100 results found for "coefficient_symmetry" in Class 10.
रेखा आधारित डिजाइन में बहुत अधिक सममिति कब कमजोर लग सकती है?
When can too much symmetry look weak in line-based design?
#symmetry
#line design
#visual interest
A जब विषय स्पष्ट हो / When subject is clear
B जब संतुलन बने / When balance is created
C जब वह गति और दृश्य रुचि को कम कर दे / When it reduces movement and visual interest
D जब रेखा नियंत्रित हो / When line is controlled
Explanation opens after your attempt
Correct Answer
C. जब वह गति और दृश्य रुचि को कम कर दे / When it reduces movement and visual interest
Step 1
Concept
Too much symmetry can make composition static and predictable. Exam tip: consider both balance and interest.
Step 2
Why this answer is correct
The correct answer is C. जब वह गति और दृश्य रुचि को कम कर दे / When it reduces movement and visual interest. Too much symmetry can make composition static and predictable. Exam tip: consider both balance and interest.
Step 3
Exam Tip
अत्यधिक सममिति कभी कभी रचना को स्थिर और पूर्वानुमेय बनाती है। परीक्षा में संतुलन और रुचि दोनों देखें।
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रेखीय संतुलन में सममिति के बिना संतुलन कैसे संभव है?
How is balance possible in linear composition without symmetry?
#balance
#asymmetry
#line weight
A दोनों ओर समान प्रतिलिपि बनाकर ही / Only by making equal copies on both sides
B सभी रेखाएं हटाकर / By removing all lines
C रेखा भार, दिशा और खाली स्थान को संतुलित करके / By balancing line weight, direction, and empty space
D केवल रंग बदलकर / Only by changing colour
Explanation opens after your attempt
Correct Answer
C. रेखा भार, दिशा और खाली स्थान को संतुलित करके / By balancing line weight, direction, and empty space
Step 1
Concept
In asymmetrical balance, control of visual weight is important. Exam tip: do not treat balance only as equality.
Step 2
Why this answer is correct
The correct answer is C. रेखा भार, दिशा और खाली स्थान को संतुलित करके / By balancing line weight, direction, and empty space. In asymmetrical balance, control of visual weight is important. Exam tip: do not treat balance only as equality.
Step 3
Exam Tip
असममित संतुलन में दृश्य भार का नियंत्रण महत्वपूर्ण होता है। परीक्षा में संतुलन को केवल समानता न मानें।
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किस रेखा से किसी वस्तु का केंद्र और सममिति जांचना आसान होता है?
Which line makes it easier to check centre and symmetry of an object?
#visual-art
#line
#hard
#class-10
A मध्य रेखा / Centre line
B जिगजैग रेखा / Zigzag line
C सर्पिल रेखा / Spiral line
D बिखरी रेखा / Scattered line
Explanation opens after your attempt
Correct Answer
A. मध्य रेखा / Centre line
Step 1
Concept
Centre line checks proportion and symmetry on both sides. In exams remember its use in face and vessels.
Step 2
Why this answer is correct
The correct answer is A. मध्य रेखा / Centre line. Centre line checks proportion and symmetry on both sides. In exams remember its use in face and vessels.
Step 3
Exam Tip
मध्य रेखा दोनों ओर के अनुपात और सममिति को जांचती है। परीक्षा में चेहरे और पात्र में इसका उपयोग याद रखें।
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रेखा से सममिति दिखाने का अच्छा तरीका कौन सा है?
What is a good way to show symmetry through line?
#visual-art
#line
#class-10
#medium
A मध्य रेखा के दोनों ओर समान रेखाएं / Similar lines on both sides of a centre line
B सभी रेखाएं एक ओर रखना / Keeping all lines on one side
C एक तरफ गहरी दूसरी तरफ खाली / Dark on one side and empty on other
D मध्य रेखा हटाना / Removing centre line
Explanation opens after your attempt
Correct Answer
A. मध्य रेखा के दोनों ओर समान रेखाएं / Similar lines on both sides of a centre line
Step 1
Concept
A centre line helps check symmetry. In exams remember its use in face and object drawing.
Step 2
Why this answer is correct
The correct answer is A. मध्य रेखा के दोनों ओर समान रेखाएं / Similar lines on both sides of a centre line. A centre line helps check symmetry. In exams remember its use in face and object drawing.
Step 3
Exam Tip
मध्य रेखा सममिति जांचने में मदद करती है। परीक्षा में चेहरे और वस्तु चित्रण में इसका उपयोग याद रखें।
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सममित संतुलन में रुचि बढ़ाने का सबसे सुरक्षित तरीका क्या है?
What is the safest way to increase interest in symmetrical balance?
#symmetry
#variety
#balance
A सममिति पूरी तरह तोड़ देना / Break symmetry completely
B मुख्य सममिति रखते हुए सूक्ष्म रंग या बनावट बदलाव देना / Keep main symmetry with subtle colour or texture variation
C केंद्र हटाना / Remove centre
D दोनों ओर असंबंधित तत्व रखना / Keep unrelated elements on both sides
Explanation opens after your attempt
Correct Answer
B. मुख्य सममिति रखते हुए सूक्ष्म रंग या बनावट बदलाव देना / Keep main symmetry with subtle colour or texture variation
Step 1
Concept
Subtle change gives interest without breaking symmetry. Exam tip: remember symmetry with variation.
Step 2
Why this answer is correct
The correct answer is B. मुख्य सममिति रखते हुए सूक्ष्म रंग या बनावट बदलाव देना / Keep main symmetry with subtle colour or texture variation. Subtle change gives interest without breaking symmetry. Exam tip: remember symmetry with variation.
Step 3
Exam Tip
सूक्ष्म बदलाव सममिति को तोड़े बिना रुचि देता है। परीक्षा में symmetry with variation याद रखें।
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यदि दोनों ओर समान आकार हैं पर एक ओर बहुत गहरा मान है तो क्या होगा?
If both sides have same shapes but one side has very dark value what happens?
#visual weight
#value
#symmetry
A दृश्य भार असमान हो सकता है / Visual weight can become unequal
B सममिति हमेशा पूर्ण रहेगी / Symmetry will always remain complete
C मान का भार से संबंध नहीं / Value has no relation to weight
D रंग समाप्त होगा / Colour will end
Explanation opens after your attempt
Correct Answer
A. दृश्य भार असमान हो सकता है / Visual weight can become unequal
Step 1
Concept
Value changes visual weight. Exam tip: observe value along with size in balance.
Step 2
Why this answer is correct
The correct answer is A. दृश्य भार असमान हो सकता है / Visual weight can become unequal. Value changes visual weight. Exam tip: observe value along with size in balance.
Step 3
Exam Tip
मान दृश्य भार को बदल देता है। परीक्षा में संतुलन में size के साथ value भी देखें।
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यदि दोनों ओर समान आकार हैं पर एक ओर रंग बहुत गहरा है तो सममिति पर क्या असर होगा?
If both sides have same shapes but one side has very dark colour what happens to symmetry?
#symmetry
#value
#visual weight
A दृश्य भार असमान हो सकता है / Visual weight may become unequal
B सममिति हमेशा पूर्ण रहेगी / Symmetry will always remain complete
C रंग का कोई प्रभाव नहीं / Colour has no effect
D बनावट मिट जाएगी / Texture will disappear
Explanation opens after your attempt
Correct Answer
A. दृश्य भार असमान हो सकता है / Visual weight may become unequal
Step 1
Concept
Value can change weight despite symmetrical shapes. Exam tip: observe value balance in symmetry.
Step 2
Why this answer is correct
The correct answer is A. दृश्य भार असमान हो सकता है / Visual weight may become unequal. Value can change weight despite symmetrical shapes. Exam tip: observe value balance in symmetry.
Step 3
Exam Tip
सममित आकार के बावजूद मान भार बदल सकता है। परीक्षा में symmetry में value balance देखें।
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यदि खाली स्थान असमान है तो भी वह कब प्रभावी हो सकता है?
When can uneven empty space still be effective?
#negative space
#asymmetry
#balance
A जब वह दृश्य भार और भाव को संतुलित कर रहा हो / When it balances visual weight and mood
B जब वह अनियोजित हो / When it is unplanned
C जब वह मुख्य विषय छिपाए / When it hides main subject
D जब वह पढ़ने को कठिन बनाए / When it makes reading difficult
Explanation opens after your attempt
Correct Answer
A. जब वह दृश्य भार और भाव को संतुलित कर रहा हो / When it balances visual weight and mood
Step 1
Concept
Uneven space can also give balance if planned. Exam tip: understand asymmetrical space.
Step 2
Why this answer is correct
The correct answer is A. जब वह दृश्य भार और भाव को संतुलित कर रहा हो / When it balances visual weight and mood. Uneven space can also give balance if planned. Exam tip: understand asymmetrical space.
Step 3
Exam Tip
असमान स्थान भी योजना से संतुलन दे सकता है। परीक्षा में asymmetrical space समझें।
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ताजमहल के मुख्य मकबरे में चार कोनों पर बनी मीनारों का स्थापत्य उद्देश्य क्या माना जाता है?
What is the architectural purpose of the minarets at the four corners of the Taj Mahal's main tomb?
#taj mahal
#minarets
#symmetry
A सममित संतुलन और दृश्य गरिमा बढ़ाना / To enhance symmetry and visual dignity
B अनाज भंडारण करना / To store grain
C घोड़ों को बांधना / To tie horses
D भूमिगत जल निकालना / To drain underground water
Explanation opens after your attempt
Correct Answer
A. सममित संतुलन और दृश्य गरिमा बढ़ाना / To enhance symmetry and visual dignity
Step 1
Concept
The minarets of the Taj Mahal strengthen its symmetrical plan. In Mughal architecture, pay attention to balance and proportion.
Step 2
Why this answer is correct
The correct answer is A. सममित संतुलन और दृश्य गरिमा बढ़ाना / To enhance symmetry and visual dignity. The minarets of the Taj Mahal strengthen its symmetrical plan. In Mughal architecture, pay attention to balance and proportion.
Step 3
Exam Tip
ताजमहल की मीनारें सममित योजना को मजबूत करती हैं। मुगल स्थापत्य में संतुलन और अनुपात पर ध्यान दें।
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शाहजहां के स्थापत्य में संगमरमर और सममिति का प्रयोग शाही छवि को कैसे मजबूत करता था?
How did the use of marble and symmetry in Shah Jahan's architecture strengthen the royal image?
#indian history famous rulers hard shah jahan
A इससे सौंदर्य वैभव और शाही शक्ति का प्रदर्शन होता था / It displayed beauty grandeur and royal power
B इससे केवल कृषि बढ़ती थी / It only increased agriculture
C इससे चोल नौसेना बनती थी / It created the Chola navy
D इससे नंद वंश बनता था / It created the Nanda dynasty
Explanation opens after your attempt
Correct Answer
A. इससे सौंदर्य वैभव और शाही शक्ति का प्रदर्शन होता था / It displayed beauty grandeur and royal power
Step 1
Concept
Shah Jahan's architecture symbolized Mughal grandeur. Treat the Taj Mahal as a major example of this style.
Step 2
Why this answer is correct
The correct answer is A. इससे सौंदर्य वैभव और शाही शक्ति का प्रदर्शन होता था / It displayed beauty grandeur and royal power. Shah Jahan's architecture symbolized Mughal grandeur. Treat the Taj Mahal as a major example of this style.
Step 3
Exam Tip
शाहजहां का स्थापत्य मुगल वैभव का प्रतीक था। ताजमहल को इस शैली का प्रमुख उदाहरण मानें।
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शाहजहाँकालीन स्थापत्य में सममिति का प्रयोग किस बात को दर्शाता है?
What does the use of symmetry in Shah Jahan period architecture show?
#indian-history-medieval-history-shahjahan
A संतुलित सौंदर्य और शाही व्यवस्था की भावना / Sense of balanced beauty and royal order
B सैन्य अव्यवस्था / Military disorder
C सिक्का संकट / Currency crisis
D ग्राम पंचायत विरोध / Opposition to village councils
Explanation opens after your attempt
Correct Answer
A. संतुलित सौंदर्य और शाही व्यवस्था की भावना / Sense of balanced beauty and royal order
Step 1
Concept
Marble and symmetrical planning are prominent in Shah Jahan's buildings. Exam tip is to link it with mature Mughal architecture.
Step 2
Why this answer is correct
The correct answer is A. संतुलित सौंदर्य और शाही व्यवस्था की भावना / Sense of balanced beauty and royal order. Marble and symmetrical planning are prominent in Shah Jahan's buildings. Exam tip is to link it with mature Mughal architecture.
Step 3
Exam Tip
शाहजहाँ की इमारतों में संगमरमर और सममित योजना प्रमुख हैं। परीक्षा में इसे मुगल स्थापत्य की परिपक्व शैली से जोड़ें।
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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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संख्या रेखा पर (3) के सापेक्ष (4.6) का सममित बिंदु कौन सा होगा?
What will be the point symmetric to (4.6) with respect to (3) on the number line?
#number-line
#symmetry
#midpoint
#decimals
A (1.4)
B (2.4)
C (3.4)
D (5.6)
Explanation opens after your attempt
Step 1
Concept
For the symmetric point (3) is the midpoint so the other point is \(2\times3-4.6=1.4\). In symmetry the midpoint is equally distant from both endpoints.
Step 2
Why this answer is correct
The correct answer is A. (1.4). For the symmetric point (3) is the midpoint so the other point is \(2\times3-4.6=1.4\). In symmetry the midpoint is equally distant from both endpoints.
Step 3
Exam Tip
सममित बिंदु के लिए (3) मध्य बिंदु होगा इसलिए दूसरा बिंदु \(2\times3-4.6=1.4\) है। सममिति में मध्य बिंदु दोनों सिरों से बराबर दूरी पर होता है।
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संख्या रेखा पर (1.75) का (0) के सापेक्ष सममित बिंदु कौन सा होगा?
What will be the point symmetric to (1.75) with respect to (0) on the number line?
#number-line
#symmetry
#opposite-numbers
#decimals
A (-1.75)
B (-0.75)
C (0.75)
D (1.75)
Explanation opens after your attempt
Correct Answer
A. (-1.75)
Step 1
Concept
The symmetric point about (0) is the opposite number, so the answer is (-1.75). Opposite numbers are at equal distance.
Step 2
Why this answer is correct
The correct answer is A. (-1.75). The symmetric point about (0) is the opposite number, so the answer is (-1.75). Opposite numbers are at equal distance.
Step 3
Exam Tip
(0) के सापेक्ष सममित बिंदु विपरीत संख्या होता है इसलिए उत्तर (-1.75) है। विपरीत संख्याएं बराबर दूरी पर होती हैं।
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कौन सा विकल्प संख्या रेखा पर (0) से समान दूरी पर स्थित दो बिंदु दिखाता है?
Which option shows two points at equal distance from (0) on the number line?
#number-line
#opposite-numbers
#distance
#symmetry
A (2.5) और (-2.5) / (2.5) and (-2.5)
B (2.5) और (-2) / (2.5) and (-2)
C (1.5) और (2.5) / (1.5) and (2.5)
D (0.5) और (1.5) / (0.5) and (1.5)
Explanation opens after your attempt
Correct Answer
A. (2.5) और (-2.5) / (2.5) and (-2.5)
Step 1
Concept
Both (2.5) and (-2.5) are (2.5) units from (0). Opposite numbers are equally distant from the origin.
Step 2
Why this answer is correct
The correct answer is A. (2.5) और (-2.5) / (2.5) and (-2.5). Both (2.5) and (-2.5) are (2.5) units from (0). Opposite numbers are equally distant from the origin.
Step 3
Exam Tip
(2.5) और (-2.5) दोनों की (0) से दूरी (2.5) है। विपरीत संख्याएं मूल बिंदु से बराबर दूरी पर होती हैं।
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संख्या रेखा पर (-1) और (1) के बीच ठीक बीच का बिंदु कौन-सा है?
What is the exact middle point between (-1) and (1) on the number line?
#midpoint
#symmetry
#number-line
A (0)
B (1)
C -(1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The midpoint is \(\frac{-1+1}{2}=0\). Symmetric points have midpoint (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The midpoint is \(\frac{-1+1}{2}=0\). Symmetric points have midpoint (0).
Step 3
Exam Tip
मध्य बिंदु \(\frac{-1+1}{2}=0\) है। सममित बिंदुओं का मध्य (0) होता है।
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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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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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(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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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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बहुपद \(10x^3-6x^2+2x-1\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(10x^3-6x^2+2x-1\)?
#coefficient
#x-term
A (10)
B (-6)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the (x)-term (2x) is (2). Look only at the term containing \(x^1\).
Step 2
Why this answer is correct
The correct answer is C. (2). The coefficient of the (x)-term (2x) is (2). Look only at the term containing \(x^1\).
Step 3
Exam Tip
(x) वाले पद (2x) का गुणांक (2) है। केवल उसी पद को देखें जिसमें \(x^1\) हो।
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\(2x^3-7\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(2x^3-7\)?
#coefficient
#missing-power
A (2)
B (0)
C (-7)
D (3)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\) term, so the coefficient is (0). A missing power can be treated as a term with zero coefficient.
Step 2
Why this answer is correct
The correct answer is B. (0). There is no \(x^2\) term, so the coefficient is (0). A missing power can be treated as a term with zero coefficient.
Step 3
Exam Tip
\(x^2\) का कोई पद नहीं है इसलिए गुणांक (0) है। अनुपस्थित घात को शून्य गुणांक वाला पद माना जा सकता है।
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