समीकरणों (4x+ay=32) और (12x+21y=96) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?
#linear equations
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#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, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (7). For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 3
Exam Tip
अनंत हल के लिए (4/12=a/21=32/96) होना चाहिए। इसलिए (a=7) सही है।
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समीकरणों (px+9y=45) और (20x+30y=103) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+9y=45) and (20x+30y=103) to have no solution?
#linear equations
#expert
#no solution
#parameter
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 2
Why this answer is correct
The correct answer is B. (6). For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/20=9/30) और (45/103) अलग होना चाहिए। इससे (p=6) मिलता है।
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यदि (5x+8y=37) और (15x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (5x+8y=37) and (15x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
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#inconsistent
#condition
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A (m=111)
B \(m\ne111\)
C (m=37)
D (m=74)
Explanation opens after your attempt
Correct Answer
B. \(m\ne111\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 2
Why this answer is correct
The correct answer is B. \(m\ne111\). The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए।
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समीकरणों (7x-4y=29) और (21x-12y=87) के लिए सही निष्कर्ष कौन-सा है?
Which conclusion is correct for the equations (7x-4y=29) and (21x-12y=87)?
#linear equations
#expert
#coincident lines
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A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D अलग समानांतर रेखाएं / Distinct parallel lines
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident 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 (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (9x+5y=41) और (18x+10y=85) के लिए हलों की संख्या क्या होगी?
How many solutions will the equations (9x+5y=41) and (18x+10y=85) have?
#linear equations
#expert
#parallel lines
#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 ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (9/18=5/10) but (41/85) 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 (9/18=5/10) but (41/85) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (9/18=5/10) लेकिन (41/85) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (11x+14y=53) और (17x+22y=83) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (11x+14y=53) and (17x+22y=83)?
#linear equations
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#unique solution
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A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 3
Exam Tip
यहां \(11/17 \ne 14/22\), इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरणों (kx+14y=42) और (18x+21y=63) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (kx+14y=42) and (18x+21y=63) to have infinitely many solutions?
#linear equations
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#parameter
#infinite solutions
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A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 2
Why this answer is correct
The correct answer is C. (12). For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 3
Exam Tip
अनंत हल के लिए (k/18=14/21=42/63) होना चाहिए। इसलिए (k=12) सही है।
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समीकरणों (13x+qy=52) और (26x+18y=104) के अनंत हल होने के लिए (q) का मान क्या है?
What is the value of (q) for the equations (13x+qy=52) and (26x+18y=104) to have infinitely many solutions?
#linear equations
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#dependent pair
#parameter
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 2
Why this answer is correct
The correct answer is C. (9). The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)।
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समीकरणों (12x+py=60) और (3x+5y=16) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (12x+py=60) and (3x+5y=16) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
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A (p=20)
B \(p\ne20\)
C (p=5)
D (p=12)
Explanation opens after your attempt
Correct Answer
B. \(p\ne20\)
Step 1
Concept
For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne20\). For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(12/3 \ne p/5\) होना चाहिए। इसलिए \(p\ne20\) सही शर्त है।
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समीकरणों (8x+ay=72) और (24x+30y=216) के अनंत हल होने के लिए (a) क्या होगा?
What will (a) be for the equations (8x+ay=72) and (24x+30y=216) to have infinitely many solutions?
#linear equations
#expert
#ratio condition
#parameter
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 3
Exam Tip
अनंत हल के लिए (8/24=a/30=72/216) होना चाहिए। इससे (a=10) मिलता है।
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समीकरणों (bx+16y=64) और (14x+28y=131) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+16y=64) and (14x+28y=131) to have no solution?
#linear equations
#expert
#no solution
#parameter
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/14=16/28) और (64/131) अलग होना चाहिए। इसलिए (b=8)।
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समीकरणों (22x+33y=99) और (2x+3y=12) के ग्राफ के बारे में सही कथन कौन-सा है?
Which statement is correct about the graph of the equations (22x+33y=99) and (2x+3y=12)?
#linear equations
#expert
#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 (22/2=33/3) but (99/12) 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 (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (22/2=33/3) लेकिन (99/12) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
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समीकरणों (30x+18y=126) और (5x+3y=21) के ग्राफ में क्या दिखेगा?
What will be shown in the graph of the equations (30x+18y=126) and (5x+3y=21)?
#linear equations
#expert
#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 (6) 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 (6) times the second. Therefore, both equations show the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (6) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।
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समीकरणों (5x+17y=69) और (12x+41y=166) के ग्राफ का सही वर्णन क्या है?
What is the correct description of the graph of the equations (5x+17y=69) and (12x+41y=166)?
#linear equations
#expert
#graph
#intersecting lines
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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 \(5/12 \ne 17/41\), 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 \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(5/12 \ne 17/41\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
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समीकरणों (10x+13y-71=0) और (30x+39y-213=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for the equations (10x+13y-71=0) and (30x+39y-213=0)?
#linear equations
#expert
#ratio relation
#infinite solutions
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A (10 / 30=13 / 39 \ne (-71) / (-213))
B (10 / 30 \ne 13 / 39)
C (10 / 30=13 / 39=(-71) / (-213))
D (10 / 30=(-71) / (-213) \ne 13 / 39)
Explanation opens after your attempt
Correct Answer
C. (10 / 30=13 / 39=(-71) / (-213))
Step 1
Concept
Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (10 / 30=13 / 39=(-71) / (-213)). Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (16x-9y+55=0) और (32x-18y+113=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for the equations (16x-9y+55=0) and (32x-18y+113=0)?
#linear equations
#expert
#ratio relation
#no solution
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A (16 / 32=(-9) / (-18) \ne 55 / 113)
B (16 / 32 \ne (-9) / (-18))
C (16 / 32=(-9) / (-18)=55 / 113)
D (16 / 32=55 / 113 \ne (-9) / (-18))
Explanation opens after your attempt
Correct Answer
A. (16 / 32=(-9) / (-18) \ne 55 / 113)
Step 1
Concept
The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is A. (16 / 32=(-9) / (-18) \ne 55 / 113). The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (15x+8y-47=0) और (30x+17y-94=0) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for the equations (15x+8y-47=0) and (30x+17y-94=0)?
#linear equations
#expert
#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 \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 3
Exam Tip
यहां \(15/30 \ne 8/17\), इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है।
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यदि (cx+18y=72) और (24x+48y=145) का कोई हल नहीं है, तो (c) क्या होगा?
If (cx+18y=72) and (24x+48y=145) have no solution, what will (c) be?
#linear equations
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#parameter
#no solution
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 3
Exam Tip
कोई हल नहीं के लिए (c/24=18/48) और (72/145) अलग होना चाहिए। इसलिए (c=9)।
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समीकरणों (7x+dy=63) और (28x+36y=252) के अनंत हल होने के लिए (d) का मान क्या है?
What is the value of (d) for the equations (7x+dy=63) and (28x+36y=252) to have infinitely many solutions?
#linear equations
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#parameter
#dependent pair
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 3
Exam Tip
अनंत हल के लिए (7/28=d/36=63/252) होना चाहिए। इसलिए (d=9)।
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समीकरणों (17x+py=51) और (8x+3y=25) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (17x+py=51) and (8x+3y=25) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
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A (p=51 / 8)
B (p\ne51 / 8)
C (p=3)
D (p=17)
Explanation opens after your attempt
Correct Answer
B. (p\ne51 / 8)
Step 1
Concept
For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne51 / 8\). For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(17/8 \ne p/3\) होना चाहिए। इसलिए \(p\ne51/8\) सही शर्त है।
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यदि (11x+7y=59) और (33x+21y=n) के अनंत हल हैं, तो (n) कितना होगा?
If (11x+7y=59) and (33x+21y=n) have infinitely many solutions, what is (n)?
#linear equations
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A (175)
B (176)
C (177)
D (178)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (3) times the first. Therefore, (n=177).
Step 2
Why this answer is correct
The correct answer is C. (177). The second equation must be (3) times the first. Therefore, (n=177).
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=177) होगा।
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यदि (16x-8y=64) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?
If (16x-8y=64) and (2x-y=t) are inconsistent, what is the correct condition for (t)?
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A (t=8)
B \(t\ne8\)
C (t=64)
D (t=16)
Explanation opens after your attempt
Correct Answer
B. \(t\ne8\)
Step 1
Concept
The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne8\). The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए (64/t) अलग होना चाहिए इसलिए \(t\ne8\)।
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समीकरणों (8x+15y=73) और (24x+45y=219) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing the equations (8x+15y=73) and (24x+45y=219)?
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#observation
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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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समीकरणों (24x+32y=96) और (3x+4y=13) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing the equations (24x+32y=96) and (3x+4y=13)?
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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 (24/3=32/4) but (96/13) 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 (24/3=32/4) but (96/13) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (24/3=32/4) लेकिन (96/13) अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (19x+12y=71) और (9x+6y=35) 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 the equations (19x+12y=71) and (9x+6y=35)?
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A (19 / 9=12 / 6), इसलिए अनंत हल / 6), so infinitely many solutions
B (19 / 9=12 / 6), इसलिए कोई हल नहीं / 6), so no solution
C (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
D (19 / 9=71 / 35), इसलिए संपाती / 35), so coincident
Explanation opens after your attempt
Correct Answer
C. (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), 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. \(19 / 9 \ne 12 / 6\), इसलिए एक अद्वितीय हल / 6), 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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समीकरणों (30x+45y=210) और (2x+3y=14) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (30x+45y=210) and (2x+3y=14)?
#linear equations
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#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 (15) 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 (15) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (15) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरणों (26x+39y=117) और (2x+3y=10) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (26x+39y=117) and (2x+3y=10)?
#linear equations
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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 (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 3
Exam Tip
यहां (26/2=39/3) लेकिन (117/10) अलग है। इसलिए यह असंगत युग्म है।
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समीकरणों (18x+7y=61) और (9x+4y=32) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (18x+7y=61) and (9x+4y=32)?
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#consistent independent
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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 \(18/9 \ne 7/4\), 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 \(18/9 \ne 7/4\), so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(18/9 \ne 7/4\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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एक दुकान में दो वस्तुओं के लिए (6x+11y=420) और (18x+33y=1260) समीकरण बनते हैं। हलों की संख्या क्या होगी?
In a shop, the equations for two items are (6x+11y=420) and (18x+33y=1260). How many solutions will there be?
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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 (3) 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 (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) 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 (9x+4y=380) और (18x+8y=775) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (9x+4y=380) and (18x+8y=775) are formed. What type of system is this?
#linear equations
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#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 (380/775) 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 (380/775) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (380/775) अलग है। इसलिए प्रणाली असंगत है।
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दो संख्याओं के लिए (7x+5y=58) और (4x-3y=11) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?
For two numbers, the equations (7x+5y=58) and (4x-3y=11) are formed. What will be the solution status?
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#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 (7/4 \ne 5/(-3)), 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 (7/4 \ne 5/(-3)), so the lines intersect. Such a pair has one unique solution.
Step 3
Exam Tip
यहां (7/4 \ne 5/(-3)), इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।
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समीकरणों (11x+18y=86) और (33x+54y=258) में तीनों अनुपातों का संबंध क्या है?
What is the relation among all three ratios in the equations (11x+18y=86) and (33x+54y=258)?
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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 (11/33=18/54=86/258). 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 (11/33=18/54=86/258). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (11/33=18/54=86/258)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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समीकरणों (18x+27y=126) और (2x+3y=16) के लिए कौन-सा संबंध सही है?
Which relation is correct for the equations (18x+27y=126) and (2x+3y=16)?
#linear equations
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A (18 / 2 \ne 27 / 3)
B (18 / 2=27 / 3=126 / 16)
C (18 / 2=27 / 3 \ne 126 / 16)
D (18 / 2=126 / 16 \ne 27 / 3)
Explanation opens after your attempt
Correct Answer
C. (18 / 2=27 / 3 \ne 126 / 16)
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. \(18 / 2=27 / 3 \ne 126 / 16\). 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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समीकरणों (12x+13y=55) और (24x+25y=107) के लिए कौन-सा कथन सही है?
Which statement is correct for the equations (12x+13y=55) and (24x+25y=107)?
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A (12 / 24=13 / 25), इसलिए कोई हल नहीं / 25), so no solution
B (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), 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. (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), so one unique solution
Step 1
Concept
Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(12 / 24 \ne 13 / 25\), इसलिए एक अद्वितीय हल / 25), so one unique solution. Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(12/24 \ne 13/25\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
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A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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समीकरणों (13x+8y=49) और (26x+16y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+8y=49) and (26x+16y=r) to be inconsistent?
#linear equations
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#inconsistent
#parameter
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A (r=98)
B \(r\ne98\)
C (r=49)
D (r=100)
Explanation opens after your attempt
Correct Answer
B. \(r\ne98\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 2
Why this answer is correct
The correct answer is B. \(r\ne98\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r\ne98\)।
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समीकरणों (10x+9y=38) और (20x+ay=91) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for the equations (10x+9y=38) and (20x+ay=91) to have no solution?
#linear equations
#expert
#no solution
#parameter
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A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 2
Why this answer is correct
The correct answer is C. (18). For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 3
Exam Tip
कोई हल नहीं के लिए (10/20=9/a) और (38/91) अलग होना चाहिए। इससे (a=18) मिलता है।
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समीकरणों (12x+ky=132) और (3x+10y=33) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (12x+ky=132) and (3x+10y=33) to have infinitely many solutions?
#linear equations
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#infinite solutions
#parameter
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A (38)
B (39)
C (40)
D (41)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (4) times the second. Therefore, (k=40).
Step 2
Why this answer is correct
The correct answer is C. (40). The first equation must be (4) times the second. Therefore, (k=40).
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=40) है।
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यदि (lx+17y=68) और (20x+34y=139) का कोई हल नहीं है, तो (l) का मान क्या होगा?
If (lx+17y=68) and (20x+34y=139) have no solution, what will be the value of (l)?
#linear equations
#expert
#parameter
#parallel lines
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 3
Exam Tip
कोई हल नहीं के लिए (l/20=17/34) और (68/139) अलग होना चाहिए। इसलिए (l=10)।
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समीकरणों (18x+13y=89) और (36x+26y=178) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (18x+13y=89) and (36x+26y=178)?
#linear equations
#expert
#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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समीकरणों (24x-18y=102) और (4x-3y=18) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (24x-18y=102) and (4x-3y=18)?
#linear equations
#expert
#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 (24/4=(-18)/(-3)) but (102/18) 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 (24/4=(-18)/(-3)) but (102/18) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (24/4=(-18)/(-3)) लेकिन (102/18) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (29x+12y=101) और (14x+6y=49) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (29x+12y=101) and (14x+6y=49)?
#linear equations
#expert
#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 \(29/14 \ne 12/6\), 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 \(29/14 \ne 12/6\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(29/14 \ne 12/6\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरणों (5x+9y=64) और (15x+27y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?
What is the correct condition on (t) for the equations (5x+9y=64) and (15x+27y=t) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
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A (t=192)
B \(t\ne192\)
C (t=64)
D (t=128)
Explanation opens after your attempt
Correct Answer
B. \(t\ne192\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne192\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t\ne192\)।
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समीकरणों (6x+ay=42) और (18x+33y=126) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 2
Why this answer is correct
The correct answer is C. (11). For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 3
Exam Tip
अनंत हल के लिए (6/18=a/33=42/126) होना चाहिए। इसलिए (a=11) सही है।
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समीकरणों (px+10y=50) और (14x+35y=122) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+10y=50) and (14x+35y=122) to have no solution?
#linear equations
#expert
#no solution
#parameter
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/14=10/35) और (50/122) अलग होना चाहिए। इसलिए (p=4)।
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समीकरणों (11x+ky=70) और (5x+4y=31) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (11x+ky=70) and (5x+4y=31) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
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A (k=44 / 5)
B (k\ne44 / 5)
C (k=4)
D (k=11)
Explanation opens after your attempt
Correct Answer
B. (k\ne44 / 5)
Step 1
Concept
For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k\ne44 / 5\). For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(11/5 \ne k/4\) होना चाहिए। इसलिए \(k\ne44/5\) सही शर्त है।
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समीकरणों (12x-7y+29=0) और (36x-21y+91=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (12x-7y+29=0) and (36x-21y+91=0)?
#linear equations
#expert
#ratio relation
#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 (12/36=(-7)/(-21)) but (29/91) 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 (12/36=(-7)/(-21)) but (29/91) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (12/36=(-7)/(-21)) लेकिन (29/91) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (7x+19y=86) और (13x+35y=158) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in the equations (7x+19y=86) and (13x+35y=158)?
#linear equations
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#ratio comparison
#unique solution
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A (7 / 13=19 / 35), इसलिए कोई हल नहीं / 35), so no solution
B (7 / 13=19 / 35), इसलिए अनंत हल / 35), so infinitely many solutions
C (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
Step 1
Concept
The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 13 \ne 19 / 35\), इसलिए एक अद्वितीय हल / 35), so one unique solution. The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 3
Exam Tip
पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक अद्वितीय हल देती हैं।
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दो वस्तुओं की कीमतों के लिए (10x+3y=470) और (20x+6y=955) समीकरण बने। यह प्रणाली कैसी है?
For prices of two items, the equations (10x+3y=470) and (20x+6y=955) are formed. What type of system is this?
#linear equations
#expert
#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 (470/955) 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 (470/955) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (470/955) अलग है। इसलिए प्रणाली असंगत है।
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समीकरणों (21x+8y=97) और (42x+16y=194) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (21x+8y=97) and (42x+16y=194)?
#linear equations
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#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 and have infinitely many solutions.
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 and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं और अनंत हल हैं।
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