A. दूसरा (5), कटान ((4,0)), ((5,0))/Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
A. दूसरा (4), कटान ((3,0)), ((4,0))/Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
A. दर्शक का ध्यान बार बार बिखर सकता है/Viewer attention can scatter repeatedly
Step 1
Concept
Too many small contrast points can create visual noise. Exam tip: control contrast placement.
Step 2
Why this answer is correct
The correct answer is A. दर्शक का ध्यान बार बार बिखर सकता है / Viewer attention can scatter repeatedly. Too many small contrast points can create visual noise. Exam tip: control contrast placement.
Step 3
Exam Tip
अधिक छोटे विरोध बिंदु दृश्य शोर बना सकते हैं। परीक्षा में contrast placement नियंत्रित करें।
B. प्रथम विश्व युद्ध के बाद न्यायपूर्ण शांति की रूपरेखा देना/Giving a framework for just peace after World War I
Step 1
Concept
The Fourteen Points were linked with peace and self determination after war. For exams connect Wilson with the League of Nations.
Step 2
Why this answer is correct
The correct answer is B. प्रथम विश्व युद्ध के बाद न्यायपूर्ण शांति की रूपरेखा देना / Giving a framework for just peace after World War I. The Fourteen Points were linked with peace and self determination after war. For exams connect Wilson with the League of Nations.
Step 3
Exam Tip
चौदह सूत्र युद्ध के बाद शांति और आत्मनिर्णय जैसे विचारों से जुड़े थे। परीक्षा में विल्सन को राष्ट्र संघ से जोड़ें।
D. खुली कूटनीति और गुप्त क्षेत्रीय वादों के बीच संघर्ष था/There was conflict between open diplomacy and secret territorial promises
Step 1
Concept
Wilson wanted open and just peace but many secret agreements already existed. For exams understand the difference between idealism and power politics.
Step 2
Why this answer is correct
The correct answer is D. खुली कूटनीति और गुप्त क्षेत्रीय वादों के बीच संघर्ष था / There was conflict between open diplomacy and secret territorial promises. Wilson wanted open and just peace but many secret agreements already existed. For exams understand the difference between idealism and power politics.
Step 3
Exam Tip
विल्सन खुली और न्यायपूर्ण शांति चाहते थे पर कई गुप्त समझौते पहले से थे। परीक्षा में आदर्शवाद और शक्ति राजनीति का अंतर समझें।
A. आदर्शवादी शांति और दंडात्मक शर्तों के बीच तनाव/Tension between idealistic peace and punitive terms
Step 1
Concept
Wilson wanted idealistic peace but the treaty imposed harsh terms on Germany. For exams understand the difference between ideas and real politics.
Step 2
Why this answer is correct
The correct answer is A. आदर्शवादी शांति और दंडात्मक शर्तों के बीच तनाव / Tension between idealistic peace and punitive terms. Wilson wanted idealistic peace but the treaty imposed harsh terms on Germany. For exams understand the difference between ideas and real politics.
Step 3
Exam Tip
विल्सन आदर्शवादी शांति चाहते थे पर संधि में जर्मनी पर कठोर शर्तें लगीं। परीक्षा में विचार और वास्तविक राजनीति का अंतर समझें।
A. इसने लोगों को अपनी राजनीतिक व्यवस्था चुनने का सिद्धांत दिया/It gave the principle that peoples could choose their political order
Step 1
Concept
Self-determination gave a new direction to questions of nations and borders. For exams connect it with the post-war peace plan.
Step 2
Why this answer is correct
The correct answer is A. इसने लोगों को अपनी राजनीतिक व्यवस्था चुनने का सिद्धांत दिया / It gave the principle that peoples could choose their political order. Self-determination gave a new direction to questions of nations and borders. For exams connect it with the post-war peace plan.
Step 3
Exam Tip
स्वनिर्णय ने राष्ट्रों और सीमाओं के प्रश्न को नई दिशा दी। परीक्षा में इसे युद्धोत्तर शांति योजना से जोड़ें।
Wilson's Fourteen Points were linked with the peace plan after the First World War. For exams connect them with the background of the League of Nations.
Step 2
Why this answer is correct
The correct answer is C. प्रथम विश्व युद्ध / First World War. Wilson's Fourteen Points were linked with the peace plan after the First World War. For exams connect them with the background of the League of Nations.
Step 3
Exam Tip
विल्सन के चौदह सूत्र प्रथम विश्व युद्ध के बाद शांति योजना से जुड़े थे। परीक्षा में इन्हें राष्ट्र संघ की पृष्ठभूमि से जोड़ें।
A. अल्पसंख्यक सुरक्षा और प्रांतीय स्वायत्तता की चिंता/Concern for minority safeguards and provincial autonomy
Step 1
Concept
The Fourteen Points show disagreement over constitutional representation. Exam tip: remember sequence of 1928 and 1929.
Step 2
Why this answer is correct
The correct answer is A. अल्पसंख्यक सुरक्षा और प्रांतीय स्वायत्तता की चिंता / Concern for minority safeguards and provincial autonomy. The Fourteen Points show disagreement over constitutional representation. Exam tip: remember sequence of 1928 and 1929.
Step 3
Exam Tip
चौदह सूत्र संवैधानिक प्रतिनिधित्व के मतभेद को दिखाते हैं। परीक्षा में 1928 और 1929 का क्रम याद रखें।
B. संयुक्त नागरिक राष्ट्रवाद और अल्पसंख्यक सुरक्षा की अलग मांग/Joint civic nationalism and separate demand for minority safeguards
Step 1
Concept
Both documents show different constitutional ideas of representation. Exam tip: remember the sequence of 1928 and 1929.
Step 2
Why this answer is correct
The correct answer is B. संयुक्त नागरिक राष्ट्रवाद और अल्पसंख्यक सुरक्षा की अलग मांग / Joint civic nationalism and separate demand for minority safeguards. Both documents show different constitutional ideas of representation. Exam tip: remember the sequence of 1928 and 1929.
Step 3
Exam Tip
दोनों दस्तावेज प्रतिनिधित्व की अलग संवैधानिक सोच दिखाते हैं। परीक्षा में 1928 और 1929 का क्रम याद रखें।
A. मुस्लिम बहुल प्रांतों की राजनीतिक सुरक्षा/Political safeguards for Muslim-majority provinces
Step 1
Concept
The Fourteen Points show concern over central power and minority safeguards. Exam tip: remember constitutional differences.
Step 2
Why this answer is correct
The correct answer is A. मुस्लिम बहुल प्रांतों की राजनीतिक सुरक्षा / Political safeguards for Muslim-majority provinces. The Fourteen Points show concern over central power and minority safeguards. Exam tip: remember constitutional differences.
Step 3
Exam Tip
चौदह सूत्र केंद्र की शक्ति और अल्पसंख्यक सुरक्षा पर चिंता दिखाते हैं। परीक्षा में संवैधानिक मतभेद याद रखें।
A. अल्पसंख्यक सुरक्षा और प्रतिनिधित्व की पद्धति/Method of minority safeguards and representation
Step 1
Concept
Both documents show different ideas of constitutional representation. Exam tip: remember the sequence of 1928 and 1929.
Step 2
Why this answer is correct
The correct answer is A. अल्पसंख्यक सुरक्षा और प्रतिनिधित्व की पद्धति / Method of minority safeguards and representation. Both documents show different ideas of constitutional representation. Exam tip: remember the sequence of 1928 and 1929.
Step 3
Exam Tip
दोनों दस्तावेज संवैधानिक प्रतिनिधित्व की अलग सोच दिखाते हैं। परीक्षा में 1928 और 1929 का क्रम याद रखें।
A. अल्पसंख्यक प्रतिनिधित्व और संघीय सुरक्षा की मांग रखी/It raised demands for minority representation and federal safeguards
Step 1
Concept
The Fourteen Points show constitutional differences. Exam tip is to remember the debates of 1928 and 1929.
Step 2
Why this answer is correct
The correct answer is A. अल्पसंख्यक प्रतिनिधित्व और संघीय सुरक्षा की मांग रखी / It raised demands for minority representation and federal safeguards. The Fourteen Points show constitutional differences. Exam tip is to remember the debates of 1928 and 1929.
Step 3
Exam Tip
चौदह सूत्र संवैधानिक मतभेदों को दिखाते हैं। परीक्षा में 1928 और 1929 की बहस याद रखें।
D. संवैधानिक प्रतिनिधित्व और अल्पसंख्यक सुरक्षा/Constitutional representation and minority safeguards
Step 1
Concept
Both documents were linked with debate on constitutional rights and representation. Exam tip: remember sequence of 1928 and 1929.
Step 2
Why this answer is correct
The correct answer is D. संवैधानिक प्रतिनिधित्व और अल्पसंख्यक सुरक्षा / Constitutional representation and minority safeguards. Both documents were linked with debate on constitutional rights and representation. Exam tip: remember sequence of 1928 and 1929.
Step 3
Exam Tip
दोनों दस्तावेज संवैधानिक अधिकारों और प्रतिनिधित्व की बहस से जुड़े थे। परीक्षा में 1928 और 1929 का क्रम याद रखें।
A. मुस्लिम बहुल प्रांतों की स्वायत्तता और सुरक्षा/Autonomy and security of Muslim-majority provinces
Step 1
Concept
The Fourteen Points showed concern about central power and minority safeguards. Exam tip: understand constitutional differences.
Step 2
Why this answer is correct
The correct answer is A. मुस्लिम बहुल प्रांतों की स्वायत्तता और सुरक्षा / Autonomy and security of Muslim-majority provinces. The Fourteen Points showed concern about central power and minority safeguards. Exam tip: understand constitutional differences.
Step 3
Exam Tip
चौदह सूत्र केंद्र की शक्ति और अल्पसंख्यक सुरक्षा पर चिंता दिखाते थे। परीक्षा में संवैधानिक मतभेद समझें।
A. मुस्लिम अल्पसंख्यक सुरक्षा को अपर्याप्त मानना/Considering Muslim minority safeguards inadequate
Step 1
Concept
The Fourteen Points were linked with debate on minority representation. Exam tip: remember differences in constitutional demands.
Step 2
Why this answer is correct
The correct answer is A. मुस्लिम अल्पसंख्यक सुरक्षा को अपर्याप्त मानना / Considering Muslim minority safeguards inadequate. The Fourteen Points were linked with debate on minority representation. Exam tip: remember differences in constitutional demands.
Step 3
Exam Tip
चौदह सूत्र अल्पसंख्यक प्रतिनिधित्व की बहस से जुड़े थे। परीक्षा में संवैधानिक मांगों के मतभेद याद रखें।
A. संविधान निर्माण में अल्पसंख्यक सुरक्षा पर असहमति/Disagreement over minority safeguards in constitution making
Step 1
Concept
These documents showed deep differences over representation and rights. Exam tip: remember the constitutional debate of 1928-29.
Step 2
Why this answer is correct
The correct answer is A. संविधान निर्माण में अल्पसंख्यक सुरक्षा पर असहमति / Disagreement over minority safeguards in constitution making. These documents showed deep differences over representation and rights. Exam tip: remember the constitutional debate of 1928-29.
Step 3
Exam Tip
इन दस्तावेजों ने प्रतिनिधित्व और अधिकारों पर गहरे मतभेद दिखाए। परीक्षा में 1928-29 की संवैधानिक बहस याद रखें।
A. मुस्लिम राजनीतिक प्रतिनिधित्व और सुरक्षा/Muslim political representation and safeguards
Step 1
Concept
The Fourteen Points raised minority rights after the Nehru Report. Exam tip is to link it with constitutional differences.
Step 2
Why this answer is correct
The correct answer is A. मुस्लिम राजनीतिक प्रतिनिधित्व और सुरक्षा / Muslim political representation and safeguards. The Fourteen Points raised minority rights after the Nehru Report. Exam tip is to link it with constitutional differences.
Step 3
Exam Tip
चौदह सूत्र ने नेहरू रिपोर्ट के बाद अल्पसंख्यक अधिकारों की मांग रखी। परीक्षा में इसे संवैधानिक मतभेदों से जोड़ें।
The Fourteen Points resulted from disagreement over minority rights. Exam tip: remember constitutional debates of 1928-29.
Step 2
Why this answer is correct
The correct answer is A. नेहरू रिपोर्ट / Nehru Report. The Fourteen Points resulted from disagreement over minority rights. Exam tip: remember constitutional debates of 1928-29.
Step 3
Exam Tip
चौदह सूत्र अल्पसंख्यक अधिकारों पर असहमति का परिणाम थे। परीक्षा में 1928-29 की संवैधानिक बहस याद रखें।
A. अल्पसंख्यक अधिकार और पृथक प्रतिनिधित्व/Minority rights and separate representation
Step 1
Concept
A section of Muslim League found minority safeguards in the Nehru Report insufficient. Exam tip: understand constitutional debates.
Step 2
Why this answer is correct
The correct answer is A. अल्पसंख्यक अधिकार और पृथक प्रतिनिधित्व / Minority rights and separate representation. A section of Muslim League found minority safeguards in the Nehru Report insufficient. Exam tip: understand constitutional debates.
Step 3
Exam Tip
नेहरू रिपोर्ट पर मुस्लिम लीग के एक हिस्से को अल्पसंख्यक सुरक्षा अपर्याप्त लगी। परीक्षा में संवैधानिक बहसों को समझें।
A. संवैधानिक ढाँचे और अल्पसंख्यक प्रतिनिधित्व/Constitutional framework and minority representation
Step 1
Concept
After the Nehru Report differences emerged over representation and rights. Exam tip is to link it with constitutional politics.
Step 2
Why this answer is correct
The correct answer is A. संवैधानिक ढाँचे और अल्पसंख्यक प्रतिनिधित्व / Constitutional framework and minority representation. After the Nehru Report differences emerged over representation and rights. Exam tip is to link it with constitutional politics.
Step 3
Exam Tip
नेहरू रिपोर्ट के बाद प्रतिनिधित्व और अधिकारों पर मतभेद उभरे। परीक्षा में इसे संवैधानिक राजनीति से जोड़ें।
When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 2
Why this answer is correct
The correct answer is C. ( (8,0) ) और ( (0,4) ). When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 3
Exam Tip
(y=0) पर (x=8) और (x=0) पर (y=4)। दो सही बिंदु मिलने पर रेखा आसानी से बनती है।
When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 2
Why this answer is correct
The correct answer is C. ( (8,0) ) और ( (0,4) ). When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 3
Exam Tip
(y=0) पर (x=8) और (x=0) पर (y=4)। सही दो बिंदु मिलें तो रेखा आसानी से बनती है।
At least (2) points are enough to draw a straight line. In exams, a third point may be used for checking.
Step 2
Why this answer is correct
The correct answer is A. (2) बिंदु / (2) points. At least (2) points are enough to draw a straight line. In exams, a third point may be used for checking.
Step 3
Exam Tip
एक सीधी रेखा खींचने के लिए कम से कम (2) बिंदु पर्याप्त होते हैं। परीक्षा में तीसरा बिंदु जाँच के लिए लिया जा सकता है।
A. \(-\sqrt{13}\) और \(\sqrt{13}\)/\(-\sqrt{13}\) and \(\sqrt{13}\)
Step 1
Concept
Points at the same distance from (0) occur on both sides, so the values are \(\pm\sqrt{13}\). In distance questions, check both directions.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{13}\) और \(\sqrt{13}\) / \(-\sqrt{13}\) and \(\sqrt{13}\). Points at the same distance from (0) occur on both sides, so the values are \(\pm\sqrt{13}\). In distance questions, check both directions.
Step 3
Exam Tip
(0) से समान दूरी पर दोनों ओर बिंदु होते हैं, इसलिए मान \(\pm\sqrt{13}\) होंगे। दूरी वाले प्रश्नों में दोनों दिशाएँ जाँचें।
A. दो बिंदु, (x=-5) पर स्पर्श/Two points, touching at (x=-5)
Step 1
Concept
The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-5) पर स्पर्श / Two points, touching at (x=-5). The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-5) और (14) हैं तथा ((x+5)2) के कारण (-5) पर स्पर्श है। टिप: बाहरी (11) शून्यक नहीं बदलता।
Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-11) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
A. दो बिंदु, (x=-4) पर स्पर्श/Two points, touching at (x=-4)
Step 1
Concept
The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-4) पर स्पर्श / Two points, touching at (x=-4). The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-4) और (12) हैं तथा ((x+4)2) के कारण (-4) पर स्पर्श है। टिप: बाहरी (9) शून्यक नहीं बदलता।
Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-7) और (2) हैं। टिप: समान (x)-मान को एक बार गिनें।
A. दो बिंदु, (x=-3) पर स्पर्श/Two points, touching at (x=-3)
Step 1
Concept
The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-3) पर स्पर्श / Two points, touching at (x=-3). The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-3) और (10) हैं तथा ((x+3)2) के कारण (-3) पर स्पर्श है। टिप: बाहरी (7) शून्यक नहीं बदलता।
A. दो बिंदु, (x=-2) पर स्पर्श/Two points, touching at (x=-2)
Step 1
Concept
The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-2) पर स्पर्श / Two points, touching at (x=-2). The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-2) और (7) हैं, तथा ((x+2)2) के कारण (-2) पर स्पर्श है। टिप: बाहरी (5) शून्यक नहीं बदलता।
A. दो बिंदु, (x=2) पर स्पर्श/Two points, touching at (x=2)
Step 1
Concept
The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=2) पर स्पर्श / Two points, touching at (x=2). The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.
Step 3
Exam Tip
शून्यक (2) और (-1) हैं, तथा ((x-2)2) के कारण (x=2) पर स्पर्श है। टिप: बाहरी (3) शून्यक नहीं बदलता।
The zeroes are (-3) and (1), so there are two distinct meeting points. Tip: count the repeated zero (1) only once for distinct points.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. The zeroes are (-3) and (1), so there are two distinct meeting points. Tip: count the repeated zero (1) only once for distinct points.
Step 3
Exam Tip
शून्यक (-3) और (1) हैं, इसलिए दो अलग बिंदु मिलेंगे। टिप: दोहराए हुए शून्यक (1) को अलग गिनती में एक बार गिनें।
When (p(a)=0), the point is ((a,0)). Tip: place the function value as the second coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((-2,0)) और ((3,0)) / ((-2,0)) and ((3,0)). When (p(a)=0), the point is ((a,0)). Tip: place the function value as the second coordinate.
Step 3
Exam Tip
(p(a)=0) होने पर बिंदु ((a,0)) बनता है। टिप: फलन मान को दूसरे निर्देशांक में रखें।
Points showing zeroes have (y=0). Tip: check the second coordinate when choosing points.
Step 2
Why this answer is correct
The correct answer is B. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0)). Points showing zeroes have (y=0). Tip: check the second coordinate when choosing points.
Step 3
Exam Tip
शून्यक दिखाने वाले बिंदुओं में (y=0) होता है। टिप: बिंदु चुनते समय दूसरा निर्देशांक देखें।
A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0)). A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 3
Exam Tip
शून्यक (a) से कटान बिंदु ((a,0)) बनता है। टिप: शून्यक को (y)-निर्देशांक न बनाएं।
Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)), ((3,0)), ((8,0)). Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 3
Exam Tip
शून्यकों को (x)-निर्देशांक बनाकर (y=0) लिया जाता है। इसलिए कटाव बिंदु ((-1,0)), ((3,0)), और ((8,0)) होंगे।
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
A. दूसरा (7), कटान ((6,0)), ((7,0))/Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (11). The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (5) है इसलिए दूसरा शून्यक (11) होगा। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
A. दूसरा (7), कटान ((4,0)), ((7,0))/Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-9). The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (-2) है, इसलिए दूसरा शून्यक (-9) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य से जोड़ें।
The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (3) है इसलिए दूसरा शून्यक (-5) होगा। टिप: \(\frac{a+b}{2}\) को सममिति अक्ष के बराबर रखें।
The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (10). The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दोनों शून्यकों का औसत (4) है इसलिए दूसरा शून्यक (10) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य मान से जोड़ें।
The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (2) है, इसलिए दूसरा शून्यक (-5) होगा। टिप: \( \frac{a+b}{2} \) को सममिति अक्ष के बराबर रखें।
The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is C. (7). The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (1) होगा इसलिए दूसरा शून्यक (7) है। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
A. दूसरा (3), कटान ((2,0)), ((3,0))/Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,25)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,25)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,25)) शून्यक नहीं बताता।
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-20)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-20)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,-20)) शून्यक नहीं बताता।
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,18)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,18)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं (y)-अक्ष कटान से नहीं। टिप: ((0,18)) शून्यक नहीं बताता।
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-15)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-15)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,-15)) शून्यक नहीं बताता।
Both have the same (x)-value (3), so there is one distinct zero. Tip: count a repeated value once for distinct count.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Both have the same (x)-value (3), so there is one distinct zero. Tip: count a repeated value once for distinct count.
Step 3
Exam Tip
दोनों में (x)-मान समान (3) है इसलिए अलग शून्यक एक है। टिप: दोहराए मान को अलग गिनती में एक बार लें।
B. क्योंकि उनके (y)-मान (0) नहीं हैं/Because their (y)-values are not (0)
Step 1
Concept
At (3) and (5), (p(x)) is (4) and (-1). Tip: for a zero, the function value must be exactly (0).
Step 2
Why this answer is correct
The correct answer is B. क्योंकि उनके (y)-मान (0) नहीं हैं / Because their (y)-values are not (0). At (3) and (5), (p(x)) is (4) and (-1). Tip: for a zero, the function value must be exactly (0).
Step 3
Exam Tip
(3) और (5) पर (p(x)) क्रमशः (4) और (-1) है। टिप: शून्यक के लिए फलन मान बिल्कुल (0) होना चाहिए।
The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.
Step 2
Why this answer is correct
The correct answer is C. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0)). The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.
Step 3
Exam Tip
(p(a)=0) का बिंदु ((a,0)) होता है। टिप: (p(x)) ग्राफ में (y)-निर्देशांक होता है।
For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2-\sqrt{3}\). For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 3
Exam Tip
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है।
A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\)/Other \(\sqrt{5}\), \(k=\sqrt{5}\)
Step 1
Concept
The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\). The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 3
Exam Tip
गुणनफल (5) है, इसलिए दूसरा शून्यक \(\frac{5}{\sqrt{5}}=\sqrt{5}\) होगा। योग \(2\sqrt{5}=2k\), अतः \(k=\sqrt{5}\) है।
The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-1). The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (8) है और औसत \(\frac{-10+8}{2}=-1\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-2). The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (4) है और औसत \(\frac{-8+4}{2}=-2\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (7). The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (2) होगा, इसलिए दूसरा शून्यक (7) है। टिप: परवलय में सममिति अक्ष शून्यकों के मध्य से गुजरता है।
At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 2
Why this answer is correct
The correct answer is A. बहुपद का मान / Value of the polynomial. At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। ग्राफ पढ़ते समय (y=0) वाले बिंदु देखें।
A. दर्शक का ध्यान विभाजित होगा/Viewer attention will divide
Step 1
Concept
Equal emphasis weakens visual order. Exam tip: separate primary and supporting focus.
Step 2
Why this answer is correct
The correct answer is A. दर्शक का ध्यान विभाजित होगा / Viewer attention will divide. Equal emphasis weakens visual order. Exam tip: separate primary and supporting focus.
Step 3
Exam Tip
बराबर जोर दृश्य क्रम को कमजोर करता है। परीक्षा में प्राथमिक और सहायक केंद्र अलग करें।
The correct answer is A. वे स्थानिक तर्क को तोड़ते हैं / They break spatial logic. Inconsistent vanishing points confuse depth. Exam tip: check perspective consistency.
Step 3
Exam Tip
असंगत लुप्त बिंदु गहराई को भ्रमित करते हैं। परीक्षा में perspective consistency जांचें।
A. दर्शक का ध्यान विभाजित होगा/Viewer's attention will divide
Step 1
Concept
Too many equal emphases weaken visual order. Exam tip: focal hierarchy is important.
Step 2
Why this answer is correct
The correct answer is A. दर्शक का ध्यान विभाजित होगा / Viewer's attention will divide. Too many equal emphases weaken visual order. Exam tip: focal hierarchy is important.
Step 3
Exam Tip
अधिक समान जोर दृश्य क्रम को कमजोर करता है। परीक्षा में focal hierarchy जरूरी है।
A. दर्शक का ध्यान बिखर सकता है/Viewer's attention may scatter
Step 1
Concept
Too many focal points can divide attention. Exam tip: create focal hierarchy.
Step 2
Why this answer is correct
The correct answer is A. दर्शक का ध्यान बिखर सकता है / Viewer's attention may scatter. Too many focal points can divide attention. Exam tip: create focal hierarchy.
Step 3
Exam Tip
बहुत अधिक केंद्र बिंदु ध्यान को बांट सकते हैं। परीक्षा में focal hierarchy बनाएं।
A. यह अत्यंत प्राचीन पर्वतमाला है/It is a very ancient mountain range
Step 1
Concept
Aravalli is an ancient range eroded over a long time. For exams remember Aravalli as older than Himalaya.
Step 2
Why this answer is correct
The correct answer is A. यह अत्यंत प्राचीन पर्वतमाला है / It is a very ancient mountain range. Aravalli is an ancient range eroded over a long time. For exams remember Aravalli as older than Himalaya.
Step 3
Exam Tip
अरावली लंबे समय से अपक्षयित प्राचीन पर्वतमाला है। परीक्षा में अरावली को हिमालय से पुराना याद रखें।
Self-determination was linked with the rights of smaller nations. For exams connect it with post-World War I peace.
Step 2
Why this answer is correct
The correct answer is C. आत्मनिर्णय / Self-Determination. Self-determination was linked with the rights of smaller nations. For exams connect it with post-World War I peace.
Step 3
Exam Tip
आत्मनिर्णय छोटे राष्ट्रों के अधिकार से जुड़ा विचार था। परीक्षा में इसे प्रथम विश्व युद्ध के बाद की शांति से जोड़ें।
C. जनताओं को अपना शासन चुनने का अधिकार/Right of Peoples to Choose Their Government
Step 1
Concept
Self-determination meant the right of peoples to choose their government. For exams connect it with post-war peace.
Step 2
Why this answer is correct
The correct answer is C. जनताओं को अपना शासन चुनने का अधिकार / Right of Peoples to Choose Their Government. Self-determination meant the right of peoples to choose their government. For exams connect it with post-war peace.
Step 3
Exam Tip
आत्मनिर्णय का अर्थ लोगों को अपना शासन चुनने का अधिकार देना था। परीक्षा में इसे युद्धोत्तर शांति से जोड़ें।
C. युद्ध के बाद शांति व्यवस्था/Post-war Peace Order
Step 1
Concept
Wilson's Fourteen Points were linked with peace after World War I. For exams, also connect him with the idea of the League of Nations.
Step 2
Why this answer is correct
The correct answer is C. युद्ध के बाद शांति व्यवस्था / Post-war Peace Order. Wilson's Fourteen Points were linked with peace after World War I. For exams, also connect him with the idea of the League of Nations.
Step 3
Exam Tip
विल्सन के चौदह सूत्र प्रथम विश्व युद्ध के बाद शांति व्यवस्था से जुड़े थे। परीक्षा में उन्हें लीग ऑफ नेशंस के विचार से भी जोड़ें।
