C. एम एस स्वामीनाथन कृषि विज्ञान/M S Swaminathan agricultural science
Step 1
Concept
M S Swaminathan is linked with agricultural science and the Green Revolution. Identify the scientific name of 2024 separately.
Step 2
Why this answer is correct
The correct answer is C. एम एस स्वामीनाथन कृषि विज्ञान / M S Swaminathan agricultural science. M S Swaminathan is linked with agricultural science and the Green Revolution. Identify the scientific name of 2024 separately.
Step 3
Exam Tip
एम एस स्वामीनाथन कृषि विज्ञान और हरित क्रांति से जुड़े हैं। परीक्षा में 2024 के वैज्ञानिक नाम को अलग पहचानें।
In 2019 Pranab Mukherjee was linked with public life Bhupen Hazarika with art and Nanaji Deshmukh with social work. Remember the year by fields.
Step 2
Why this answer is correct
The correct answer is C. 2019 / 2019. In 2019 Pranab Mukherjee was linked with public life Bhupen Hazarika with art and Nanaji Deshmukh with social work. Remember the year by fields.
Step 3
Exam Tip
2019 में प्रणब मुखर्जी सार्वजनिक जीवन भूपेन हजारिका कला और नानाजी देशमुख समाज कार्य से जुड़े थे। परीक्षा में क्षेत्र पहचानकर वर्ष याद करें।
Pranab Mukherjee received the Bharat Ratna in 2019. Remember him in the 2019 group.
Step 2
Why this answer is correct
The correct answer is D. प्रणब मुखर्जी 2024 / Pranab Mukherjee 2024. Pranab Mukherjee received the Bharat Ratna in 2019. Remember him in the 2019 group.
Step 3
Exam Tip
प्रणब मुखर्जी को 2019 में भारत रत्न मिला था। परीक्षा में उन्हें 2019 के समूह में याद रखें।
Lata Mangeshkar received the Bharat Ratna in 2001 not in 1999. Keep the music names of 1999 and 2001 separate.
Step 2
Why this answer is correct
The correct answer is D. लता मंगेशकर 1999 / Lata Mangeshkar 1999. Lata Mangeshkar received the Bharat Ratna in 2001 not in 1999. Keep the music names of 1999 and 2001 separate.
Step 3
Exam Tip
लता मंगेशकर को 2001 में भारत रत्न मिला था न कि 1999 में। परीक्षा में 1999 और 2001 के संगीत नाम अलग रखें।
Karpoori Thakur was announced posthumously for the Bharat Ratna in 2024. Link him with Bihar and social justice.
Step 2
Why this answer is correct
The correct answer is A. कर्पूरी ठाकुर / Karpoori Thakur. Karpoori Thakur was announced posthumously for the Bharat Ratna in 2024. Link him with Bihar and social justice.
Step 3
Exam Tip
कर्पूरी ठाकुर को 2024 में मरणोपरांत भारत रत्न घोषित किया गया। परीक्षा में उन्हें बिहार और सामाजिक न्याय से जोड़ें।
Among the 2024 announced names L K Advani was the living recipient. Remember the other 2024 names as posthumous.
Step 2
Why this answer is correct
The correct answer is B. एल के आडवाणी / L K Advani. Among the 2024 announced names L K Advani was the living recipient. Remember the other 2024 names as posthumous.
Step 3
Exam Tip
2024 के घोषित नामों में एल के आडवाणी जीवित प्राप्तकर्ता थे। परीक्षा में बाकी 2024 नामों को मरणोपरांत रूप में याद रखें।
In 2024 L K Advani was the living announced recipient. Remember the other 2024 names as posthumous.
Step 2
Why this answer is correct
The correct answer is C. एल के आडवाणी / L K Advani. In 2024 L K Advani was the living announced recipient. Remember the other 2024 names as posthumous.
Step 3
Exam Tip
2024 में एल के आडवाणी जीवित घोषित प्राप्तकर्ता थे। परीक्षा में बाकी 2024 नामों को मरणोपरांत रूप में याद रखें।
Aruna Asaf Ali Gulzarilal Nanda and A P J Abdul Kalam were all honoured in 1997. Remember the three names of 1997.
Step 2
Why this answer is correct
The correct answer is A. ए पी जे अब्दुल कलाम / A P J Abdul Kalam. Aruna Asaf Ali Gulzarilal Nanda and A P J Abdul Kalam were all honoured in 1997. Remember the three names of 1997.
Step 3
Exam Tip
अरुणा आसफ अली गुलजारीलाल नंदा और ए पी जे अब्दुल कलाम सभी 1997 में सम्मानित हुए। परीक्षा में 1997 के तीन नाम याद रखें।
Satyajit Ray Maulana Azad and J R D Tata were all honoured in 1992. Remember the 1992 group together.
Step 2
Why this answer is correct
The correct answer is A. जे आर डी टाटा / J R D Tata. Satyajit Ray Maulana Azad and J R D Tata were all honoured in 1992. Remember the 1992 group together.
Step 3
Exam Tip
सत्यजीत राय मौलाना आजाद और जे आर डी टाटा तीनों 1992 में सम्मानित हुए। परीक्षा में 1992 का समूह साथ याद रखें।
In 2019 Pranab Mukherjee was linked with public life Bhupen Hazarika with art and Nanaji Deshmukh with social work. Identify the fields of 2019.
Step 2
Why this answer is correct
The correct answer is C. 2019 / 2019. In 2019 Pranab Mukherjee was linked with public life Bhupen Hazarika with art and Nanaji Deshmukh with social work. Identify the fields of 2019.
Step 3
Exam Tip
2019 में प्रणब मुखर्जी सार्वजनिक जीवन भूपेन हजारिका कला और नानाजी देशमुख समाज कार्य से जुड़े थे। परीक्षा में 2019 के क्षेत्रों को पहचानें।
P V Narasimha Rao was announced for the Bharat Ratna posthumously in 2024. Connect him with economic reforms.
Step 2
Why this answer is correct
The correct answer is A. पी वी नरसिम्हा राव / P V Narasimha Rao. P V Narasimha Rao was announced for the Bharat Ratna posthumously in 2024. Connect him with economic reforms.
Step 3
Exam Tip
पी वी नरसिम्हा राव को 2024 में मरणोपरांत भारत रत्न घोषित किया गया। परीक्षा में उन्हें आर्थिक सुधारों से जोड़ें।
M S Swaminathan was announced for the Bharat Ratna posthumously in 2024. Link him with the Green Revolution and agricultural science.
Step 2
Why this answer is correct
The correct answer is C. एम एस स्वामीनाथन / M S Swaminathan. M S Swaminathan was announced for the Bharat Ratna posthumously in 2024. Link him with the Green Revolution and agricultural science.
Step 3
Exam Tip
एम एस स्वामीनाथन को 2024 में मरणोपरांत भारत रत्न घोषित किया गया। परीक्षा में उन्हें हरित क्रांति और कृषि विज्ञान से जोड़ें।
In 2019 three persons and in 2024 five persons received or were announced for the Bharat Ratna. Remember the recent year counts.
Step 2
Why this answer is correct
The correct answer is B. 2019 तीन 2024 पांच / 2019 three 2024 five. In 2019 three persons and in 2024 five persons received or were announced for the Bharat Ratna. Remember the recent year counts.
Step 3
Exam Tip
2019 में तीन और 2024 में पांच व्यक्तियों को भारत रत्न मिला या घोषित किया गया। परीक्षा में हाल के वर्षों की संख्या याद रखें।
In 1991 Rajiv Gandhi and Sardar Patel were posthumous while Morarji Desai was a living recipient. Remember this pattern for the year.
Step 2
Why this answer is correct
The correct answer is B. 1991 / 1991. In 1991 Rajiv Gandhi and Sardar Patel were posthumous while Morarji Desai was a living recipient. Remember this pattern for the year.
Step 3
Exam Tip
1991 में राजीव गांधी और सरदार पटेल मरणोपरांत थे जबकि मोरारजी देसाई जीवित प्राप्तकर्ता थे। परीक्षा में इस वर्ष की संरचना याद रखें।
B. लाल बहादुर शास्त्री 1966/Lal Bahadur Shastri 1966
Step 1
Concept
Lal Bahadur Shastri became the first posthumous Bharat Ratna recipient in 1966. Link the start of posthumous awards with him.
Step 2
Why this answer is correct
The correct answer is B. लाल बहादुर शास्त्री 1966 / Lal Bahadur Shastri 1966. Lal Bahadur Shastri became the first posthumous Bharat Ratna recipient in 1966. Link the start of posthumous awards with him.
Step 3
Exam Tip
लाल बहादुर शास्त्री 1966 में पहले मरणोपरांत भारत रत्न प्राप्तकर्ता बने। परीक्षा में मरणोपरांत श्रेणी की शुरुआत उनसे जोड़ें।
Substituting ((2,8)) gives \(13\cdot2+4\cdot8=58\), not (52). Check every point in the equation before drawing the graph.
Step 2
Why this answer is correct
The correct answer is D. ((2,8)). Substituting ((2,8)) gives \(13\cdot2+4\cdot8=58\), not (52). Check every point in the equation before drawing the graph.
Step 3
Exam Tip
((2,8)) रखने पर \(13\cdot2+4\cdot8=58\), जो (52) नहीं है। ग्राफ बनाने से पहले हर बिंदु को समीकरण में जांचें।
Substituting ((-4,1)) makes (x+y=-3) and (2x-y=-9) both true. Substituting the intersection point in both equations is the fastest check.
Step 2
Why this answer is correct
The correct answer is A. (x+y=-3), (2x-y=-9). Substituting ((-4,1)) makes (x+y=-3) and (2x-y=-9) both true. Substituting the intersection point in both equations is the fastest check.
Step 3
Exam Tip
((-4,1)) रखने पर (x+y=-3) और (2x-y=-9) दोनों सही हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में रखना सबसे तेज जांच है।
Substituting ((4,3)) gives (2x+5y=31) but not (3x-y=7); the true common point is (\left\(\frac{66}{17},\frac{79}{17}\right\)). Verify in both equations before choosing.
Step 2
Why this answer is correct
The correct answer is A. ((4,3)). Substituting ((4,3)) gives (2x+5y=31) but not (3x-y=7); the true common point is (\left\(\frac{66}{17},\frac{79}{17}\right\)). Verify in both equations before choosing.
Step 3
Exam Tip
((4,3)) रखने पर (2x+5y=31) और (3x-y=9) नहीं; सही साझा बिंदु (\left\(\frac{66}{17},\frac{79}{17}\right\)) है। सही उत्तर चुनने से पहले दोनों समीकरणों में जांच करें।
Substituting ((4,3)) does not give (2x+5y=29), so it is not correct; the true solution is (\left\(\frac{64}{17},\frac{73}{17}\right\)). Check a point in both equations.
Step 2
Why this answer is correct
The correct answer is C. ((4,3)). Substituting ((4,3)) does not give (2x+5y=29), so it is not correct; the true solution is (\left\(\frac{64}{17},\frac{73}{17}\right\)). Check a point in both equations.
Step 3
Exam Tip
((4,3)) रखने पर (2x+5y=23) नहीं, इसलिए यह गलत होता; सही हल (\left\(\frac{64}{17},\frac{73}{17}\right\)) है। विकल्प जांचते समय दोनों समीकरणों में बिंदु रखना जरूरी है।
Substituting ((-1,6)) makes (2x+y=4) and (x-y=-7) both true. The intersection point must lie on both lines.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=4), (x-y=-7). Substituting ((-1,6)) makes (2x+y=4) and (x-y=-7) both true. The intersection point must lie on both lines.
Step 3
Exam Tip
((-1,6)) रखने पर (2x+y=4) और (x-y=-7) दोनों सही हैं। प्रतिच्छेद बिंदु दोनों रेखाओं पर होना चाहिए।
B. केवल ((10,0)) और ((0,12)) रेखा पर हैं/Only ((10,0)) and ((0,12)) lie on the line
Step 1
Concept
((10,0)) and ((0,12)) satisfy the equation, but ((5,6)) does not give (60). Check points before drawing the graph.
Step 2
Why this answer is correct
The correct answer is B. केवल ((10,0)) और ((0,12)) रेखा पर हैं / Only ((10,0)) and ((0,12)) lie on the line. ((10,0)) and ((0,12)) satisfy the equation, but ((5,6)) does not give (60). Check points before drawing the graph.
Step 3
Exam Tip
((10,0)) और ((0,12)) समीकरण को संतुष्ट करते हैं, लेकिन ((5,6)) देने पर (60) नहीं मिलता। ग्राफ बनाने से पहले बिंदुओं की जांच करें।
Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 2
Why this answer is correct
The correct answer is A. \(2x+y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\). Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 3
Exam Tip
(\left\(\frac{5}{2},-\frac{3}{2}\right\)) रखने पर \(2x+y=\frac{7}{2}\) और \(x-2y=\frac{11}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचें।
Substituting ((0,4)) gives \(4\cdot0-9\cdot4=-36\), not (36). Check every point in the equation before drawing the graph.
Step 2
Why this answer is correct
The correct answer is D. ((0,4)). Substituting ((0,4)) gives \(4\cdot0-9\cdot4=-36\), not (36). Check every point in the equation before drawing the graph.
Step 3
Exam Tip
((0,4)) रखने पर \(4\cdot0-9\cdot4=-36\), जो (36) नहीं है। ग्राफ बनाने से पहले हर बिंदु को समीकरण में जांचें।
Substituting ((-2,-3)) makes (x+y=-5) and (2x-y=-1) both true. Substituting the intersection point in both equations is the fastest check.
Step 2
Why this answer is correct
The correct answer is A. (x+y=-5), (2x-y=-1). Substituting ((-2,-3)) makes (x+y=-5) and (2x-y=-1) both true. Substituting the intersection point in both equations is the fastest check.
Step 3
Exam Tip
((-2,-3)) रखने पर (x+y=-5) और (2x-y=-1) दोनों सही हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में रखना सबसे तेज जांच है।
Substituting ((3,5)) gives (3x+y=14) but (x-2y=-7), so it is not correct; the true common point is (\left\(\frac{23}{7},\frac{29}{7}\right\)). Detecting option errors is also important.
Step 2
Why this answer is correct
The correct answer is A. ((3,5)). Substituting ((3,5)) gives (3x+y=14) but (x-2y=-7), so it is not correct; the true common point is (\left\(\frac{23}{7},\frac{29}{7}\right\)). Detecting option errors is also important.
Step 3
Exam Tip
((3,5)) रखने पर (3x+y=14) और (x-2y=-7), इसलिए यह नहीं; सही साझा बिंदु (\left\(\frac{23}{7},\frac{29}{7}\right\)) है। विकल्पों की जांच में गलती पकड़ना भी महत्वपूर्ण है।
A. तीनों बिंदु रेखा पर हैं/All three points lie on the line
Step 1
Concept
Substituting all three points makes (5x+4y=40) true. In a graph, three correct points should lie on the same straight line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बिंदु रेखा पर हैं / All three points lie on the line. Substituting all three points makes (5x+4y=40) true. In a graph, three correct points should lie on the same straight line.
Step 3
Exam Tip
तीनों बिंदु रखने पर (5x+4y=40) सत्य मिलता है। ग्राफ में तीन सही बिंदु एक ही सीधी रेखा पर आने चाहिए।
Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=1), \(x+2y=\frac{13}{2}\). Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 3
Exam Tip
(\left\(-\frac{3}{2},4\right\)) रखने पर (2x+y=1) और \(x+2y=\frac{13}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचना चाहिए।
Substituting ((-3,2)) makes (x+y=-1) and (2x-y=-8) true. Substituting the intersection point in both equations is the fastest check.
Step 2
Why this answer is correct
The correct answer is A. (x+y=-1), (2x-y=-8). Substituting ((-3,2)) makes (x+y=-1) and (2x-y=-8) true. Substituting the intersection point in both equations is the fastest check.
Step 3
Exam Tip
((-3,2)) रखने पर (x+y=-1) और (2x-y=-8) दोनों सही हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में रखना सबसे तेज जांच है।
B. केवल ((6,0)) और ((0,8)) रेखा पर हैं/Only ((6,0)) and ((0,8)) lie on the line
Step 1
Concept
((6,0)) and ((0,8)) satisfy the equation, but ((3,4)) does not give (24). Check points before plotting the graph.
Step 2
Why this answer is correct
The correct answer is B. केवल ((6,0)) और ((0,8)) रेखा पर हैं / Only ((6,0)) and ((0,8)) lie on the line. ((6,0)) and ((0,8)) satisfy the equation, but ((3,4)) does not give (24). Check points before plotting the graph.
Step 3
Exam Tip
((6,0)) और ((0,8)) समीकरण को संतुष्ट करते हैं, लेकिन ((3,4)) देने पर (24) नहीं मिलता। ग्राफ से पहले बिंदुओं की जांच करें।
Substituting (\left\(\frac{7}{2},-\frac{1}{2}\right\)) makes (x-y=4) and \(2x+y=\frac{13}{2}\) true. Check the point in both equations.
Step 2
Why this answer is correct
The correct answer is A. (x-y=4), \(2x+y=\frac{13}{2}\). Substituting (\left\(\frac{7}{2},-\frac{1}{2}\right\)) makes (x-y=4) and \(2x+y=\frac{13}{2}\) true. Check the point in both equations.
Step 3
Exam Tip
(\left\(\frac{7}{2},-\frac{1}{2}\right\)) रखने पर (x-y=4) और \(2x+y=\frac{13}{2}\) सत्य हैं। विकल्पों में बिंदु को दोनों समीकरणों में जांचें।
A. ((2,-3)) दोनों समीकरणों को संतुष्ट करता है/((2,-3)) satisfies both equations
Step 1
Concept
The intersection point always lies on both lines, so it satisfies both equations. A graphical solution can always be checked in both equations.
Step 2
Why this answer is correct
The correct answer is A. ((2,-3)) दोनों समीकरणों को संतुष्ट करता है / ((2,-3)) satisfies both equations. The intersection point always lies on both lines, so it satisfies both equations. A graphical solution can always be checked in both equations.
Step 3
Exam Tip
प्रतिच्छेद बिंदु हमेशा दोनों रेखाओं पर होता है, इसलिए वह दोनों समीकरणों को संतुष्ट करता है। ग्राफीय समाधान को हमेशा दोनों समीकरणों में जांच सकते हैं।
A. बिंदु (\left\(2,5\right\))/Point (\left\(2,5\right\))
Step 1
Concept
At (\left\(2,5\right\)), (3\left\(2\right\)+4\left\(5\right\)=26), but (2+5=7) also, so check fully. The correct non-common point is (\left\(4,\frac{7}{2}\right\)).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(2,5\right\)) / Point (\left\(2,5\right\)). At (\left\(2,5\right\)), (3\left\(2\right\)+4\left\(5\right\)=26), but (2+5=7) also, so check fully. The correct non-common point is (\left\(4,\frac{7}{2}\right\)).
Step 3
Exam Tip
(\left\(2,5\right\)) पर (3\left\(2\right\)+4\left\(5\right\)=26), लेकिन (2+5=7) भी है, इसलिए जाँच पूरी करें। सही अलग बिंदु (\left\(4,\frac{7}{2}\right\)) है।
A. बिंदु (\left\(1,5\right\))/Point (\left\(1,5\right\))
Step 1
Concept
At (\left\(1,5\right\)), (2\left\(1\right\)+5\left\(5\right\)=27), but (1+5=6). To be a common solution, both equations must be true.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(1,5\right\)) / Point (\left\(1,5\right\)). At (\left\(1,5\right\)), (2\left\(1\right\)+5\left\(5\right\)=27), but (1+5=6). To be a common solution, both equations must be true.
Step 3
Exam Tip
(\left\(1,5\right\)) पर (2\left\(1\right\)+5\left\(5\right\)=27), लेकिन (1+5=6)। सामान्य हल बनने के लिए दोनों समीकरण सत्य होने चाहिए।
B. बिंदु (\left\(3,6\right\))/Point (\left\(3,6\right\))
Step 1
Concept
At (\left\(3,6\right\)), (2\left\(3\right\)+3\left\(6\right\)=24), but (3+6=9). For a common solution, both equations must be true.
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(3,6\right\)) / Point (\left\(3,6\right\)). At (\left\(3,6\right\)), (2\left\(3\right\)+3\left\(6\right\)=24), but (3+6=9). For a common solution, both equations must be true.
Step 3
Exam Tip
(\left\(3,6\right\)) पर (2\left\(3\right\)+3\left\(6\right\)=24), लेकिन (3+6=9)। सामान्य हल के लिए दोनों समीकरण सत्य होने चाहिए।
B. बिंदु (\left\(3,2\right\))/Point (\left\(3,2\right\))
Step 1
Concept
At (\left\(3,2\right\)), (3-2\left\(2\right\)=-1), so it is not correct. The correct solution is (\left\(\frac{18}{7},\frac{23}{7}\right\)).
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(3,2\right\)) / Point (\left\(3,2\right\)). At (\left\(3,2\right\)), (3-2\left\(2\right\)=-1), so it is not correct. The correct solution is (\left\(\frac{18}{7},\frac{23}{7}\right\)).
Step 3
Exam Tip
(\left\(3,2\right\)) पर (3-2\left\(2\right\)=-1) है इसलिए यह नहीं है। सही हल (\left\(\frac{18}{7},\frac{23}{7}\right\)) है।
B. बिंदु (\left\(4,3\right\))/Point (\left\(4,3\right\))
Step 1
Concept
At (\left\(4,3\right\)), (4+3\left\(3\right\)=13), so check options carefully. The correct intersection is (\left\(\frac{24}{7},\frac{27}{7}\right\)).
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(4,3\right\)) / Point (\left\(4,3\right\)). At (\left\(4,3\right\)), (4+3\left\(3\right\)=13), so check options carefully. The correct intersection is (\left\(\frac{24}{7},\frac{27}{7}\right\)).
Step 3
Exam Tip
(\left\(4,3\right\)) पर (4+3\left\(3\right\)=13) नहीं है इसलिए विकल्प जाँचें। सही प्रतिच्छेद (\left\(\frac{24}{7},\frac{27}{7}\right\)) है।
Substituting ( (4,3) ) gives (4(4)-3=13), so checking is necessary. The correct solution is ( \left\(\frac{18}{5},\frac{17}{5}\right\) ).
Step 2
Why this answer is correct
The correct answer is C. ( (4,3) ). Substituting ( (4,3) ) gives (4(4)-3=13), so checking is necessary. The correct solution is ( \left\(\frac{18}{5},\frac{17}{5}\right\) ).
Step 3
Exam Tip
( (4,3) ) रखने पर (4(4)-3=13) नहीं है, इसलिए जाँच जरूरी है। सही हल ( \left\(\frac{18}{5},\frac{17}{5}\right\) ) है।
Putting ( (3,2) ) gives (2(3)+3(2)=12), so it is not correct. The correct solution is ( \(\frac{21}{5},\frac{16}{5}\) ), so recalculation is needed in such options.
Step 2
Why this answer is correct
The correct answer is A. ( (3,2) ). Putting ( (3,2) ) gives (2(3)+3(2)=12), so it is not correct. The correct solution is ( \(\frac{21}{5},\frac{16}{5}\) ), so recalculation is needed in such options.
Step 3
Exam Tip
( (3,2) ) रखने पर (2(3)+3(2)=12) है, इसलिए यह भी सही नहीं है। सही हल ( \( \frac{21}{5},\frac{16}{5}\) ) होता है, अतः ऐसे विकल्पों में पुनः गणना जरूरी है।
At ( (5,1) ), (5+1=6) and (5-1=4). To check a solution substitute the point in both equations.
Step 2
Why this answer is correct
The correct answer is B. (x+y=6) और (x-y=4) / (x+y=6) and (x-y=4). At ( (5,1) ), (5+1=6) and (5-1=4). To check a solution substitute the point in both equations.
Step 3
Exam Tip
( (5,1) ) पर (5+1=6) और (5-1=4)। हल जाँचने के लिए दिए बिंदु को दोनों समीकरणों में रखें।
(5x-2-18x+9=(5x-3)(x-3)), so the roots are \(\frac{3}{5}\) and (3). In exams, verify the answer quickly by factorisation.
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\frac{3}{5}\). (5x-2-18x+9=(5x-3)(x-3)), so the roots are \(\frac{3}{5}\) and (3). In exams, verify the answer quickly by factorisation.
Step 3
Exam Tip
(5x-2-18x+9=(5x-3)(x-3)), इसलिए मूल \(\frac{3}{5}\) और (3) हैं। परीक्षा में गुणनखंड विधि से उत्तर जल्दी जांचें।
(3x-2-10x+3=(3x-1)(x-3)), so the roots are \(\frac{1}{3}\) and (3). In exams, you may verify by completing square or factoring.
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\frac{1}{3}\). (3x-2-10x+3=(3x-1)(x-3)), so the roots are \(\frac{1}{3}\) and (3). In exams, you may verify by completing square or factoring.
Step 3
Exam Tip
(3x-2-10x+3=(3x-1)(x-3)), इसलिए मूल \(\frac{1}{3}\) और (3) हैं। परीक्षा में पूर्ण वर्ग या गुणनखंड दोनों से जांच सकते हैं।
The sum of these roots is \(\frac{5t+3}{4}\), and the product is (\frac{t(t+3)}{4}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 2
Why this answer is correct
The correct answer is A. हर (t) के लिए / For every (t). The sum of these roots is \(\frac{5t+3}{4}\), and the product is (\frac{t(t+3)}{4}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 3
Exam Tip
इन जड़ों का योग \(\frac{5t+3}{4}\) और गुणनफल (\frac{t(t+3)}{4}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से मेल खाते हैं।
Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (8) हमेशा एक जड़ है / (8) is always one root. Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 3
Exam Tip
(x=8) रखने पर (64-8(a+8)+8a=0) मिलता है। इसलिए (8) हमेशा एक जड़ है और दूसरी जड़ (a) है।
The sum of these two roots is \(\frac{4t+2}{3}\), and the product is (\frac{t(t+2)}{3}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 2
Why this answer is correct
The correct answer is C. हर (t) पर / For every (t). The sum of these two roots is \(\frac{4t+2}{3}\), and the product is (\frac{t(t+2)}{3}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 3
Exam Tip
इन दोनों जड़ों का योग \(\frac{4t+2}{3}\) और गुणनफल (\frac{t(t+2)}{3}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से मेल खाते हैं।
Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is B. (6) हमेशा जड़ है / (6) is always a root. Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 3
Exam Tip
(x=6) रखने पर (36-6(a+6)+6a=0) मिलता है। इसलिए (6) हमेशा एक जड़ है और दूसरी जड़ (a) है।
The sum is \(\frac{3t+1}{2}\) and the product is (\frac{t(t+1)}{2}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) for every (t).
Step 2
Why this answer is correct
The correct answer is A. हर (t) के लिए / For every (t). The sum is \(\frac{3t+1}{2}\) and the product is (\frac{t(t+1)}{2}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) for every (t).
Step 3
Exam Tip
इन जड़ों का योग \(\frac{3t+1}{2}\) और गुणनफल (\frac{t(t+1)}{2}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से हर (t) पर मेल खाते हैं।
Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) हमेशा एक जड़ है / (4) is always a root. Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 3
Exam Tip
(x=4) रखने पर (16-4(a+4)+4a=0) मिलता है। अतः (4) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (3) हमेशा एक जड़ है / (3) is always a root. Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 3
Exam Tip
(x=3) रखने पर (9-3(a+3)+3a=0) मिलता है। इसलिए (3) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
Since (p\(1+\sqrt{3}\)=0), \(1+\sqrt{3}\) is a zero. To prove a number is a zero, show that the polynomial value is (0).
Step 2
Why this answer is correct
The correct answer is A. यह (p(x)) का शून्यक है / It is a zero of (p(x)). Since (p\(1+\sqrt{3}\)=0), \(1+\sqrt{3}\) is a zero. To prove a number is a zero, show that the polynomial value is (0).
Step 3
Exam Tip
(p\(1+\sqrt{3}\)=0), इसलिए \(1+\sqrt{3}\) शून्यक है। किसी संख्या को शून्यक सिद्ध करने के लिए बहुपद का मान (0) दिखाएँ।
