100 results found for "coefficient_identification" in Class 10.
कौन-सा व्यंजक (x) में बहुपद है?
Which expression is a polynomial in (x)?
#polynomial_identification
#fraction_coefficient
#basics
A \(x^{\frac{3}{2}}+1\)
B \(x^2+\frac{1}{3}x+2\)
C \(\frac{1}{x^2}+1\)
D \(\sqrt{x^3}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+\frac{1}{3}x+2\)
Step 1
Concept
In \(x^2+\frac{1}{3}x+2\), the powers of (x) are (2), (1), and (0). So it is a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+\frac{1}{3}x+2\). In \(x^2+\frac{1}{3}x+2\), the powers of (x) are (2), (1), and (0). So it is a polynomial.
Step 3
Exam Tip
\(x^2+\frac{1}{3}x+2\) में (x) की घातें (2), (1) और (0) हैं। इसलिए यह बहुपद है।
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कौन-सा व्यंजक एक चर वाला बहुपद है जिसमें वास्तविक गुणांक हैं?
Which expression is a polynomial in one variable with real coefficients?
#real_coefficients
#polynomial_identification
#irrational_coefficient
A \(\sqrt{2}x^2-3x+1\)
B \(\sqrt{x}+2\)
C \(x^{-2}+1\)
D \(\frac{1}{x}+3\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}x^2-3x+1\)
Step 1
Concept
\(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}x^2-3x+1\). \(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.
Step 3
Exam Tip
\(\sqrt{2}\) एक वास्तविक संख्या है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह बहुपद है।
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\(\frac{x^2+1}{2}\) के बारे में कौन-सा कथन सही है?
Which statement is correct about \(\frac{x^2+1}{2}\)?
#real_coefficients
#polynomial_identification
#basics
A यह बहुपद है / It is a polynomial
B यह बहुपद नहीं है / It is not a polynomial
C इसमें दो चर हैं / It has two variables
D इसकी घात परिभाषित नहीं है / Its degree is undefined
Explanation opens after your attempt
Correct Answer
A. यह बहुपद है / It is a polynomial
Step 1
Concept
\(\frac{x^2+1}{2}=\frac{1}{2}x^2+\frac{1}{2}\) and the coefficients are real. So it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. यह बहुपद है / It is a polynomial. \(\frac{x^2+1}{2}=\frac{1}{2}x^2+\frac{1}{2}\) and the coefficients are real. So it is a polynomial.
Step 3
Exam Tip
\(\frac{x^2+1}{2}=\frac{1}{2}x^2+\frac{1}{2}\) है और गुणांक वास्तविक हैं। इसलिए यह बहुपद है।
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यदि किसी स्थान पर ज्वारीय खारा जल और मैंग्रोव दोनों मिलते हों तो सही पहचान क्या है?
If a place has both tidal saline water and mangroves what is the correct identification?
#sundarbans
#mangrove
#tidal-water
A सुंदरवन / Sundarbans
B लद्दाख / Ladakh
C अरावली / Aravalli
D दक्कन ट्रैप / Deccan Trap
Explanation opens after your attempt
Correct Answer
A. सुंदरवन / Sundarbans
Step 1
Concept
Sundarbans is the tidal saline mangrove area of Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 2
Why this answer is correct
The correct answer is A. सुंदरवन / Sundarbans. Sundarbans is the tidal saline mangrove area of Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 3
Exam Tip
सुंदरवन गंगा ब्रह्मपुत्र डेल्टा का ज्वारीय खारा मैंग्रोव क्षेत्र है। परीक्षा में यह संकेत तुरंत पहचानें।
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यदि नदी पश्चिम की ओर दरार घाटी से बहकर अरब सागर में जाए तो सही पहचान क्या है?
If a river flows westward through a rift valley into the Arabian Sea what is the correct identification?
#narmada
#rift-valley
#arabian-sea
A नर्मदा / Narmada
B गंगा / Ganga
C ब्रह्मपुत्र / Brahmaputra
D महानदी / Mahanadi
Explanation opens after your attempt
Correct Answer
A. नर्मदा / Narmada
Step 1
Concept
Narmada flows west through a rift valley into the Arabian Sea. For exams treat Narmada and Tapi as exceptions.
Step 2
Why this answer is correct
The correct answer is A. नर्मदा / Narmada. Narmada flows west through a rift valley into the Arabian Sea. For exams treat Narmada and Tapi as exceptions.
Step 3
Exam Tip
नर्मदा दरार घाटी से पश्चिम की ओर अरब सागर में गिरती है। परीक्षा में नर्मदा और तापी को अपवाद मानें।
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यदि किसी क्षेत्र में ज्वारीय खारा दलदल और मैंग्रोव दोनों मिलते हों तो सही पहचान क्या होगी?
If an area has both tidal saline marsh and mangroves what would be the correct identification?
#sundarbans
#mangrove
#tidal-delta
A लद्दाख / Ladakh
B सुंदरवन / Sundarbans
C अरावली / Aravalli
D थार / Thar
Explanation opens after your attempt
Correct Answer
B. सुंदरवन / Sundarbans
Step 1
Concept
Sundarbans is the tidal saline mangrove area of the Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 2
Why this answer is correct
The correct answer is B. सुंदरवन / Sundarbans. Sundarbans is the tidal saline mangrove area of the Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 3
Exam Tip
सुंदरवन गंगा ब्रह्मपुत्र डेल्टा का ज्वारीय खारा मैंग्रोव क्षेत्र है। परीक्षा में यह संकेत तुरंत पहचानें।
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यदि किसी स्थल में ज्वारीय खारा दलदल और मैंग्रोव दोनों हों तो सबसे उपयुक्त पहचान क्या होगी?
If a place has both tidal saline marsh and mangroves what is the most suitable identification?
#sundarbans
#mangrove
#tidal-marsh
A सुंदरवन / Sundarbans
B लद्दाख / Ladakh
C अरावली / Aravalli
D थार / Thar
Explanation opens after your attempt
Correct Answer
A. सुंदरवन / Sundarbans
Step 1
Concept
Sundarbans is the tidal saline mangrove area of the Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 2
Why this answer is correct
The correct answer is A. सुंदरवन / Sundarbans. Sundarbans is the tidal saline mangrove area of the Ganga Brahmaputra Delta. For exams identify this clue quickly.
Step 3
Exam Tip
सुंदरवन गंगा ब्रह्मपुत्र डेल्टा का ज्वारीय खारा मैंग्रोव क्षेत्र है। परीक्षा में यह संकेत तुरंत पहचानें।
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खादर मिट्टी की सबसे सरल पहचान क्या है?
What is the simplest identification of Khadar soil?
#khadar
#new-alluvium
#soil
A पुरानी जलोढ़ मिट्टी / Old alluvium
B नई जलोढ़ मिट्टी / New alluvium
C काली मिट्टी / Black soil
D पर्वतीय मिट्टी / Mountain soil
Explanation opens after your attempt
Correct Answer
B. नई जलोढ़ मिट्टी / New alluvium
Step 1
Concept
Khadar is new alluvium formed by river floods. For exams remember Khadar as new and fertile.
Step 2
Why this answer is correct
The correct answer is B. नई जलोढ़ मिट्टी / New alluvium. Khadar is new alluvium formed by river floods. For exams remember Khadar as new and fertile.
Step 3
Exam Tip
खादर नदी की बाढ़ से बनी नई जलोढ़ मिट्टी है। परीक्षा में खादर को नया और उपजाऊ याद रखें।
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चिचेन इत्ज़ा की कठिन पहचान में कौन सा सांस्कृतिक संपर्क प्रमुख माना जाता है?
In advanced identification of Chichen Itza which cultural contact is considered important?
#chichen-itza
#maya
#toltec
A माया और टोल्टेक प्रभाव / Maya and Toltec influence
B रोमन और गॉथिक प्रभाव / Roman and Gothic influence
C मुगल और चोल प्रभाव / Mughal and Chola influence
D नॉर्स और सेल्टिक प्रभाव / Norse and Celtic influence
Explanation opens after your attempt
Correct Answer
A. माया और टोल्टेक प्रभाव / Maya and Toltec influence
Step 1
Concept
Chichen Itza has architectural signs of Maya and Toltec influences. For exams remember Mexico and Mesoamerica.
Step 2
Why this answer is correct
The correct answer is A. माया और टोल्टेक प्रभाव / Maya and Toltec influence. Chichen Itza has architectural signs of Maya and Toltec influences. For exams remember Mexico and Mesoamerica.
Step 3
Exam Tip
चिचेन इत्ज़ा में माया और टोल्टेक प्रभावों के स्थापत्य संकेत मिलते हैं। परीक्षा में मेक्सिको और मेसोअमेरिका याद रखें।
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मिश्रित विश्व धरोहर स्थल की विशेषज्ञ पहचान क्या होगी?
What is the expert identification of a mixed World Heritage Site?
#mixed-heritage
#cultural-natural
#world-heritage
A जहां केवल आधुनिक इमारतें हों / Where only modern buildings exist
B जहां सांस्कृतिक और प्राकृतिक दोनों असाधारण मूल्य हों / Where both cultural and natural exceptional values exist
C जहां केवल युद्ध स्मारक हो / Where there is only a war memorial
D जहां कोई संरक्षण नियम न हो / Where there are no conservation rules
Explanation opens after your attempt
Correct Answer
B. जहां सांस्कृतिक और प्राकृतिक दोनों असाधारण मूल्य हों / Where both cultural and natural exceptional values exist
Step 1
Concept
A mixed site meets both cultural and natural criteria. For exams understand such sites as a separate category.
Step 2
Why this answer is correct
The correct answer is B. जहां सांस्कृतिक और प्राकृतिक दोनों असाधारण मूल्य हों / Where both cultural and natural exceptional values exist. A mixed site meets both cultural and natural criteria. For exams understand such sites as a separate category.
Step 3
Exam Tip
मिश्रित स्थल सांस्कृतिक और प्राकृतिक दोनों मानदंडों को पूरा करता है। परीक्षा में ऐसे स्थलों को अलग श्रेणी समझें।
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1998 में भारत रत्न पाने वाले दोनों व्यक्तियों की सही पहचान क्या है?
What is the correct identification of both Bharat Ratna recipients in 1998?
#bharat ratna awards
#1998
#important dates
A अमर्त्य सेन और पंडित रवि शंकर / Amartya Sen and Pandit Ravi Shankar
B एम एस सुब्बुलक्ष्मी और सी सुब्रमण्यम / M S Subbulakshmi and C Subramaniam
C लता मंगेशकर और उस्ताद बिस्मिल्लाह खान / Lata Mangeshkar and Ustad Bismillah Khan
D सचिन तेंदुलकर और सी एन आर राव / Sachin Tendulkar and C N R Rao
Explanation opens after your attempt
Correct Answer
B. एम एस सुब्बुलक्ष्मी और सी सुब्रमण्यम / M S Subbulakshmi and C Subramaniam
Step 1
Concept
In 1998 M S Subbulakshmi and C Subramaniam received the Bharat Ratna. Distinguish music and Green Revolution policy.
Step 2
Why this answer is correct
The correct answer is B. एम एस सुब्बुलक्ष्मी और सी सुब्रमण्यम / M S Subbulakshmi and C Subramaniam. In 1998 M S Subbulakshmi and C Subramaniam received the Bharat Ratna. Distinguish music and Green Revolution policy.
Step 3
Exam Tip
1998 में एम एस सुब्बुलक्ष्मी और सी सुब्रमण्यम को भारत रत्न मिला। परीक्षा में संगीत और हरित क्रांति नीति को अलग अलग पहचानें।
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ताना भगत आंदोलन की विशेषज्ञ पहचान क्या है?
What is the expert identification of the Tana Bhagat Movement?
#indian history
#tana bhagat
#oraon
#gk
A सिर्फ सैनिक विद्रोह / Only military mutiny
B गुरुद्वारा प्रबंधन आंदोलन / Gurdwara management movement
C ओरांव समाज का धार्मिक-सामाजिक सुधार और औपनिवेशिक विरोध / Religious-social reform and anti-colonial protest of the Oraon community
D नौसेना वेतन संघर्ष / Naval wage struggle
Explanation opens after your attempt
Correct Answer
C. ओरांव समाज का धार्मिक-सामाजिक सुधार और औपनिवेशिक विरोध / Religious-social reform and anti-colonial protest of the Oraon community
Step 1
Concept
The Tana Bhagat Movement was linked with the Oraon community and Jatra Bhagat. Study it as both reform and resistance.
Step 2
Why this answer is correct
The correct answer is C. ओरांव समाज का धार्मिक-सामाजिक सुधार और औपनिवेशिक विरोध / Religious-social reform and anti-colonial protest of the Oraon community. The Tana Bhagat Movement was linked with the Oraon community and Jatra Bhagat. Study it as both reform and resistance.
Step 3
Exam Tip
ताना भगत आंदोलन ओरांव समुदाय और जत्रा भगत से जुड़ा था। इसे अहिंसक सुधार और प्रतिरोध दोनों के रूप में पढ़ें।
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अशोक के शिलालेखों में प्रियदर्शी और अशोक की पहचान किस अभिलेख से स्पष्ट हुई?
Which inscription clarified the identification of Piyadassi with Ashoka in Ashokan records?
#ancient-history
#maski
#ashoka
A मास्की लघु शिलालेख / Maski minor rock edict
B मंदसौर अभिलेख / Mandsaur inscription
C ऐहोल अभिलेख / Aihole inscription
D जूनागढ़ अभिलेख / Junagadh inscription
Explanation opens after your attempt
Correct Answer
A. मास्की लघु शिलालेख / Maski minor rock edict
Step 1
Concept
The name Ashoka in the Maski edict clarified the identity of Piyadassi. For exams, remember the relation between name and title.
Step 2
Why this answer is correct
The correct answer is A. मास्की लघु शिलालेख / Maski minor rock edict. The name Ashoka in the Maski edict clarified the identity of Piyadassi. For exams, remember the relation between name and title.
Step 3
Exam Tip
मास्की लेख में अशोक नाम मिलने से प्रियदर्शी की पहचान स्पष्ट हुई। परीक्षा में नाम और उपाधि का संबंध याद रखें।
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सिंधु सभ्यता के लोग व्यापार में पहचान के लिए किस वस्तु का उपयोग करते थे?
What object did Indus people commonly use for identification in trade?
#seals
#indus_trade
#ancient_history
A सिक्के / Coins
B मुहरें / Seals
C ताम्रपत्र / Copper plates
D कागज / Paper
Explanation opens after your attempt
Correct Answer
B. मुहरें / Seals
Step 1
Concept
Seals were used in the Indus Civilization for trade and identification. Animal seals are frequently asked in exams.
Step 2
Why this answer is correct
The correct answer is B. मुहरें / Seals. Seals were used in the Indus Civilization for trade and identification. Animal seals are frequently asked in exams.
Step 3
Exam Tip
सिंधु सभ्यता में मुहरों का उपयोग व्यापार और पहचान के लिए होता था। पशु आकृतियों वाली मुहरें परीक्षा में अक्सर पूछी जाती हैं।
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यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?
If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D सदैव दो हल / Always two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 3
Exam Tip
यह स्थिति अलग-अलग समांतर रेखाएँ बनाती है। इसलिए युग्म असंगत होता है।
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समीकरणों (6x+7y=55) और (6x-2y=10) को हल करने पर (y) का मान क्या है?
Solving (6x+7y=55) and (6x-2y=10), what is the value of (y)?
#pair-linear-equations-same-coefficient
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (9y=45), so (y=5). Equal coefficients make subtraction faster.
Step 2
Why this answer is correct
The correct answer is C. (5). Subtracting the second equation from the first gives (9y=45), so (y=5). Equal coefficients make subtraction faster.
Step 3
Exam Tip
पहले समीकरण में से दूसरा घटाने पर (9y=45), इसलिए (y=5)। समान गुणांक दिखें तो घटाने की विधि तेज होती है।
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समीकरणों (13x-6y=8) और (13x+4y=48) में (y) का मान क्या है?
In (13x-6y=8) and (13x+4y=48), what is the value of (y)?
#pair-linear-equations
#same-coefficient
#elimination
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Subtracting the first equation from the second gives (10y=40), so (y=4). When (x)-coefficients are equal, subtract directly.
Step 2
Why this answer is correct
The correct answer is C. (4). Subtracting the first equation from the second gives (10y=40), so (y=4). When (x)-coefficients are equal, subtract directly.
Step 3
Exam Tip
दूसरे में से पहला घटाने पर (10y=40), इसलिए (y=4)। समान (x)-गुणांक होने पर सीधे घटाएं।
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यदि (4x+9y=41) और (4x-3y=5), तो (y) का मान क्या है?
If (4x+9y=41) and (4x-3y=5), what is the value of (y)?
#pair-linear-equations
#elimination
#same-coefficient
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (12y=36), so (y=3). When coefficients are equal, subtraction is efficient.
Step 2
Why this answer is correct
The correct answer is B. (3). Subtracting the second equation from the first gives (12y=36), so (y=3). When coefficients are equal, subtraction is efficient.
Step 3
Exam Tip
पहले समीकरण में से दूसरा घटाने पर (12y=36), इसलिए (y=3)। समान गुणांक दिखें तो घटाना आसान होता है।
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विलोपन विधि से (x+2y=13) और (3x-2y=23) का हल निकालें।
Find the solution of (x+2y=13) and (3x-2y=23) by elimination.
#linear equations
#elimination
#opposite coefficients
#medium
#class 10
A ( (6,4) )
B ( (8,3) )
C ( (9,2) )
D ( (7,3) )
Explanation opens after your attempt
Correct Answer
C. ( (9,2) )
Step 1
Concept
Adding both equations gives (4x=36), so (x=9) and (y=2). Identify opposite (2y) terms.
Step 2
Why this answer is correct
The correct answer is C. ( (9,2) ). Adding both equations gives (4x=36), so (x=9) and (y=2). Identify opposite (2y) terms.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (4x=36), इसलिए (x=9) और (y=2)। विपरीत (2y) पदों को पहचानें।
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विलोपन विधि से (3x+2y=23) और (3x-y=11) को हल करें।
Solve (3x+2y=23) and (3x-y=11) by elimination.
#linear equations
#elimination
#equal coefficient
#medium
#class 10
A ( (5,4) )
B ( (4,5) )
C ( (6,3) )
D ( (3,6) )
Explanation opens after your attempt
Correct Answer
A. ( (5,4) )
Step 1
Concept
Subtracting the second equation from the first gives (3y=12), so (y=4) and (x=5). Equal (x)-coefficients make elimination faster.
Step 2
Why this answer is correct
The correct answer is A. ( (5,4) ). Subtracting the second equation from the first gives (3y=12), so (y=4) and (x=5). Equal (x)-coefficients make elimination faster.
Step 3
Exam Tip
पहले समीकरण से दूसरे को घटाने पर (3y=12), इसलिए (y=4) और (x=5)। समान (x) गुणांक दिखें तो विलोपन तेज होता है।
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यदि (3x-2y=4) और (x=4), तो (y) का मान क्या है?
If (3x-2y=4) and (x=4), what is the value of (y)?
#linear equations
#substitution
#negative coefficient
#easy
#class 10
A (y=1)
B (y=2)
C (y=3)
D (y=4)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) gives (12-2y=4), so (y=4). Check signs while solving a term with a negative coefficient.
Step 2
Why this answer is correct
The correct answer is D. (y=4). Putting (x=4) gives (12-2y=4), so (y=4). Check signs while solving a term with a negative coefficient.
Step 3
Exam Tip
(x=4) रखने पर (12-2y=4), इसलिए (y=4)। ऋण गुणांक वाले पद को हल करते समय चिन्ह जांचें।
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यदि (2x-y=1) और (x=5), तो (y) का मान क्या है?
If (2x-y=1) and (x=5), what is (y)?
#linear equations
#substitution
#negative coefficient
#easy
#class 10
A (y=9)
B (y=8)
C (y=7)
D (y=6)
Explanation opens after your attempt
Step 1
Concept
(10-y=1), so (y=9). In this type of question, solve (-y) correctly.
Step 2
Why this answer is correct
The correct answer is A. (y=9). (10-y=1), so (y=9). In this type of question, solve (-y) correctly.
Step 3
Exam Tip
(10-y=1), इसलिए (y=9)। इस प्रकार के प्रश्न में (-y) को सही तरह हल करें।
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विलोपन विधि से हल करें: (3x+y=11) और (3x-y=7)।
Solve by elimination: (3x+y=11) and (3x-y=7).
#linear equations
#elimination
#equal coefficients
#easy
#class 10
A ( (2,5) )
B ( (4,-1) )
C ( (1,8) )
D ( (3,2) )
Explanation opens after your attempt
Correct Answer
D. ( (3,2) )
Step 1
Concept
Adding gives (6x=18), so (x=3) and (y=2). In elimination, remove the variable with equal coefficients first.
Step 2
Why this answer is correct
The correct answer is D. ( (3,2) ). Adding gives (6x=18), so (x=3) and (y=2). In elimination, remove the variable with equal coefficients first.
Step 3
Exam Tip
जोड़ने पर (6x=18), इसलिए (x=3) और (y=2)। विलोपन में पहले उस चर को हटाएँ जिसके गुणांक समान हों।
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रेखाएं (3x-8y=11) और (6x-16y=25) का ग्राफीय निष्कर्ष क्या है?
What is the graphical conclusion for (3x-8y=11) and (6x-16y=25)?
#graphical method
#parallel lines
#no solution
#negative coefficient
A अद्वितीय समाधान / Unique solution
B अनंत समाधान / Infinitely many solutions
C कोई समाधान नहीं / No solution
D दोनों रेखाएं समान हैं / Both lines are same
Explanation opens after your attempt
Correct Answer
C. कोई समाधान नहीं / No solution
Step 1
Concept
\(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
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रेखाएं (2x-5y=7) और (4x-10y=16) का ग्राफीय निष्कर्ष क्या है?
What is the graphical conclusion for (2x-5y=7) and (4x-10y=16)?
#graphical method
#parallel lines
#no solution
#negative coefficient
A अद्वितीय समाधान / Unique solution
B अनंत समाधान / Infinitely many solutions
C कोई समाधान नहीं / No solution
D दोनों रेखाएं समान हैं / Both lines are same
Explanation opens after your attempt
Correct Answer
C. कोई समाधान नहीं / No solution
Step 1
Concept
\(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
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किस युग्म की रेखाएं अलग गुणांक अनुपातों के कारण एक अद्वितीय समाधान देंगी?
Which pair will give a unique solution because of different coefficient ratios?
#graphical method
#unique solution
#intersecting lines
#ratio test
A (4x+8y=16), (x+2y=5)
B (5x-2y=11), (x+y=7)
C (6x-3y=9), (2x-y=3)
D (7x+14y=28), (x+2y=4)
Explanation opens after your attempt
Correct Answer
B. (5x-2y=11), (x+y=7)
Step 1
Concept
For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is B. (5x-2y=11), (x+y=7). For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 3
Exam Tip
(5x-2y=11) और (x+y=7) में \(\frac{5}{1}\neq\frac{-2}{1}\), इसलिए रेखाएं प्रतिच्छेदी हैं। अलग गुणांक अनुपात अद्वितीय समाधान देता है।
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रेखाएं (x-3y=2) और (2x-6y=9) का ग्राफीय निष्कर्ष क्या है?
What is the graphical conclusion for (x-3y=2) and (2x-6y=9)?
#graphical method
#parallel lines
#no solution
#negative coefficient
A अद्वितीय समाधान / Unique solution
B अनंत समाधान / Infinitely many solutions
C कोई समाधान नहीं / No solution
D दोनों रेखाएं समान हैं / Both lines are same
Explanation opens after your attempt
Correct Answer
C. कोई समाधान नहीं / No solution
Step 1
Concept
\(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
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रेखाएं (2x-3y=6) और (4x-6y=13) के लिए सही ग्राफीय निष्कर्ष कौन सा है?
Which graphical conclusion is correct for (2x-3y=6) and (4x-6y=13)?
#linear equations
#graphical method
#negative coefficient
#parallel lines
A एक अद्वितीय समाधान / One unique solution
B कोई समाधान नहीं / No solution
C अनंत समाधान / Infinitely many solutions
D दो प्रतिच्छेद / Two intersections
Explanation opens after your attempt
Correct Answer
B. कोई समाधान नहीं / No solution
Step 1
Concept
\(\frac{2}{4}=\frac{-3}{-6}\neq\frac{6}{13}\), so the lines are parallel. Distinct parallel lines have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. \(\frac{2}{4}=\frac{-3}{-6}\neq\frac{6}{13}\), so the lines are parallel. Distinct parallel lines have no intersection.
Step 3
Exam Tip
\(\frac{2}{4}=\frac{-3}{-6}\neq\frac{6}{13}\), इसलिए रेखाएं समांतर हैं। समांतर अलग-अलग रेखाओं का कोई प्रतिच्छेद नहीं होता।
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यदि (p(x)=x-2 +px+q) और (p(1)=0,\ p(2)=0), तो (p+q) क्या है?
If (p(x)=x-2 +px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?
#coefficient-finding
#zeroes
#quadratic
A -(1)
B (1)
C -(2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 2
Why this answer is correct
The correct answer is A. -(1). The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 3
Exam Tip
शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)।
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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 (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 (x=2) और (x=-3), (p(x)=ax-2 +bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?
If (x=2) and (x=-3) are zeroes of (p(x)=ax-2 +bx+c), what is \(\frac{c}{a}\)?
#zeroes
#coefficient-relation
#quadratic
A -(6)
B (6)
C -(1)
D (1)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 3
Exam Tip
शून्यकों का गुणनफल (2\cdot(-3)=-6) है और यह \(\frac{c}{a}\) के बराबर होता है। गुणनफल में संकेत पर विशेष ध्यान दें।
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यदि (p(x)=x-2 -(m+4)x+4m) के शून्यक (4) और (m) हैं, तो कौन-सा कथन सही है?
If the zeroes of (p(x)=x-2 -(m+4)x+4m) are (4) and (m), which statement is correct?
#zeroes
#coefficients
#concept
A यह हर वास्तविक (m) के लिए सही है / It is true for every real (m)
B यह केवल (m=4) के लिए सही है / It is true only for (m=4)
C यह केवल (m=0) के लिए सही है / It is true only for (m=0)
D यह कभी सही नहीं है / It is never true
Explanation opens after your attempt
Correct Answer
A. यह हर वास्तविक (m) के लिए सही है / It is true for every real (m)
Step 1
Concept
The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).
Step 2
Why this answer is correct
The correct answer is A. यह हर वास्तविक (m) के लिए सही है / It is true for every real (m). The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).
Step 3
Exam Tip
योग (4+m) और गुणनफल (4m) हैं, जो दिए बहुपद से मिलते हैं। इसलिए कथन हर वास्तविक (m) के लिए सही है।
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(p(x)=4x-6 -5x-4 +2x-2 -11) में \(x^5\) का गुणांक क्या है?
What is the coefficient of \(x^5\) in (p(x)=4x-6 -5x-4 +2x-2 -11)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (4)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 3
Exam Tip
\(x^5\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^5\) मानें।
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(p(x)=6x-6 -5x-5 +4x-3 -2x-2 +x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?
What is the sum of coefficients of odd-power terms in (p(x)=6x-6 -5x-5 +4x-3 -2x-2 +x-7)?
#coefficients
#odd powers
#polynomial
A (-2)
B (0)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (-5), (4), and (1). Their sum is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (-5), (4), and (1). Their sum is (0).
Step 3
Exam Tip
विषम घातों \(x^5\), \(x^3\) और (x) के गुणांक (-5), (4) और (1) हैं। उनका योग (0) है।
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यदि (p(x)=4x-4 +kx-3 -6x+1) में सभी गुणांकों का योग (5) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=4x-4 +kx-3 -6x+1) is (5), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (4+k+0-6+1=k-1), so (k-1=5) and (k=6). The sum of coefficients is found by (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (6). The sum of coefficients is (4+k+0-6+1=k-1), so (k-1=5) and (k=6). The sum of coefficients is found by (p(1)).
Step 3
Exam Tip
गुणांकों का योग (4+k+0-6+1=k-1) है, इसलिए (k-1=5) और (k=6)। गुणांकों का योग (p(1)) से मिलता है।
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(p(x)=8x-4 -3x-3 -4x+2) में सभी गुणांकों का योग क्या है?
What is the sum of all coefficients in (p(x)=8x-4 -3x-3 -4x+2)?
#sum of coefficients
#evaluation
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of all coefficients is (8-3+0-4+2=3). It is also equal to (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (3). The sum of all coefficients is (8-3+0-4+2=3). It is also equal to (p(1)).
Step 3
Exam Tip
सभी गुणांकों का योग (8-3+0-4+2=3) है। यह (p(1)) के बराबर भी होता है।
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((3x-2)\(2x^2+x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((3x-2)\(2x^2+x-5\))?
#multiplication
#coefficient
#expansion
A (-1)
B (1)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-1). ((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 3
Exam Tip
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), इसलिए \(x^2\) का गुणांक (-1) है। विस्तार के बाद समान पद मिलाएं।
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(p(x)=5x-4 -3x-3 +2x-2 -x+8) और (q(x)=-2x-4 +7x-3 -5x-2 +4x-6) के योग में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in the sum of (p(x)=5x-4 -3x-3 +2x-2 -x+8) and (q(x)=-2x-4 +7x-3 -5x-2 +4x-6)?
#addition
#coefficient
#like terms
A (3)
B (4)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
The coefficients of \(x^3\) are (-3) and (7), so the sum is (4). Add only coefficients of like powers.
Step 2
Why this answer is correct
The correct answer is B. (4). The coefficients of \(x^3\) are (-3) and (7), so the sum is (4). Add only coefficients of like powers.
Step 3
Exam Tip
\(x^3\) के गुणांक (-3) और (7) हैं, इसलिए योग (4) है। समान घात के गुणांक ही जोड़ें।
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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)=3x-2 +(m-1 )x-2) के शून्यकों का योग (0) है, तो (m) क्या है?
If the sum of zeroes of (p(x)=3x-2 +(m-1 )x-2) is (0), what is (m)?
#sum-zeroes
#parameter
#coefficient
A (1)
B (0)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{m-1}{3}\); setting it to (0) gives (m-1 =0). When the sum is zero, the coefficient of (x) becomes zero.
Step 2
Why this answer is correct
The correct answer is A. (1). The sum is \(-\frac{m-1}{3}\); setting it to (0) gives (m-1 =0). When the sum is zero, the coefficient of (x) becomes zero.
Step 3
Exam Tip
योग \(-\frac{m-1}{3}\) है, इसे (0) रखने पर (m-1 =0) मिलता है। शून्य योग में (x) का गुणांक (0) हो जाता है।
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यदि (p(x)=x-2 +px+q) के शून्यक (4) और (-5) हैं, तो (p+q) क्या है?
If the zeroes of (p(x)=x-2 +px+q) are (4) and (-5), what is (p+q)?
#coefficient-finding
#zeroes
#quadratic
A (-19)
B (-21)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
The sum is (-1), so (p=1), and the product is (-20), so (q=-20). Hence (p+q=-19).
Step 2
Why this answer is correct
The correct answer is A. (-19). The sum is (-1), so (p=1), and the product is (-20), so (q=-20). Hence (p+q=-19).
Step 3
Exam Tip
योग (-1) है, इसलिए (p=1), और गुणनफल (-20) है, इसलिए (q=-20)। अतः (p+q=-19) है।
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यदि (x=2) और (x=-1), (p(x)=ax-2 +bx+c) के शून्यक हैं, तो \(\frac{b}{a}\) का मान क्या है?
If (x=2) and (x=-1) are zeroes of (p(x)=ax-2 +bx+c), what is \(\frac{b}{a}\)?
#relations-zeroes
#coefficient
#quadratic
A -(1)
B (1)
C -(2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (2+(-1)=1), and it equals \(-\frac{b}{a}\). Therefore \(\frac{b}{a}=-1\).
Step 2
Why this answer is correct
The correct answer is A. -(1). The sum of zeroes is (2+(-1)=1), and it equals \(-\frac{b}{a}\). Therefore \(\frac{b}{a}=-1\).
Step 3
Exam Tip
शून्यकों का योग (2+(-1)=1) है और योग \(-\frac{b}{a}\) होता है। इसलिए \(\frac{b}{a}=-1\) है।
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यदि बहुपद (p(x)=kx-3 +2x-2 -3x+1) वास्तव में द्विघात बहुपद है, तो (k) का मान क्या होगा?
If (p(x)=kx-3 +2x-2 -3x+1) is actually a quadratic polynomial, what must be the value of (k)?
#degree
#quadratic
#coefficient
A (0)
B (1)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
For it to be quadratic, the coefficient of \(x^3\) must be (0), while the coefficient of \(x^2\) is non-zero. Focus on the leading non-zero term.
Step 2
Why this answer is correct
The correct answer is A. (0). For it to be quadratic, the coefficient of \(x^3\) must be (0), while the coefficient of \(x^2\) is non-zero. Focus on the leading non-zero term.
Step 3
Exam Tip
द्विघात होने के लिए \(x^3\) का गुणांक (0) होना चाहिए और \(x^2\) का गुणांक अशून्य है। घात पहचानते समय प्रमुख पद पर ध्यान दें।
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(p(x)=3x-5 -2x-4 +7x-6) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in (p(x)=3x-5 -2x-4 +7x-6)?
#missing term
#coefficient
#polynomial
A (0)
B (3)
C (-2)
D (7)
Explanation opens after your attempt
Step 1
Concept
The \(x^3\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^3\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 3
Exam Tip
\(x^3\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^3\) मानें।
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(p(x)=5x-5 -3x-4 +2x-3 -x+6) में विषम घात वाले पदों के गुणांकों का योग क्या है?
What is the sum of coefficients of odd-power terms in (p(x)=5x-5 -3x-4 +2x-3 -x+6)?
#coefficients
#odd powers
#polynomial
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (5), (2), and (-1). Their sum is (6).
Step 2
Why this answer is correct
The correct answer is C. (6). The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (5), (2), and (-1). Their sum is (6).
Step 3
Exam Tip
विषम घातों \(x^5\), \(x^3\) और (x) के गुणांक (5), (2) और (-1) हैं। उनका योग (6) है।
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यदि बहुपद (p(x)=3x-3 +kx-2 -7x+2) में सभी गुणांकों का योग (5) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=3x-3 +kx-2 -7x+2) is (5), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (3+k-7+2=k-2), so (k-2=5) and (k=7). The sum of coefficients is (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (7). The sum of coefficients is (3+k-7+2=k-2), so (k-2=5) and (k=7). The sum of coefficients is (p(1)).
Step 3
Exam Tip
गुणांकों का योग (3+k-7+2=k-2) है, इसलिए (k-2=5) और (k=7)। गुणांकों का योग (p(1)) होता है।
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(p(x)=7x-3 -4x-2 -2x-1) में सभी गुणांकों का योग क्या है?
What is the sum of all coefficients in (p(x)=7x-3 -4x-2 -2x-1)?
#sum of coefficients
#evaluation
#polynomial
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of all coefficients is (7-4-2-1=0). It is also equal to (p(1)).
Step 2
Why this answer is correct
The correct answer is A. (0). The sum of all coefficients is (7-4-2-1=0). It is also equal to (p(1)).
Step 3
Exam Tip
सभी गुणांकों का योग (7-4-2-1=0) है। यह (p(1)) के बराबर भी होता है।
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((2x-1)\(x^2-3x+4\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((2x-1)\(x^2-3x+4\))?
#multiplication
#coefficient
#expansion
A (-7)
B (-6)
C (-5)
D (8)
Explanation opens after your attempt
Step 1
Concept
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-7). ((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 3
Exam Tip
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), इसलिए गुणांक (-7) है। विस्तार के बाद समान पद मिलाएं।
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(p(x)=4x-3 -7x-2 +2x-5) और (q(x)=-x-3 +3x-2 -6x+9) के योग में (x) का गुणांक क्या है?
What is the coefficient of (x) in the sum of (p(x)=4x-3 -7x-2 +2x-5) and (q(x)=-x-3 +3x-2 -6x+9)?
#addition
#coefficient
#like terms
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficients of (x) are (2) and (-6), so the sum is (-4). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is B. (-4). The coefficients of (x) are (2) and (-6), so the sum is (-4). Add coefficients of like powers only.
Step 3
Exam Tip
(x) के गुणांक (2) और (-6) हैं, इसलिए योग (-4) है। समान घात के गुणांक ही जोड़ें।
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यदि (p(x)=x-3 +ax-2 +bx+8) के शून्यक (-1), (-2) और (-4) हैं, तो (a+b) क्या है?
If the zeroes of (p(x)=x-3 +ax-2 +bx+8) are (-1), (-2), and (-4), what is (a+b)?
#polynomials
#cubic_zeroes
#coefficients
#hard
A (21)
B (7)
C (14)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The polynomial is ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8). Hence (a+b=21).
Step 2
Why this answer is correct
The correct answer is A. (21). The polynomial is ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8). Hence (a+b=21).
Step 3
Exam Tip
बहुपद ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8) है। इसलिए (a+b=21)।
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किस बहुपद की घात (4) है?
Which polynomial has degree (4)?
#polynomials
#degree
#zero_coefficient
#hard
A \(7x^4+0x^5-3x+1\)
B \(0x^6+5x^3-2\)
C \(x^2+x+1\)
D (9)
Explanation opens after your attempt
Correct Answer
A. \(7x^4+0x^5-3x+1\)
Step 1
Concept
The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).
Step 2
Why this answer is correct
The correct answer is A. \(7x^4+0x^5-3x+1\). The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).
Step 3
Exam Tip
\(0x^5\) पद घात नहीं बढ़ाता क्योंकि उसका गुणांक (0) है। सबसे बड़ा शून्येतर घात (4) है।
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यदि \(x^2+ax+b\) के शून्यक (4) और (-7) हैं, तो (a-b) क्या होगा?
If the zeroes of \(x^2+ax+b\) are (4) and (-7), what is (a-b)?
#polynomials
#zeroes
#coefficient_relation
#hard
A (25)
B (31)
C (-25)
D (-31)
Explanation opens after your attempt
Step 1
Concept
The sum is (-3), so (a=3), and the product is (-28), so (b=-28). Hence (a-b=31).
Step 2
Why this answer is correct
The correct answer is B. (31). The sum is (-3), so (a=3), and the product is (-28), so (b=-28). Hence (a-b=31).
Step 3
Exam Tip
योग (-3) है इसलिए (a=3) और गुणनफल (-28) है इसलिए (b=-28)। अतः (a-b=31) 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 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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(p(x)=2x-4 -3x-3 +5x-9) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=2x-4 -3x-3 +5x-9)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (-3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).
Step 3
Exam Tip
\(x^2\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^2\) मानें।
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(p(x)=3x-4 -5x-2 +2x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?
What is the sum of coefficients of the odd-power terms in (p(x)=3x-4 -5x-2 +2x-7)?
#coefficients
#odd powers
#polynomial
A (-7)
B (-5)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
The only odd-power term is (2x), so the sum is (2). Do not treat \(x^0\) as an odd power.
Step 2
Why this answer is correct
The correct answer is C. (2). The only odd-power term is (2x), so the sum is (2). Do not treat \(x^0\) as an odd power.
Step 3
Exam Tip
विषम घात वाला केवल (2x) पद है, इसलिए योग (2) है। \(x^0\) को विषम घात न मानें।
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यदि बहुपद (p(x)=2x-3 +kx-2 -8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=2x-3 +kx-2 -8x+3) is (0), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (3). The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 3
Exam Tip
गुणांकों का योग (2+k-8+3=k-3) है, इसलिए (k=3)। गुणांकों का योग (p(1)) से भी मिलता है।
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(p(x)=5x-3 -2x-2 +x-4) में सभी गुणांकों का योग क्या है?
What is the sum of all coefficients in (p(x)=5x-3 -2x-2 +x-4)?
#sum of coefficients
#evaluation
#polynomial
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).
Step 2
Why this answer is correct
The correct answer is A. (0). The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).
Step 3
Exam Tip
सभी गुणांकों का योग (5-2+1-4=0) है। यह (p(1)) के बराबर भी होता है।
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((x-2)\(3x^2+4x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((x-2)\(3x^2+4x-5\))?
#multiplication
#coefficient
#expansion
A (-4)
B (-2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is B. (-2). ((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 3
Exam Tip
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), इसलिए \(x^2\) का गुणांक (-2) है। विस्तार में समान पद मिलाएं।
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(p(x)=3x-3 -2x-2 +5x-1) और (q(x)=-x-3 +7x-2 -4x+6) के योग में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in the sum of (p(x)=3x-3 -2x-2 +5x-1) and (q(x)=-x-3 +7x-2 -4x+6)?
#addition
#coefficient
#like terms
A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.
Step 2
Why this answer is correct
The correct answer is B. (5). The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.
Step 3
Exam Tip
\(x^2\) के गुणांक (-2) और (7) हैं, जिनका योग (5) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=3x-3 -7x-2 +2x-11) में \(x^2\) के गुणांक और अचर पद का योग क्या है?
In (p(x)=3x-3 -7x-2 +2x-11), what is the sum of the coefficient of \(x^2\) and the constant term?
#coefficient
#constant term
#signs
A (-18)
B (-11)
C (-7)
D (4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.
Step 2
Why this answer is correct
The correct answer is A. (-18). The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.
Step 3
Exam Tip
\(x^2\) का गुणांक (-7) और अचर पद (-11) है, इसलिए योग (-18) है। संकेत सहित जोड़ना न भूलें।
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\(5x^2-6x+2\) और \(2x^2+9x-1\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(5x^2-6x+2\) and \(2x^2+9x-1\)?
#coefficients
#like terms
#polynomials
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-6) in the first polynomial and (9) in the second, so the sum is (3). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is C. (3). The coefficient of (x) is (-6) in the first polynomial and (9) in the second, so the sum is (3). Add coefficients of like powers only.
Step 3
Exam Tip
पहले बहुपद में (x) का गुणांक (-6) और दूसरे में (9) है, योग (3) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=7x-4 -2x-2 +9) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in (p(x)=7x-4 -2x-2 +9)?
#coefficient
#missing term
#quartic
A (7)
B (-2)
C (0)
D (9)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\)-term, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\)-term, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 3
Exam Tip
\(x^3\) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^3\) समझें।
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(p(x)=x-5 +3x-3 -2) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-5 +3x-3 -2)?
#missing power
#coefficient zero
#polynomial
A \(x^5\)
B \(x^4\)
C \(x^3\)
D \(x^0\)
Explanation opens after your attempt
Correct Answer
B. \(x^4\)
Step 1
Concept
The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^4\). The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 3
Exam Tip
इस बहुपद में \(x^4\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है।
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बहुपद (p(x)=5x-3 +0x-2 -4x+12) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 +0x-2 -4x+12)?
#coefficient
#missing term
#polynomial
A (0)
B (5)
C (-4)
D (12)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 3
Exam Tip
\(x^2\) वाला पद \(0x^2\) है इसलिए गुणांक (0) है। अनुपस्थित या शून्य पद का गुणांक (0) माना जाता है।
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(p(x)=8x-4 -5x-3 +2x-6) में \(x^4\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^4\)-term in (p(x)=8x-4 -5x-3 +2x-6)?
#coefficient
#quartic term
#polynomial
A (8)
B (-5)
C (2)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (8). The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 3
Exam Tip
\(x^4\) वाले पद \(8x^4\) का गुणांक (8) है। घात और गुणांक को अलग पहचानें।
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बहुपद (p(z)=-6z-5 +4z-4 -z+8) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(z)=-6z-5 +4z-4 -z+8)?
#leading coefficient
#degree
#polynomial
A (-6)
B (4)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-6). The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 3
Exam Tip
सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है।
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यदि (p(x)=9x-2 +cx-5) में (x) का गुणांक (-4) है, तो (c) क्या है?
If the coefficient of (x) in (p(x)=9x-2 +cx-5) is (-4), what is (c)?
#coefficient
#parameter
#polynomial
A (-9)
B (-5)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 2
Why this answer is correct
The correct answer is C. (-4). In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 3
Exam Tip
(cx) में (x) का गुणांक (c) है। दिया है कि (c=-4)।
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(p(x)=0x-5 +7x-3 -2x+1) की घात क्या है?
What is the degree of (p(x)=0x-5 +7x-3 -2x+1)?
#degree
#zero coefficient
#polynomial
A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 3
Exam Tip
\(0x^5\) का गुणांक (0) है इसलिए वह पद नहीं गिना जाएगा। सबसे बड़ी प्रभावी घात (3) है।
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बहुपद \(7x^4-3x^3+0x^2+5\) में प्रभावी पदों की संख्या कितनी है?
How many effective terms are there in the polynomial \(7x^4-3x^3+0x^2+5\)?
#terms
#zero coefficient
#polynomial
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term \(0x^2\) is not effective, so the terms are \(7x^4\), \(-3x^3\), and (5). Do not count a term with zero coefficient.
Step 2
Why this answer is correct
The correct answer is B. (3). The term \(0x^2\) is not effective, so the terms are \(7x^4\), \(-3x^3\), and (5). Do not count a term with zero coefficient.
Step 3
Exam Tip
\(0x^2\) प्रभावी पद नहीं है इसलिए पद \(7x^4\), \(-3x^3\) और (5) हैं। शून्य गुणांक वाले पद को न गिनें।
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(p(x)=5x-3 -8x-2 +13x-21) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 -8x-2 +13x-21)?
#coefficient
#sign
#polynomial
A (5)
B (-8)
C (13)
D (-21)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is B. (-8). The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 3
Exam Tip
\(x^2\) वाले पद \(-8x^2\) का गुणांक (-8) है। संकेत सहित गुणांक लिखना जरूरी है।
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\(x^2+\sqrt{5}x-7\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(x^2+\sqrt{5}x-7\)?
#real-coefficient
#polynomial
#definition
A यह बहुपद नहीं है क्योंकि \(\sqrt{5}\) है / It is not a polynomial because \(\sqrt{5}\) is present
B यह (x) में बहुपद है / It is a polynomial in (x)
C यह केवल नियत बहुपद है / It is only a constant polynomial
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
B. यह (x) में बहुपद है / It is a polynomial in (x)
Step 1
Concept
\(\sqrt{5}\) is a real coefficient and the powers of (x) are whole numbers. So it is a polynomial in (x).
Step 2
Why this answer is correct
The correct answer is B. यह (x) में बहुपद है / It is a polynomial in (x). \(\sqrt{5}\) is a real coefficient and the powers of (x) are whole numbers. So it is a polynomial in (x).
Step 3
Exam Tip
\(\sqrt{5}\) वास्तविक गुणांक है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह (x) में बहुपद है।
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बहुपद \(2x^4+3x^2-5x+7\) में \(x^3\) के गुणांक और (x) के गुणांक का योग क्या है?
In \(2x^4+3x^2-5x+7\), what is the sum of the coefficient of \(x^3\) and the coefficient of (x)?
#coefficients
#missing-term
#sum
A (-5)
B (0)
C (5)
D (3)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).
Step 3
Exam Tip
\(x^3\) का गुणांक (0) और (x) का गुणांक (-5) है। योग (-5) है।
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निम्न में से कौन सा (t) में बहुपद है?
Which of the following is a polynomial in (t)?
#polynomial-in-t
#definition
#real-coefficient
A \(t^2+\sqrt{t}+1\)
B \(t^{-2}+3\)
C \(4t^3-\frac{1}{2}t+7\)
D \(\frac{2}{t}+t\)
Explanation opens after your attempt
Correct Answer
C. \(4t^3-\frac{1}{2}t+7\)
Step 1
Concept
In \(4t^3-\frac{1}{2}t+7\), the powers of (t) are (3), (1), and (0). All are whole numbers.
Step 2
Why this answer is correct
The correct answer is C. \(4t^3-\frac{1}{2}t+7\). In \(4t^3-\frac{1}{2}t+7\), the powers of (t) are (3), (1), and (0). All are whole numbers.
Step 3
Exam Tip
\(4t^3-\frac{1}{2}t+7\) में (t) की घातें (3), (1) और (0) हैं। ये सभी पूर्ण संख्याएँ हैं।
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निम्न में से किस बहुपद में प्रमुख गुणांक (1) नहीं है?
Which of the following polynomials does not have leading coefficient (1)?
#leading-coefficient
#monic-polynomial
#classification
A \(x^3+2x+5\)
B \(x^2-4\)
C \(3x^2+x+1\)
D \(x^5-x\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+x+1\)
Step 1
Concept
The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 2
Why this answer is correct
The correct answer is C. \(3x^2+x+1\). The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 3
Exam Tip
\(3x^2+x+1\) का प्रमुख पद \(3x^2\) है। इसका प्रमुख गुणांक (3) है, (1) नहीं।
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किस विकल्प में बहुपद \(6x^3+0x^2-2x+9\) को सरल रूप में सही लिखा गया है?
Which option correctly writes \(6x^3+0x^2-2x+9\) in simplified form?
#zero-coefficient
#simplification
#polynomial
A \(6x^3-2x+9\)
B \(6x^3+2x+9\)
C \(6x^3+x^2-2x+9\)
D \(6x^3-2x\)
Explanation opens after your attempt
Correct Answer
A. \(6x^3-2x+9\)
Step 1
Concept
The value of \(0x^2\) is (0), so that term vanishes. The remaining terms stay unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(6x^3-2x+9\). The value of \(0x^2\) is (0), so that term vanishes. The remaining terms stay unchanged.
Step 3
Exam Tip
\(0x^2\) का मान (0) है इसलिए वह पद हट जाता है। बाकी पद जैसे हैं वैसे रहते हैं।
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निम्न में से कौन सा बहुपद (x) में है लेकिन (y) में नहीं है?
Which of the following is a polynomial in (x) but not in (y)?
#one-variable
#variable-identification
#polynomial
A \(x^2+3x+1\)
B \(y^2+3y+1\)
C (xy+1)
D (x+y+1)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+1\)
Step 1
Concept
\(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+1\). \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 3
Exam Tip
\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है।
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यदि \(x^3+2x^2+cx+5\) में (x) का गुणांक (6) है, तो (c+5) क्या होगा?
If the coefficient of (x) in \(x^3+2x^2+cx+5\) is (6), what will be (c+5)?
#coefficient
#parameter
#evaluation
A (6)
B (9)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 2
Why this answer is correct
The correct answer is C. (11). The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 3
Exam Tip
(x) का गुणांक (c=6) है। इसलिए (c+5=11) होगा।
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बहुपद \(3x^4-5x^2+2x-8\) का प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^4-5x^2+2x-8\)?
#leading-coefficient
#degree-four
#polynomial
A (3)
B (-5)
C (2)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 3
Exam Tip
प्रमुख पद \(3x^4\) है। इसलिए प्रमुख गुणांक (3) है।
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निम्न में से किस बहुपद में (x) का गुणांक (0) है?
In which of the following polynomials is the coefficient of (x) equal to (0)?
#coefficient
#missing-x-term
#polynomial
A \(x^2+5x+6\)
B \(3x^2-4\)
C \(2x^3+x-1\)
D (7x-9)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-4\)
Step 1
Concept
In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-4\). In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 3
Exam Tip
\(3x^2-4\) में (x) का पद नहीं है। इसलिए (x) का गुणांक (0) है।
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बहुपद \(7x^5-3x^4+x^2-11\) में अनुपस्थित \(x^3\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^3\) term in \(7x^5-3x^4+x^2-11\)?
#missing-term
#coefficient
#degree
A (7)
B (-3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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यदि (p(x)=2x-3 +mx-2 -x+4) में \(x^2\) का गुणांक (-5) है, तो (m) क्या है?
If the coefficient of \(x^2\) in (p(x)=2x-3 +mx-2 -x+4) is (-5), what is (m)?
#coefficient
#parameter
#polynomial
A (5)
B (-5)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 2
Why this answer is correct
The correct answer is B. (-5). The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणक (m) है। दिया है (m=-5), इसलिए उत्तर (-5) है।
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बहुपद \(4x^3-2x^2+7x-9\) में \(x^2\) के गुणांक और नियत पद का योग क्या है?
In the polynomial \(4x^3-2x^2+7x-9\), what is the sum of the coefficient of \(x^2\) and the constant term?
#coefficient
#constant-term
#polynomial
A (-11)
B (-7)
C (7)
D (11)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^2\) is (-2) and the constant term is (-9). Their sum is (-11).
Step 2
Why this answer is correct
The correct answer is A. (-11). The coefficient of \(x^2\) is (-2) and the constant term is (-9). Their sum is (-11).
Step 3
Exam Tip
\(x^2\) का गुणांक (-2) और नियत पद (-9) है। उनका योग (-11) 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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\(3x^2-2x+1\) और \(x^2+4x+7\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(3x^2-2x+1\) and \(x^2+4x+7\)?
#coefficients
#like terms
#polynomials
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is A. (2). The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 3
Exam Tip
पहले बहुपद में (x) का गुणांक (-2) और दूसरे में (4) है, योग (2) है। समान घात के गुणांक ही जोड़ें।
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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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निम्न में से एक चर वाला बहुपद कौन सा नहीं है?
Which of the following is not a polynomial in one variable?
#one variable
#two variables
#identification
A \(2x^2+3x+1\)
B \(5t^3-t\)
C \(x^2+y+1\)
D (9z-4)
Explanation opens after your attempt
Correct Answer
C. \(x^2+y+1\)
Step 1
Concept
\(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+y+1\). \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
Step 3
Exam Tip
\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है।
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(p(x)=x-4 +2x-2 +1) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-4 +2x-2 +1)?
#missing power
#coefficient zero
#polynomial
A \(x^4\)
B \(x^3\)
C \(x^2\)
D \(x^0\)
Explanation opens after your attempt
Correct Answer
B. \(x^3\)
Step 1
Concept
The term \(x^3\) is not present in this polynomial. A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^3\). The term \(x^3\) is not present in this polynomial. A missing term has coefficient (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है।
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बहुपद (p(x)=2x-2 +0x+3) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-2 +0x+3)?
#coefficient
#missing term
#polynomial
A (0)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The (x)-term is (0x), so the coefficient of (x) is (0). Treat a missing term as having coefficient (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The (x)-term is (0x), so the coefficient of (x) is (0). Treat a missing term as having coefficient (0).
Step 3
Exam Tip
(x) वाला पद (0x) है इसलिए (x) का गुणांक (0) है। अनुपस्थित पद का गुणांक (0) मानें।
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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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बहुपद (p(y)=9y-4 -y-2 +5y-6) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(y)=9y-4 -y-2 +5y-6)?
#leading coefficient
#degree
#polynomial
A (9)
B (-1)
C (5)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (9). The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 3
Exam Tip
सबसे बड़ी घात \(y^4\) के पद का गुणांक (9) है। अग्र गुणांक वही होता है।
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(p(x)=2x-2 +kx+8) में (x) का गुणांक (5) हो तो (k) क्या है?
If the coefficient of (x) in (p(x)=2x-2 +kx+8) is (5), what is (k)?
#coefficient
#parameter
#polynomial
A (2)
B (5)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
In (kx), the coefficient of (x) is (k). It is given that (k=5).
Step 2
Why this answer is correct
The correct answer is B. (5). In (kx), the coefficient of (x) is (k). It is given that (k=5).
Step 3
Exam Tip
(kx) में (x) का गुणांक (k) है। दिया है (k=5)।
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\(3x^4+0x^3-2x+5\) की घात क्या है?
What is the degree of \(3x^4+0x^3-2x+5\)?
#degree
#zero coefficient
#polynomial
A (1)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.
Step 2
Why this answer is correct
The correct answer is C. (4). The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.
Step 3
Exam Tip
\(0x^3\) पद प्रभावी नहीं है और सबसे बड़ी अशून्य घात (4) है। शून्य गुणांक वाले पद को नजरअंदाज करें।
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(p(x)=ax-2 +bx+c) कब द्विघात बहुपद होगा?
When will (p(x)=ax-2 +bx+c) be a quadratic polynomial?
#quadratic condition
#coefficient
#concept
A (a=0)
B \(a\ne0\)
C (b=0)
D (c=0)
Explanation opens after your attempt
Correct Answer
B. \(a\ne0\)
Step 1
Concept
For a quadratic polynomial, the coefficient of \(x^2\) must not be zero. Hence \(a\ne0\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(a\ne0\). For a quadratic polynomial, the coefficient of \(x^2\) must not be zero. Hence \(a\ne0\) is necessary.
Step 3
Exam Tip
द्विघात बहुपद के लिए \(x^2\) का गुणांक शून्य नहीं होना चाहिए। इसलिए \(a\ne0\) जरूरी है।
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व्यंजक \(7x^3+2x^2-x+6\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(7x^3+2x^2-x+6\)?
#coefficient
#term
#polynomial
A (7)
B (2)
C (-1)
D (6)
Explanation opens after your attempt
Step 1
Concept
The numerical factor attached to \(x^2\) is (2). When coefficient is asked, identify the exact term.
Step 2
Why this answer is correct
The correct answer is B. (2). The numerical factor attached to \(x^2\) is (2). When coefficient is asked, identify the exact term.
Step 3
Exam Tip
\(x^2\) के साथ लगा संख्या गुणक (2) है। गुणांक पूछने पर उसी पद को पहचानें।
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इनमें से कौन सा एक चर में बहुपद है?
Which of the following is a polynomial in one variable?
#polynomial
#one variable
#identification
A (p(x)=3x-2 -5x+7)
B (p(x)=\frac{2}{x}+1)
C (p(x)=\sqrt{x}+4)
D (p(x)=x^{-2}+3)
Explanation opens after your attempt
Correct Answer
A. (p(x)=3x-2 -5x+7)
Step 1
Concept
In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
Step 2
Why this answer is correct
The correct answer is A. (p(x)=3x-2 -5x+7). In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
Step 3
Exam Tip
एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें।
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बहुपद \(6x^2-x+13\) में (x) के गुणांक का सही मान कौन सा है?
Which is the correct coefficient of (x) in \(6x^2-x+13\)?
#coefficient
#negative-one
A (6)
B (-1)
C (1)
D (13)
Explanation opens after your attempt
Step 1
Concept
(-x) means (-1x), so the coefficient is (-1). Identify the hidden (1) with its sign.
Step 2
Why this answer is correct
The correct answer is B. (-1). (-x) means (-1x), so the coefficient is (-1). Identify the hidden (1) with its sign.
Step 3
Exam Tip
(-x) का अर्थ (-1x) है इसलिए गुणांक (-1) है। छिपे हुए (1) को चिह्न सहित पहचानें।
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बहुपद \(x^3+4x^2-5\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(x^3+4x^2-5\)?
#coefficient
#missing-term
A (1)
B (4)
C (0)
D (-5)
Explanation opens after your attempt
Step 1
Concept
It has no (x)-term, so the coefficient of (x) is (0). It is important to identify missing terms quickly.
Step 2
Why this answer is correct
The correct answer is C. (0). It has no (x)-term, so the coefficient of (x) is (0). It is important to identify missing terms quickly.
Step 3
Exam Tip
इसमें (x) का पद नहीं है इसलिए (x) का गुणांक (0) है। अनुपस्थित पद को तुरंत पहचानना जरूरी है।
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