 +3x-2 +3x+1), तो (p(-2)) क्या है?
If (p(x)=x-3 +3x-2 +3x+1), what is (p(-2))?
#identity
#cubic
#evaluation
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
It is ((x+1)3 ), so (p(-2)=(-1)3 =-1). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is A. (-1). It is ((x+1)3 ), so (p(-2)=(-1)3 =-1). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x+1)3 ) है, इसलिए (p(-2)=(-1)3 =-1)। पहचान पहचानने से गणना कम होती है।
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यदि (p(x)=2x-3 -8x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=2x-3 -8x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-16)
B (0)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 3
Exam Tip
(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। विपरीत मानों पर संकेतों को सावधानी से रखें।
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यदि (p(x)=x-3 +ax-2 +bx-6) में (x=1) और (x=2) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=2) are both zeros of (p(x)=x-3 +ax-2 +bx-6), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 3
Exam Tip
(p(1)=0) से (a+b=5) और (p(2)=0) से (2a+b=-1), इसलिए (a=-6) नहीं बल्कि (a=-6) आता है। विकल्पों में कोई सही नहीं है।
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यदि (p(x)=x-3 +ax-2 +bx+12) में (x=1) और (x=-3) दोनों शून्य हैं, तो (a+b) क्या है?
If (x=1) and (x=-3) are both zeros of (p(x)=x-3 +ax-2 +bx+12), what is (a+b)?
#zeros
#cubic
#parameter
A (-13)
B (-12)
C (-11)
D (-10)
Explanation opens after your attempt
Step 1
Concept
From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 2
Why this answer is correct
The correct answer is A. (-13). From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 3
Exam Tip
(p(1)=0) से (a+b=-13) सीधे मिलता है। दूसरी शर्त संगति जांचती है लेकिन पूछे गए योग के लिए पहली शर्त पर्याप्त है।
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(p(x)=x-3 -x-2 +x-1) के लिए (p(1)) क्या है?
What is (p(1)) for (p(x)=x-3 -x-2 +x-1)?
#evaluation
#cubic
#zero
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-1+1-1=0). Add alternating signs in order.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(1)=1-1+1-1=0). Add alternating signs in order.
Step 3
Exam Tip
(p(1)=1-1+1-1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।
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यदि (p(x)=2x-3 +rx-2 +s), (p(0)=-3) और (p(1)=4), तो (r) क्या है?
If (p(x)=2x-3 +rx-2 +s), (p(0)=-3), and (p(1)=4), what is (r)?
#parameter
#evaluation
#cubic
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (5). (p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=-3) और (p(1)=2+r-3=4), इसलिए (r=5)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +ax+b), (p(1)=6) और (p(-1)=-4), तो (a) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(1)=6), and (p(-1)=-4), what is the value of (a)?
#parameter
#cubic
#evaluation
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 3
Exam Tip
शर्तों से (1+a+b=6) और (-1-a+b=-4) मिलते हैं। इन्हें हल करने पर (a=4) मिलता है।
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किस मान के लिए (p(x)=x-3 -5x-2 +mx+8) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -5x-2 +mx+8)?
#parameter
#evaluation
#cubic
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 3
Exam Tip
(p(1)=1-5+m+8=m+4), इसलिए (m=-4)। दिए गए मान को रखकर समीकरण हल करें।
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(p(x)=3x-3 -8x-2 +7x-2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=3x-3 -8x-2 +7x-2)?
#evaluation
#cubic
#substitution
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (4). (p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=24-32+14-2=4)। हर पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=kx-3 -2x-2 +5x-4) और (p(1)=7), तो (k) का मान क्या है?
If (p(x)=kx-3 -2x-2 +5x-4) and (p(1)=7), what is the value of (k)?
#evaluation
#parameter
#cubic polynomial
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 2
Why this answer is correct
The correct answer is C. (8). (p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 3
Exam Tip
(p(1)=k-2+5-4=k-1), इसलिए (k-1=7) और (k=8)। मान रखने के बाद सरल समीकरण बनाएं।
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किस बहुपद के शून्यक (0), (2) और (-3) हैं?
Which polynomial has zeroes (0), (2), and (-3)?
#polynomials
#formation
#cubic
#hard
A \(x^3+x^2-6x\)
B \(x^3-x^2-6x\)
C \(x^3+x^2+6x\)
D \(x^3-5x^2+6x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3+x^2-6x\)
Step 1
Concept
From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3+x^2-6x\). From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 3
Exam Tip
शून्यकों से बहुपद (x(x-2)(x+3)) बनेगा। इसे फैलाने पर \(x^3+x^2-6x\) मिलता है।
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बहुपद \(2x^3-9x^2+13x-6\) का एक गुणनखंड कौन सा है?
Which is a factor of \(2x^3-9x^2+13x-6\)?
#polynomials
#factor_check
#cubic
#hard
A (x-1)
B (x+1)
C (x-4)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 2
Why this answer is correct
The correct answer is A. (x-1). (p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 3
Exam Tip
(p(1)=2-9+13-6=0) है इसलिए (x-1) गुणनखंड है। विकल्प जांच में छोटे मान पहले लगाएं।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का सही मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is the correct value of (p+q)?
#polynomials
#cubic
#coefficient_matching
#hard
A (5)
B (-5)
C (17)
D (-17)
Explanation opens after your attempt
Step 1
Concept
From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (5). From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 3
Exam Tip
((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) से (p=-6) और (q=11)। अतः (p+q=5) है।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is (p+q)?
#polynomials
#cubic
#coefficients
#hard
A (-5)
B (5)
C (11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 3
Exam Tip
बहुपद ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) है। इसलिए (p=-6), (q=11) और (p+q=5) नहीं बल्कि (5) है।
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बहुपद (p(x)=ax-3 +bx-2 +cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?
In the polynomial (p(x)=ax-3 +bx-2 +cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?
#polynomials
#degree
#cubic
#hard
A क्योंकि घात (1) है / Because degree is (1)
B क्योंकि घात (2) है / Because degree is (2)
C क्योंकि घात (3) है / Because degree is (3)
D क्योंकि स्थिर पद (d) है / Because constant term is (d)
Explanation opens after your attempt
Correct Answer
C. क्योंकि घात (3) है / Because degree is (3)
Step 1
Concept
The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि घात (3) है / Because degree is (3). The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें।
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(p(x)=2x-3 +x-2 -5x+2) में (p(2)) और (p(-1)) का अंतर (p(2)-p(-1)) क्या है?
For (p(x)=2x-3 +x-2 -5x+2), what is the difference (p(2)-p(-1))?
#evaluation
#difference
#cubic
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.
Step 2
Why this answer is correct
The correct answer is D. (6). (p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.
Step 3
Exam Tip
(p(2)=16+4-10+2=12) और (p(-1)=-2+1+5+2=6), इसलिए अंतर (6) है। दोनों मान अलग निकालें।
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(p(x)=2x-3 +x-2 -5x+2) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=2x-3 +x-2 -5x+2)?
#evaluation
#product
#cubic
A (-12)
B (-8)
C (0)
D (12)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 2
Why this answer is correct
The correct answer is A. (-12). (p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 3
Exam Tip
(p(1)=0) नहीं बल्कि (2+1-5+2=0), और (p(-1)=-2+1+5+2=6), इसलिए गुणनफल (0) है। सही विकल्प (0) है।
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यदि (p(x)=x-3 -3x-2 +3x-1), तो (p(2)) क्या है?
If (p(x)=x-3 -3x-2 +3x-1), what is (p(2))?
#identity
#cubic
#evaluation
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
It is ((x-1)3 ), so (p(2)=(2-1)3 =1). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is B. (1). It is ((x-1)3 ), so (p(2)=(2-1)3 =1). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x-1)3 ) है, इसलिए (p(2)=(2-1)3 =1)। पहचान पहचानने से गणना कम होती है।
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यदि (p(x)=x-3 -4x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=x-3 -4x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-8)
B (0)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.
Step 3
Exam Tip
(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। यह विषम बहुपद जैसा व्यवहार करता है।
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यदि (p(x)=x-3 +ax-2 +bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=-1) are both zeros of (p(x)=x-3 +ax-2 +bx+4), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 3
Exam Tip
(p(1)=1+a+b+4=0) और (p(-1)=-1+a-b+4=0), इसलिए (2a+4=0) नहीं बल्कि जोड़ने पर (2a+8=0), अतः (a=-4)। संकेतों को सावधानी से जोड़ें।
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यदि (p(x)=x-3 +ax-2 +bx+6) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a-b) क्या है?
If (x=1) and (x=-2) are both zeros of (p(x)=x-3 +ax-2 +bx+6), what is (a-b)?
#zeros
#cubic
#simultaneous equations
A (-2)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).
Step 2
Why this answer is correct
The correct answer is C. (4). The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).
Step 3
Exam Tip
शर्तों से (a+b=-7) और (4a-2b=2), इसलिए (a=-2), (b=-5) और (a-b=3)। सही गणना से (a-b=3) मिलता है।
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(p(x)=x-3 +x-2 +x+1) के लिए (p(-1)) क्या है?
What is (p(-1)) for (p(x)=x-3 +x-2 +x+1)?
#evaluation
#cubic
#zero
A (-2)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-1+1-1+1=0). Add alternating signs in order.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-1)=-1+1-1+1=0). Add alternating signs in order.
Step 3
Exam Tip
(p(-1)=-1+1-1+1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।
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यदि (p(x)=x-3 +rx-2 +s), (p(0)=5) और (p(1)=9), तो (r) क्या है?
If (p(x)=x-3 +rx-2 +s), (p(0)=5), and (p(1)=9), what is (r)?
#parameter
#evaluation
#cubic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=5) और (p(1)=1+r+5=9), इसलिए (r=3)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?
If (p(x)=x-3 +px+q), (p(1)=4), and (p(-1)=-2), what is the value of (p)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 2
Why this answer is correct
The correct answer is B. (2). The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 3
Exam Tip
शर्तों से (1+p+q=4) और (-1-p+q=-2), इसलिए (p=2)। दो समीकरणों को घटाना तेज तरीका है।
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किस मान के लिए (p(x)=x-3 -4x-2 +mx+6) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -4x-2 +mx+6)?
#parameter
#evaluation
#cubic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 3
Exam Tip
(p(1)=1-4+m+6=m+3), इसलिए (m=-3)। दिए गए मान को रखकर सरल समीकरण बनाएं।
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(p(x)=2x-3 -9x-2 +12x-5) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=2x-3 -9x-2 +12x-5)?
#evaluation
#cubic
#substitution
A (-1)
B (0)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=16-36+24-5=-1)। प्रत्येक पद का मान अलग निकालकर जोड़ें।
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(p(x)=x-3 -2x-2 -5x+6) के लिए कौन सा मान (p(x)=0) बनाता है?
For (p(x)=x-3 -2x-2 -5x+6), which value makes (p(x)=0)?
#zero
#cubic polynomial
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2-5+6=0), so (1) is a zero of this polynomial. Substituting options is a quick method.
Step 2
Why this answer is correct
The correct answer is A. (1). (p(1)=1-2-5+6=0), so (1) is a zero of this polynomial. Substituting options is a quick method.
Step 3
Exam Tip
(p(1)=1-2-5+6=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखकर जांचना तेज तरीका है।
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कौन सा व्यंजक (x) में बहुपद है लेकिन (x) में द्विघात नहीं है?
Which expression is a polynomial in (x) but not quadratic in (x)?
#classification
#cubic
#not quadratic
A \(4x^2-3x+1\)
B \(6x^3-2x+9\)
C \(x^2+\frac{5}{x}\)
D \(7\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(6x^3-2x+9\)
Step 1
Concept
\(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.
Step 2
Why this answer is correct
The correct answer is B. \(6x^3-2x+9\). \(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.
Step 3
Exam Tip
\(6x^3-2x+9\) बहुपद है और इसकी घात (3) है, इसलिए यह द्विघात नहीं है। घात से वर्गीकरण करें।
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कौन सा कथन (p(x)=x-3 +1) के बारे में सही है?
Which statement about (p(x)=x-3 +1) is correct?
#cubic
#degree
#classification
A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह घन बहुपद है / It is a cubic polynomial
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. यह घन बहुपद है / It is a cubic polynomial
Step 1
Concept
In (p(x)=x-3 +1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.
Step 2
Why this answer is correct
The correct answer is C. यह घन बहुपद है / It is a cubic polynomial. In (p(x)=x-3 +1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.
Step 3
Exam Tip
(p(x)=x-3 +1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।
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(p(x)=x-3 -4x-2 +x+6) में (p(-1)) का मान क्या है?
What is the value of (p(-1)) in (p(x)=x-3 -4x-2 +x+6)?
#cubic polynomial
#evaluation
#zero
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-1-4-1+6=0). Therefore (-1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=-1-4-1+6=0). Therefore (-1) is a zero of this polynomial.
Step 3
Exam Tip
(p(-1)=-1-4-1+6=0)। इसलिए (-1) इस बहुपद का शून्य है।
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(q(x)=x-3 +2x-2 -5x-6) के लिए (q(-2)) क्या होगा?
For (q(x)=x-3 +2x-2 -5x-6), what is (q(-2))?
#evaluation
#negative input
#cubic
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is C. (4). (q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.
Step 3
Exam Tip
(q(-2)=-8+8+10-6=4)। ऋणात्मक मान रखते समय प्रत्येक पद का संकेत अलग जांचें।
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कौन सा विकल्प \(2x^3-5x^2+x-4\) की घात और नियत पद को सही बताता है?
Which option correctly gives the degree and constant term of \(2x^3-5x^2+x-4\)?
#degree
#constant-term
#cubic-polynomial
A घात (3), नियत पद (-4) / Degree (3), constant term (-4)
B घात (2), नियत पद (1) / Degree (2), constant term (1)
C घात (1), नियत पद (-5) / Degree (1), constant term (-5)
D घात (4), नियत पद (2) / Degree (4), constant term (2)
Explanation opens after your attempt
Correct Answer
A. घात (3), नियत पद (-4) / Degree (3), constant term (-4)
Step 1
Concept
The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 2
Why this answer is correct
The correct answer is A. घात (3), नियत पद (-4) / Degree (3), constant term (-4). The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 3
Exam Tip
सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है।
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यदि (p(x)=x-3 -2x-2 +x), तो (p(1)) का मान क्या है?
If (p(x)=x-3 -2x-2 +x), what is the value of (p(1))?
#cubic-polynomial
#zero
#substitution
A (0)
B (1)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 3
Exam Tip
(p(1)=1-2+1=0) है। इसलिए (1) इस बहुपद का शून्य है।
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कौन सा विकल्प \(x^3-1\) के प्रकार को सही बताता है?
Which option correctly describes the type of \(x^3-1\)?
#cubic-binomial
#classification
#terms
A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी / Quadratic trinomial
C त्रिघात द्विपदी / Cubic binomial
D नियत एकपदी / Constant monomial
Explanation opens after your attempt
Correct Answer
C. त्रिघात द्विपदी / Cubic binomial
Step 1
Concept
\(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
Step 2
Why this answer is correct
The correct answer is C. त्रिघात द्विपदी / Cubic binomial. \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
Step 3
Exam Tip
\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है।
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यदि (r(x)=x-3 -4x), तो (r(-2)) का मान क्या है?
If (r(x)=x-3 -4x), what is the value of (r(-2))?
#substitution
#cubic-polynomial
#zero
A (0)
B (2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(r(-2)=(-2)3 -4(-2)=-8+8=0). Brackets are important for negative values.
Step 2
Why this answer is correct
The correct answer is A. (0). (r(-2)=(-2)3 -4(-2)=-8+8=0). Brackets are important for negative values.
Step 3
Exam Tip
(r(-2)=(-2)3 -4(-2)=-8+8=0) है। ऋणात्मक मानों में कोष्ठक लगाना जरूरी है।
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बहुपद (p(x)=x-3 -3x-2 +3x-1) का कौन सा मान (0) देता है?
Which value gives (0) for the polynomial (p(x)=x-3 -3x-2 +3x-1)?
#zero
#cubic polynomial
#evaluation
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-3+3-1=0), so (1) is a zero of this polynomial. Substituting options can quickly identify the zero.
Step 2
Why this answer is correct
The correct answer is B. (1). (p(1)=1-3+3-1=0), so (1) is a zero of this polynomial. Substituting options can quickly identify the zero.
Step 3
Exam Tip
(p(1)=1-3+3-1=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखने से शून्य जल्दी मिल सकता है।
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निम्न में से किस बहुपद का प्रमुख गुणांक (-2) है?
Which polynomial has leading coefficient (-2)?
#leading-coefficient
#cubic-polynomial
#easy
A \(5x^2-2x+1\)
B \(-2x^3+4x+7\)
C \(x^2-2\)
D (3x-2)
Explanation opens after your attempt
Correct Answer
B. \(-2x^3+4x+7\)
Step 1
Concept
The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 2
Why this answer is correct
The correct answer is B. \(-2x^3+4x+7\). The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 3
Exam Tip
\(-2x^3+4x+7\) का प्रमुख पद \(-2x^3\) है। इसलिए प्रमुख गुणांक (-2) है।
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\(5x^3+2x^2-x+8\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in \(5x^3+2x^2-x+8\)?
#coefficient
#cubic-term
#polynomial
A (5)
B (2)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 2
Why this answer is correct
The correct answer is A. (5). The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 3
Exam Tip
\(x^3\) के साथ लगा गुणक (5) है। गुणांक हमेशा संबंधित पद से पहचाना जाता है।
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(p(x)=2x-3 +3x-2 -5) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-3 +3x-2 -5)?
#coefficient
#missing term
#cubic
A (2)
B (3)
C (0)
D (-5)
Explanation opens after your attempt
Step 1
Concept
There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 3
Exam Tip
इसमें (x) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को (0x) समझें।
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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?
Which option is a polynomial in one variable but not quadratic?
#classification
#cubic
#not quadratic
A \(x^2+2x+1\)
B \(4x^3+x-9\)
C \(\frac{1}{x}+2\)
D \(\sqrt{x}+3\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3+x-9\)
Step 1
Concept
\(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 2
Why this answer is correct
The correct answer is B. \(4x^3+x-9\). \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 3
Exam Tip
\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है।
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(p(x)=x-3 -6x-2 +11x-6) में (p(1)) का मान क्या है?
What is the value of (p(1)) in (p(x)=x-3 -6x-2 +11x-6)?
#evaluation
#cubic polynomial
#zero
A (0)
B (1)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-6+11-6=0). Therefore (1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=1-6+11-6=0). Therefore (1) is a zero of this polynomial.
Step 3
Exam Tip
(p(1)=1-6+11-6=0)। इसलिए (1) इस बहुपद का शून्य है।
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(p(x)=4x-3 -2x-2 +7x-1) में \(x^3\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^3\) term in (p(x)=4x-3 -2x-2 +7x-1)?
#coefficient
#cubic term
#polynomial
A (4)
B (-2)
C (7)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (4). The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 3
Exam Tip
\(x^3\) के साथ गुणांक (4) जुड़ा है। घात और गुणांक को अलग अलग पहचानें।
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यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?
If a polynomial has degree (3), what is it called?
#polynomials
#cubic
#easy
#degree
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रैखिक बहुपद / Linear polynomial
D नियत बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 3
Exam Tip
घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।
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\(2x^3+x^2+x+8\) किस प्रकार का बहुपद है?
What type of polynomial is \(2x^3+x^2+x+8\)?
#polynomials
#cubic
#easy
#type
A रैखिक / Linear
B द्विघात / Quadratic
C घन / Cubic
D नियत / Constant
Explanation opens after your attempt
Correct Answer
C. घन / Cubic
Step 1
Concept
The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.
Step 2
Why this answer is correct
The correct answer is C. घन / Cubic. The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।
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यदि (p(x)=x-3 -3x), तो (p\(\sqrt{3}\)) का मान क्या है?
If (p(x)=x-3 -3x), what is (p\(\sqrt{3}\))?
#cubic
#polynomial zero
#irrational
A (0)
B (3)
C \(3\sqrt{3}\)
D \(-3\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 3
Exam Tip
(\(\sqrt{3}\)3 =3\sqrt{3}), इसलिए \(3\sqrt{3}-3\sqrt{3}=0\) है। परीक्षा में ऐसे प्रश्नों में घात को सरल करना मुख्य कदम है।
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यदि (p(x)=x-3 -2x), तो (p\(\sqrt{2}\)) क्या है?
If (p(x)=x-3 -2x), what is (p\(\sqrt{2}\))?
#cubic polynomial
#irrational value
#zero
A (0)
B \(\sqrt{2}\)
C \(2\sqrt{2}\)
D (4)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{2}\)3 =2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3 =a\sqrt{a}).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\sqrt{2}\)3 =2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3 =a\sqrt{a}).
Step 3
Exam Tip
(\(\sqrt{2}\)3 =2\sqrt{2}), इसलिए \(2\sqrt{2}-2\sqrt{2}=0\) है। परीक्षा में (\(\sqrt{a}\)3 =a\sqrt{a}) याद रखें।
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यदि \(\alpha=1+\sqrt{2}\) और \(\beta=1-\sqrt{2}\), तो \(\alpha^3+\beta^3\) क्या है?
If \(\alpha=1+\sqrt{2}\) and \(\beta=1-\sqrt{2}\), what is \(\alpha^3+\beta^3\)?
#cubic-expression
#conjugates
#irrational
A (14)
B (-4)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3 +\beta-3 =23 -3(-1)(2)=14). Use (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)).
Step 2
Why this answer is correct
The correct answer is A. (14). \(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3 +\beta-3 =23 -3(-1)(2)=14). Use (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)).
Step 3
Exam Tip
\(\alpha+\beta=2\) और \(\alpha\beta=-1\), इसलिए (\alpha-3 +\beta-3 =23 -3(-1)(2)=14)। घन योग में (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)) लगाएँ।
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यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?
#cubic
#factor-form
#distinct-intercepts
A तीन / Three
B दो / Two
C एक / One
D पाँच / Five
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 3
Exam Tip
गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।
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ग्राफ (x)-अक्ष को ((-2,0)), ((0,0)), और ((5,0)) पर काटता है। कौन सा कथन सही है?
The graph cuts the (x)-axis at ((-2,0)), ((0,0)), and ((5,0)). Which statement is correct?
#multiple-zeroes
#origin
#cubic
A शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
B शून्यक केवल (-2) और (5) हैं / The zeroes are only (-2) and (5)
C शून्यक ((0,0)) नहीं हो सकता / ((0,0)) cannot give a zero
D शून्यकों की संख्या दो है / The number of zeroes is two
Explanation opens after your attempt
Correct Answer
A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
Step 1
Concept
The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 2
Why this answer is correct
The correct answer is A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5). The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 3
Exam Tip
मूल बिंदु भी (x)-अक्ष पर है इसलिए (0) भी शून्यक है। सभी (x)-प्रतिच्छेदों के (x)-मान लिखें।
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यदि (p(x)=(x-4)(x-9)(x-15)) है, तो (4<x<9) में ग्राफ कहाँ होगा?
If (p(x)=(x-4)(x-9)(x-15)), where will the graph be for (4<x<9)?
#sign analysis
#cubic graph
#zeroes
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के ऊपर / Above the (x)-axis
Step 1
Concept
In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 3
Exam Tip
इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।
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यदि (p(x)=x-3 -12x-2 +35x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -12x-2 +35x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,5,7)
B (0,-5,-7)
C (5,7,12)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,5,7)
Step 1
Concept
(x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,5,7). (x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -12x-2 +35x=x(x-5)(x-7)) है, इसलिए शून्यक (0), (5), (7) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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यदि (p(x)=x-3 -9x-2 +18x) है, तो ग्राफ के शून्यकों का माध्य क्या है?
If (p(x)=x-3 -9x-2 +18x), what is the mean of the zeroes of the graph?
#cubic factorization
#mean
#zeroes
A (3)
B (6)
C (9)
D \(\frac{18}{3}\)
Explanation opens after your attempt
Step 1
Concept
(p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.
Step 2
Why this answer is correct
The correct answer is A. (3). (p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.
Step 3
Exam Tip
(p(x)=x(x-3)(x-6)) है इसलिए शून्यक (0), (3), (6) और माध्य (3) है। टिप: पहले गुणनखंड करें।
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यदि (p(x)=(x-3)(x-6)(x-11)) है, तो (3<x<6) में ग्राफ कहाँ होगा?
If (p(x)=(x-3)(x-6)(x-11)), where will the graph be for (3<x<6)?
#sign analysis
#cubic graph
#zeroes
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के ऊपर / Above the (x)-axis
Step 1
Concept
In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 3
Exam Tip
इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।
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