यदि समीकरण (4x+6y=18) और (2x+3y=k) के अनंत हल हों, तो (k) का मान क्या होगा?
If the equations (4x+6y=18) and (2x+3y=k) have infinitely many solutions, what is the value of (k)?
#linear equations
#solvability
#parameter
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (2) times the second, so (k=9). For infinitely many solutions, keep all three ratios equal.
Step 2
Why this answer is correct
The correct answer is C. (9). The first equation must be (2) times the second, so (k=9). For infinitely many solutions, keep all three ratios equal.
Step 3
Exam Tip
पहला समीकरण दूसरे का (2) गुना होना चाहिए, इसलिए (k=9)। परीक्षा में अनंत हल के लिए तीनों अनुपात बराबर रखें।
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समीकरण (3x+ay=12) और (6x+8y=24) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (3x+ay=12) and (6x+8y=24) to have infinitely many solutions?
#linear equations
#infinite solutions
#ratio condition
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (3/6=a/8=12/24), so (a=4). Match the ratios of coefficients and constants first.
Step 2
Why this answer is correct
The correct answer is B. (4). For infinitely many solutions, (3/6=a/8=12/24), so (a=4). Match the ratios of coefficients and constants first.
Step 3
Exam Tip
अनंत हल के लिए (3/6=a/8=12/24), इसलिए (a=4)। पहले गुणांकों और स्थिर पदों के अनुपात मिलाएं।
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समीकरण (kx+5y=20) और (6x+10y=45) का कोई हल न होने के लिए (k) क्या होगा?
What should (k) be for (kx+5y=20) and (6x+10y=45) to have no solution?
#linear equations
#no solution
#parameter
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (k/6=5/10) and (20/45) must be different. This gives (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For no solution, (k/6=5/10) and (20/45) must be different. This gives (k=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (k/6=5/10) और (20/45) अलग होना चाहिए। इससे (k=3) मिलता है।
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यदि (2x+3y=7) और (4x+6y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent pair
#condition
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A (m=14)
B \(m \ne 14\)
C (m=7)
D (m=21)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 14\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 14\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 14\)।
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समीकरण (5x+2y=11) और (10x+4y=22) के लिए कौन-सा निष्कर्ष सही है?
Which conclusion is correct for (5x+2y=11) and (10x+4y=22)?
#linear equations
#coincident lines
#infinite solutions
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A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D रेखाएं लंबवत / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (2) times the first, so both lines are coincident. Coincident lines have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (2) times the first, so both lines are coincident. Coincident lines have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं।
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समीकरण (7x-3y=10) और (14x-6y=25) के लिए हलों की संख्या क्या होगी?
How many solutions will (7x-3y=10) and (14x-6y=25) have?
#linear equations
#parallel lines
#no solution
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A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
Here (7/14=(-3)/(-6)) but (10/25) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Here (7/14=(-3)/(-6)) but (10/25) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (7/14=(-3)/(-6)) लेकिन (10/25) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (3x+4y=13) और (6x+7y=25) के लिए सही विकल्प चुनिए।
Choose the correct option for (3x+4y=13) and (6x+7y=25).
#linear equations
#unique solution
#intersecting lines
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A रेखाएं संपाती हैं / Lines are coincident
B कोई हल नहीं / No solution
C रेखाएं समानांतर हैं / Lines are parallel
D एक अद्वितीय हल / One unique solution
Explanation opens after your attempt
Correct Answer
D. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(3/6 \ne 4/7\), so the lines intersect at one point. Different coefficient ratios give one unique solution.
Step 2
Why this answer is correct
The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(3/6 \ne 4/7\), so the lines intersect at one point. Different coefficient ratios give one unique solution.
Step 3
Exam Tip
यहां \(3/6 \ne 4/7\), इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग गुणांक अनुपात एक अद्वितीय हल देता है।
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यदि \(a_1/a_2=b_1/b_2=c_1/c_2\), तो ग्राफ में दोनों रेखाओं की स्थिति क्या होगी?
If \(a_1/a_2=b_1/b_2=c_1/c_2\), what will be the position of both lines in the graph?
#linear equations
#ratio test
#coincident lines
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A अलग समानांतर / Distinct parallel
B कटती हुई / Intersecting
C संपाती / Coincident
D लंबवत / Perpendicular
Explanation opens after your attempt
Correct Answer
C. संपाती / Coincident
Step 1
Concept
When all three ratios are equal, both equations represent the same line. Such a pair has infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. When all three ratios are equal, both equations represent the same line. Such a pair has infinitely many solutions.
Step 3
Exam Tip
तीनों अनुपात बराबर होने पर दोनों समीकरण एक ही रेखा दर्शाते हैं। ऐसे युग्म में अनंत हल होते हैं।
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यदि \(a_1/a_2=b_1/b_2 \ne c_1/c_2\), तो युग्म के बारे में सही कथन क्या है?
If \(a_1/a_2=b_1/b_2 \ne c_1/c_2\), which statement about the pair is correct?
#linear equations
#inconsistent
#condition
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A यह संगत और स्वतंत्र है / It is consistent and independent
B यह संगत और आश्रित है / It is consistent and dependent
C यह असंगत है / It is inconsistent
D इसमें अनंत हल हैं / It has infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. यह असंगत है / It is inconsistent
Step 1
Concept
If the first two ratios are equal and the third differs, the lines are distinct parallel. Therefore, there is no common solution.
Step 2
Why this answer is correct
The correct answer is C. यह असंगत है / It is inconsistent. If the first two ratios are equal and the third differs, the lines are distinct parallel. Therefore, there is no common solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर और तीसरा अलग हो तो रेखाएं अलग समानांतर होती हैं। इसलिए कोई सामान्य हल नहीं होता।
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समीकरण (px+2y=6) और (9x+6y=18) के अनंत हल होने के लिए (p) का मान क्या है?
What is the value of (p) for (px+2y=6) and (9x+6y=18) to have infinitely many solutions?
#linear equations
#parameter
#infinite solutions
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (p/9=2/6=6/18), so (p=3). All three ratios must be equal.
Step 2
Why this answer is correct
The correct answer is C. (3). For infinitely many solutions, (p/9=2/6=6/18), so (p=3). All three ratios must be equal.
Step 3
Exam Tip
अनंत हल के लिए (p/9=2/6=6/18), इसलिए (p=3)। तीनों अनुपात बराबर होने चाहिए।
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समीकरण (2x+qy=8) और (5x+10y=21) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (2x+qy=8) and (5x+10y=21) to have a unique solution?
#linear equations
#unique solution
#parameter
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A (q=4)
B \(q \ne 4\)
C (q=10)
D (q=2)
Explanation opens after your attempt
Correct Answer
B. \(q \ne 4\)
Step 1
Concept
For a unique solution, \(2/5 \ne q/10\) must hold. Therefore, \(q \ne 4\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(q \ne 4\). For a unique solution, \(2/5 \ne q/10\) must hold. Therefore, \(q \ne 4\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(2/5 \ne q/10\) होना चाहिए। इसलिए \(q \ne 4\) सही शर्त है।
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समीकरण (4x+ky=16) और (x+3y=4) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for (4x+ky=16) and (x+3y=4) to have infinitely many solutions?
#linear equations
#dependent pair
#parameter
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A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (4) times the second, so (k=12). A common multiplier makes the lines coincident.
Step 2
Why this answer is correct
The correct answer is C. (12). The first equation must be (4) times the second, so (k=12). A common multiplier makes the lines coincident.
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए, इसलिए (k=12)। समान गुणक से रेखाएं संपाती बनती हैं।
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समीकरण (6x+ay=30) और (2x+5y=11) का कोई हल न होने के लिए (a) का मान क्या है?
What is the value of (a) for (6x+ay=30) and (2x+5y=11) to have no solution?
#linear equations
#no solution
#parameter
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A (10)
B (12)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
For no solution, (6/2=a/5) and (30/11) must be different. This gives (a=15).
Step 2
Why this answer is correct
The correct answer is D. (15). For no solution, (6/2=a/5) and (30/11) must be different. This gives (a=15).
Step 3
Exam Tip
कोई हल नहीं के लिए (6/2=a/5) और (30/11) अलग होना चाहिए। इससे (a=15) मिलता है।
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समीकरण (8x+12y=20) और (2x+3y=6) के ग्राफ के बारे में सही कथन चुनिए।
Choose the correct statement about the graph of (8x+12y=20) and (2x+3y=6).
#linear equations
#graph
#parallel lines
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A रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
B रेखाएं संपाती हैं / Lines are coincident
C रेखाएं अलग समानांतर हैं / Lines are distinct parallel
D रेखाएं लंबवत हैं / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Step 1
Concept
Here (8/2=12/3) but (20/6) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (8/2=12/3) but (20/6) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (8/2=12/3) लेकिन (20/6) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
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समीकरण (9x+6y=15) और (3x+2y=5) के ग्राफ में क्या दिखेगा?
What will be shown in the graph of (9x+6y=15) and (3x+2y=5)?
#linear equations
#graph
#same line
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A एक ही रेखा / Same line
B दो अलग समानांतर रेखाएं / Two distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई रेखा नहीं / No line
Explanation opens after your attempt
Correct Answer
A. एक ही रेखा / Same line
Step 1
Concept
The first equation is (3) times the second. Therefore, both equations show the same line.
Step 2
Why this answer is correct
The correct answer is A. एक ही रेखा / Same line. The first equation is (3) times the second. Therefore, both equations show the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।
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समीकरण (2x+9y=17) और (5x+11y=23) के ग्राफ का सही वर्णन क्या है?
What is the correct description of the graph of (2x+9y=17) and (5x+11y=23)?
#linear equations
#graph
#unique solution
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A संपाती रेखाएं / Coincident lines
B अलग समानांतर रेखाएं / Distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 9/11\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(2/5 \ne 9/11\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 9/11\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
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यदि दो रेखाओं की ढाल समान और (y)-अवरोध भी समान हो, तो युग्म का प्रकार क्या होगा?
If two lines have the same slope and the same (y)-intercept, what will be the type of pair?
#linear equations
#slope
#dependent pair
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A असंगत / Inconsistent
B संगत और स्वतंत्र / Consistent and independent
C संगत और आश्रित / Consistent and dependent
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. संगत और आश्रित / Consistent and dependent
Step 1
Concept
Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.
Step 2
Why this answer is correct
The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.
Step 3
Exam Tip
समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित है।
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यदि दो रेखाओं की ढाल समान लेकिन (y)-अवरोध अलग हो, तो कौन-सा निष्कर्ष सही है?
If two lines have the same slope but different (y)-intercepts, which conclusion is correct?
#linear equations
#slope
#no solution
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A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 3
Exam Tip
समान ढाल और अलग अवरोध रेखाओं को अलग समानांतर बनाते हैं। इसलिए कोई सामान्य हल नहीं होता।
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यदि दो रेखाओं की ढाल अलग-अलग हो, तो युग्म की हल-स्थिति क्या होगी?
If two lines have different slopes, what will be the solution status of the pair?
#linear equations
#slope
#unique solution
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A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Lines with different slopes meet at one point. Therefore, the pair has one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Lines with different slopes meet at one point. Therefore, the pair has one unique solution.
Step 3
Exam Tip
अलग ढाल वाली रेखाएं एक बिंदु पर मिलती हैं। इसलिए युग्म का एक अद्वितीय हल होता है।
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समीकरण (2x+3y-11=0) और (6x+9y-33=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for (2x+3y-11=0) and (6x+9y-33=0)?
#linear equations
#ratio relation
#infinite solutions
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A (2 / 6=3 / 9 \ne (-11) / (-33))
B (2 / 6 \ne 3 / 9)
C (2 / 6=3 / 9=(-11) / (-33))
D (2 / 6=(-11) / (-33) \ne 3 / 9)
Explanation opens after your attempt
Correct Answer
C. (2 / 6=3 / 9=(-11) / (-33))
Step 1
Concept
Here all three ratios are equal to (1/3). Therefore, the equations will have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (2 / 6=3 / 9=(-11) / (-33)). Here all three ratios are equal to (1/3). Therefore, the equations will have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात (1/3) के बराबर हैं। इसलिए समीकरणों के अनंत हल होंगे।
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समीकरण (4x-5y+7=0) और (8x-10y+9=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for (4x-5y+7=0) and (8x-10y+9=0)?
#linear equations
#ratio relation
#no solution
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A (4 / 8=(-5) / (-10) \ne 7 / 9)
B (4 / 8 \ne (-5) / (-10))
C (4 / 8=(-5) / (-10)=7 / 9)
D (4 / 8=7 / 9 \ne (-5) / (-10))
Explanation opens after your attempt
Correct Answer
A. (4 / 8=(-5) / (-10) \ne 7 / 9)
Step 1
Concept
The first two ratios are equal and the third is different. Therefore, the lines are parallel and there is no solution.
Step 2
Why this answer is correct
The correct answer is A. (4 / 8=(-5) / (-10) \ne 7 / 9). The first two ratios are equal and the third is different. Therefore, the lines are parallel and there is no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए रेखाएं समानांतर हैं और कोई हल नहीं है।
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समीकरण (5x+6y-4=0) और (10x+9y-8=0) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for (5x+6y-4=0) and (10x+9y-8=0)?
#linear equations
#unique solution
#ratio test
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A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(5/10 \ne 6/9\), so the lines intersect at one point. In this case, the third ratio need not be checked.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(5/10 \ne 6/9\), so the lines intersect at one point. In this case, the third ratio need not be checked.
Step 3
Exam Tip
यहां \(5/10 \ne 6/9\), इसलिए रेखाएं एक बिंदु पर कटती हैं। इस स्थिति में तीसरा अनुपात देखने की जरूरत नहीं होती।
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यदि समीकरण (ax+4y=10) और (6x+8y=25) का कोई हल नहीं है, तो (a) का मान क्या है?
If the equations (ax+4y=10) and (6x+8y=25) have no solution, what is the value of (a)?
#linear equations
#parameter
#no solution
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (a/6=4/8) and (10/25) must be different. Hence (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For no solution, (a/6=4/8) and (10/25) must be different. Hence (a=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (a/6=4/8) और (10/25) अलग होना चाहिए। इसलिए (a=3)।
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समीकरण (3x+by=15) और (9x+12y=45) के अनंत हल होने के लिए (b) क्या होगा?
What will (b) be for (3x+by=15) and (9x+12y=45) to have infinitely many solutions?
#linear equations
#parameter
#dependent pair
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (3/9=b/12=15/45) must hold. Therefore, (b=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For infinitely many solutions, (3/9=b/12=15/45) must hold. Therefore, (b=4).
Step 3
Exam Tip
अनंत हल के लिए (3/9=b/12=15/45) होना चाहिए। इसलिए (b=4) है।
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समीकरण (8x+py=24) और (2x+3y=7) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (8x+py=24) and (2x+3y=7) to have a unique solution?
#linear equations
#unique solution
#parameter
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A (p=12)
B \(p \ne 12\)
C (p=3)
D (p=8)
Explanation opens after your attempt
Correct Answer
B. \(p \ne 12\)
Step 1
Concept
For a unique solution, \(8/2 \ne p/3\) must hold. Therefore, \(p \ne 12\).
Step 2
Why this answer is correct
The correct answer is B. \(p \ne 12\). For a unique solution, \(8/2 \ne p/3\) must hold. Therefore, \(p \ne 12\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(8/2 \ne p/3\) होना चाहिए। इसलिए \(p \ne 12\)।
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यदि (5x+2y=16) और (10x+4y=n) के अनंत हल हैं, तो (n) कितना होगा?
If (5x+2y=16) and (10x+4y=n) have infinitely many solutions, what is (n)?
#linear equations
#parameter
#infinite solutions
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A (24)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (2) times the first. Therefore, (n=32).
Step 2
Why this answer is correct
The correct answer is D. (32). The second equation must be (2) times the first. Therefore, (n=32).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना होना चाहिए। इसलिए (n=32) होगा।
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यदि (6x-2y=18) और (3x-y=t) असंगत हों, तो (t) के लिए सही शर्त क्या है?
If (6x-2y=18) and (3x-y=t) are inconsistent, what is the correct condition for (t)?
#linear equations
#inconsistent
#parameter
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A (t=9)
B \(t \ne 9\)
C (t=18)
D (t=6)
Explanation opens after your attempt
Correct Answer
B. \(t \ne 9\)
Step 1
Concept
The first two ratios are equal, so for inconsistency (18/t) must be different. Hence \(t \ne 9\).
Step 2
Why this answer is correct
The correct answer is B. \(t \ne 9\). The first two ratios are equal, so for inconsistency (18/t) must be different. Hence \(t \ne 9\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए (18/t) अलग होना चाहिए। अतः \(t \ne 9\)।
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समीकरण (3x+2y=8) और (9x+6y=24) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing (3x+2y=8) and (9x+6y=24)?
#linear equations
#observation
#infinite solutions
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A एक अद्वितीय हल है / There is one unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं।
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समीकरण (4x+8y=12) और (x+2y=5) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing (4x+8y=12) and (x+2y=5)?
#linear equations
#observation
#no solution
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A तीनों अनुपात बराबर हैं / All three ratios are equal
B पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
C पहले दो अनुपात अलग हैं / First two ratios are different
D रेखाएं कटती हैं / Lines intersect
Explanation opens after your attempt
Correct Answer
B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
Step 1
Concept
Here (4/1=8/2) but (12/5) is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different. Here (4/1=8/2) but (12/5) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (4/1=8/2) लेकिन (12/5) अलग है। इसलिए कोई हल नहीं होगा।
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समीकरण (7x+3y=19) और (2x+y=6) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in (7x+3y=19) and (2x+y=6)?
#linear equations
#ratio comparison
#unique solution
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A (7 / 2=3 / 1), इसलिए अनंत हल / 1), so infinitely many solutions
B (7 / 2=3 / 1), इसलिए कोई हल नहीं / 1), so no solution
C (7 / 2 \ne 3 / 1), इसलिए एक अद्वितीय हल / 1), so one unique solution
D (7 / 2=19 / 6), इसलिए संपाती / 6), so coincident
Explanation opens after your attempt
Correct Answer
C. (7 / 2 \ne 3 / 1), इसलिए एक अद्वितीय हल / 1), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 2 \ne 3 / 1\), इसलिए एक अद्वितीय हल / 1), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरण (12x+18y=30) और (2x+3y=5) का युग्म किस प्रकार का है?
What type of pair is (12x+18y=30) and (2x+3y=5)?
#linear equations
#dependent pair
#classification
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A संगत और आश्रित / Consistent and dependent
B असंगत / Inconsistent
C संगत और स्वतंत्र / Consistent and independent
D असमाधेय / Unsolvable
Explanation opens after your attempt
Correct Answer
A. संगत और आश्रित / Consistent and dependent
Step 1
Concept
The first equation is (6) times the second. Therefore, both are the same line and the pair is dependent.
Step 2
Why this answer is correct
The correct answer is A. संगत और आश्रित / Consistent and dependent. The first equation is (6) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (6) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरण (10x+15y=25) और (2x+3y=8) का युग्म किस प्रकार का है?
What type of pair is (10x+15y=25) and (2x+3y=8)?
#linear equations
#inconsistent
#classification
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A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D संपाती / Coincident
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
Here (10/2=15/3) but (25/8) is different. Therefore, this is an inconsistent pair.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (10/2=15/3) but (25/8) is different. Therefore, this is an inconsistent pair.
Step 3
Exam Tip
यहां (10/2=15/3) लेकिन (25/8) अलग है। इसलिए यह असंगत युग्म है।
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समीकरण (11x+4y=18) और (5x+2y=9) का युग्म किस प्रकार का है?
What type of pair is (11x+4y=18) and (5x+2y=9)?
#linear equations
#consistent independent
#classification
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A असंगत / Inconsistent
B संगत और आश्रित / Consistent and dependent
C संगत और स्वतंत्र / Consistent and independent
D समानांतर / Parallel
Explanation opens after your attempt
Correct Answer
C. संगत और स्वतंत्र / Consistent and independent
Step 1
Concept
Here \(11/5 \ne 4/2\), so the lines intersect. Hence, the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. Here \(11/5 \ne 4/2\), so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(11/5 \ne 4/2\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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एक दुकान पर दो वस्तुओं के लिए समीकरण (x+2y=50) और (2x+4y=100) बनते हैं। हलों की संख्या क्या होगी?
For two items in a shop, the equations are (x+2y=50) and (2x+4y=100). How many solutions will there be?
#linear equations
#word problem
#infinite solutions
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A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (2) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (2) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं।
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दो टिकटों के दामों के लिए (3x+2y=80) और (6x+4y=170) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (3x+2y=80) and (6x+4y=170) are formed. What type of system is this?
#linear equations
#word problem
#inconsistent
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A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (80/170) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (80/170) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (80/170) अलग है। इसलिए प्रणाली असंगत है।
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यदि दो संख्याओं के लिए (x+y=12) और (2x-y=3) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?
If the equations for two numbers are (x+y=12) and (2x-y=3), what will be the solution status?
#linear equations
#word problem
#unique solution
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A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
A. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here (1/2 \ne 1/(-1)), so the lines intersect. Such a pair has one unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here (1/2 \ne 1/(-1)), so the lines intersect. Such a pair has one unique solution.
Step 3
Exam Tip
यहां (1/2 \ne 1/(-1)), इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।
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समीकरण (2x+3y=13) और (4x+6y=26) के लिए \(a_1/a_2\), \(b_1/b_2\) और स्थिर पद अनुपात का संबंध क्या है?
For (2x+3y=13) and (4x+6y=26), what is the relation among \(a_1/a_2\), \(b_1/b_2\), and the constant ratio?
#linear equations
#ratio relation
#coincident
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A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (2/4=3/6=13/26)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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समीकरण (6x+9y=30) और (2x+3y=12) के लिए कौन-सा संबंध सही है?
Which relation is correct for (6x+9y=30) and (2x+3y=12)?
#linear equations
#ratio relation
#no solution
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A (6 / 2 \ne 9 / 3)
B (6 / 2=9 / 3=30 / 12)
C (6 / 2=9 / 3 \ne 30 / 12)
D (6 / 2=30 / 12 \ne 9 / 3)
Explanation opens after your attempt
Correct Answer
C. (6 / 2=9 / 3 \ne 30 / 12)
Step 1
Concept
The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 2
Why this answer is correct
The correct answer is C. \(6 / 2=9 / 3 \ne 30 / 12\). The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है। इसलिए कोई हल नहीं है।
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समीकरण (7x+5y=16) और (14x+11y=35) के लिए कौन-सा कथन सही है?
Which statement is correct for (7x+5y=16) and (14x+11y=35)?
#linear equations
#ratio comparison
#unique solution
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A (7 / 14=5 / 11), इसलिए कोई हल नहीं / 11), so no solution
B (7 / 14 \ne 5 / 11), इसलिए एक अद्वितीय हल / 11), so one unique solution
C तीनों अनुपात बराबर हैं / All three ratios are equal
D रेखाएं संपाती हैं / Lines are coincident
Explanation opens after your attempt
Correct Answer
B. (7 / 14 \ne 5 / 11), इसलिए एक अद्वितीय हल / 11), so one unique solution
Step 1
Concept
Here \(7/14 \ne 5/11\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(7 / 14 \ne 5 / 11\), इसलिए एक अद्वितीय हल / 11), so one unique solution. Here \(7/14 \ne 5/11\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(7/14 \ne 5/11\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरण (x+4y=9) और (2x+8y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (x+4y=9) and (2x+8y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
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A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 2
Why this answer is correct
The correct answer is C. (18). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=18)।
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समीकरण (3x+5y=14) और (6x+10y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (3x+5y=14) and (6x+10y=r) to be inconsistent?
#linear equations
#inconsistent
#parameter
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A (r=28)
B \(r \ne 28\)
C (r=14)
D (r=7)
Explanation opens after your attempt
Correct Answer
B. \(r \ne 28\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence \(r \ne 28\).
Step 2
Why this answer is correct
The correct answer is B. \(r \ne 28\). The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence \(r \ne 28\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 28\)।
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समीकरण (2x+3y=5) और (4x+ay=11) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for (2x+3y=5) and (4x+ay=11) to have no solution?
#linear equations
#no solution
#parameter
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For no solution, (2/4=3/a) and (5/11) must be different. This gives (a=6).
Step 2
Why this answer is correct
The correct answer is C. (6). For no solution, (2/4=3/a) and (5/11) must be different. This gives (a=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (2/4=3/a) और (5/11) अलग होना चाहिए। इससे (a=6) मिलता है।
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समीकरण (5x+ky=25) और (x+3y=5) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for (5x+ky=25) and (x+3y=5) to have infinitely many solutions?
#linear equations
#infinite solutions
#parameter
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A (12)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (5) times the second. Therefore, (k=15).
Step 2
Why this answer is correct
The correct answer is B. (15). The first equation must be (5) times the second. Therefore, (k=15).
Step 3
Exam Tip
पहला समीकरण दूसरे का (5) गुना होना चाहिए। इसलिए (k=15)।
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यदि (lx+7y=21) और (6x+14y=40) का कोई हल नहीं है, तो (l) का मान क्या होगा?
If (lx+7y=21) and (6x+14y=40) have no solution, what will be the value of (l)?
#linear equations
#parameter
#parallel lines
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
For no solution, (l/6=7/14) and (21/40) must be different. Hence (l=3).
Step 2
Why this answer is correct
The correct answer is C. (3). For no solution, (l/6=7/14) and (21/40) must be different. Hence (l=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (l/6=7/14) और (21/40) अलग होना चाहिए। इसलिए (l=3)।
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समीकरण (8x+3y=17) और (16x+6y=34) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing (8x+3y=17) and (16x+6y=34)?
#linear equations
#observation
#same line
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A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं।
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समीकरण (9x-6y=12) और (3x-2y=7) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing (9x-6y=12) and (3x-2y=7)?
#linear equations
#no solution
#observation
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A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (9/3=(-6)/(-2)) but (12/7) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (9/3=(-6)/(-2)) but (12/7) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (9/3=(-6)/(-2)) लेकिन (12/7) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (13x+2y=31) और (6x+y=14) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for (13x+2y=31) and (6x+y=14)?
#linear equations
#unique solution
#solvability
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A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(13/6 \ne 2/1\), so the lines will intersect. Hence, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(13/6 \ne 2/1\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(13/6 \ne 2/1\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरण (4x-3y=11) और (12x-9y=35) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for (4x-3y=11) and (12x-9y=35)?
#linear equations
#solvability
#no solution
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A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (4/12=(-3)/(-9)) but (11/35) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (4/12=(-3)/(-9)) but (11/35) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (4/12=(-3)/(-9)) लेकिन (11/35) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (2x+my=14) और (8x+20y=56) के अनंत हल होने के लिए (m) का मान क्या होगा?
What will be the value of (m) for (2x+my=14) and (8x+20y=56) to have infinitely many solutions?
#linear equations
#parameter
#infinite solutions
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (2/8=m/20=14/56) must hold. Therefore, (m=5).
Step 2
Why this answer is correct
The correct answer is A. (5). For infinitely many solutions, (2/8=m/20=14/56) must hold. Therefore, (m=5).
Step 3
Exam Tip
अनंत हल के लिए (2/8=m/20=14/56) होना चाहिए। इसलिए (m=5) है।
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समीकरण (7x+4y=18) और (3x+2y=10) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in (7x+4y=18) and (3x+2y=10)?
#linear equations
#ratio comparison
#unique solution
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A (7 / 3=4 / 2), इसलिए कोई हल नहीं / 2), so no solution
B (7 / 3=4 / 2), इसलिए अनंत हल / 2), so infinitely many solutions
C (7 / 3 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 3 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
Step 1
Concept
Here \(7/3 \ne 4/2\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 3 \ne 4 / 2\), इसलिए एक अद्वितीय हल / 2), so one unique solution. Here \(7/3 \ne 4/2\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 3
Exam Tip
यहां \(7/3 \ne 4/2\), इसलिए रेखाएं एक बिंदु पर कटेंगी। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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