B. केवल प्रतिच्छेद बिंदु समाधान है/Only the intersection point is the solution
Step 1
Concept
Intersecting lines have only one common point. That point is the unique solution of both equations.
Step 2
Why this answer is correct
The correct answer is B. केवल प्रतिच्छेद बिंदु समाधान है / Only the intersection point is the solution. Intersecting lines have only one common point. That point is the unique solution of both equations.
Step 3
Exam Tip
प्रतिच्छेदी रेखाएं केवल एक साझी बिंदु रखती हैं। वही बिंदु दोनों समीकरणों का अद्वितीय समाधान होता है।
For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 3
Exam Tip
प्रतिच्छेदी रेखाओं के लिए (x) और (y) के गुणांक अनुपात बराबर नहीं होते। यही अद्वितीय समाधान की शर्त है।
Thick brush strokes can make the surface look raised. Exam tip: understand brush stroke as texture effect.
Step 2
Why this answer is correct
The correct answer is C. उभरी हुई सतह / Raised surface. Thick brush strokes can make the surface look raised. Exam tip: understand brush stroke as texture effect.
Step 3
Exam Tip
मोटे ब्रश स्ट्रोक सतह को उभरा हुआ दिखा सकते हैं। परीक्षा में brush stroke को texture effect समझें।
Intersecting lines meet or cross at a point. Exam tip: remember intersecting as crossing.
Step 2
Why this answer is correct
The correct answer is B. प्रतिच्छेदी रेखाएं / Intersecting lines. Intersecting lines meet or cross at a point. Exam tip: remember intersecting as crossing.
Step 3
Exam Tip
प्रतिच्छेदी रेखाएं किसी बिंदु पर मिलती या काटती हैं। परीक्षा में intersecting को crossing से याद रखें।
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।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(4/9 \ne 15/31\) 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 \(4/9 \ne 15/31\) so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(4/9 \ne 15/31\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(3/8 \ne 13/29\), 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 \(3/8 \ne 13/29\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(3/8 \ne 13/29\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 11/19\), 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 \(2/5 \ne 11/19\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 11/19\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 11/19\) 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 \(2/5 \ne 11/19\) so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 11/19\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
Here \(4/9 \ne 7/15\) so the lines intersect at one point. If the first two ratios differ there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. Here \(4/9 \ne 7/15\) so the lines intersect at one point. If the first two ratios differ there is one unique solution.
Step 3
Exam Tip
यहां \(4/9 \ne 7/15\) इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल होता है।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(3/7 \ne 8/13\), 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 \(3/7 \ne 8/13\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(3/7 \ne 8/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
Here \(4/8 \ne 9/17\), so the lines intersect at one point. Different first two ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(4/8 \ne 9/17\), so the lines intersect at one point. Different first two ratios give a unique solution.
Step 3
Exam Tip
यहां \(4/8 \ne 9/17\), इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग पहले दो अनुपात अद्वितीय हल देते हैं।
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।
C. रेखाएं एक बिंदु पर कटती हैं/Lines intersect at one point
Step 1
Concept
Here \(6/3 \ne 11/5\) so the lines are not parallel. They intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point. Here \(6/3 \ne 11/5\) so the lines are not parallel. They intersect at one point.
Step 3
Exam Tip
यहां \(6/3 \ne 11/5\) इसलिए रेखाएं समानांतर नहीं हैं। वे एक बिंदु पर कटती हैं।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(5/3 \ne 8/4\) so the lines will not be parallel. They will intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(5/3 \ne 8/4\) so the lines will not be parallel. They will intersect at one point.
Step 3
Exam Tip
यहां \(5/3 \ne 8/4\) इसलिए रेखाएं समानांतर नहीं होंगी। वे एक बिंदु पर कटेंगी।
Here \(9/4 \ne 5/2\) so the lines intersect at one point. Therefore there is one unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here \(9/4 \ne 5/2\) so the lines intersect at one point. Therefore there is one unique solution.
Step 3
Exam Tip
यहां \(9/4 \ne 5/2\) इसलिए रेखाएं एक बिंदु पर कटती हैं। इसलिए एक अद्वितीय हल है।
Here \(1/3 \ne 5/14\) so the lines intersect at one point. Different coefficient ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(1/3 \ne 5/14\) so the lines intersect at one point. Different coefficient ratios give a unique solution.
Step 3
Exam Tip
यहां \(1/3 \ne 5/14\) इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग गुणांक अनुपात अद्वितीय हल देते हैं।
C. रेखाएं एक बिंदु पर कटती हैं/Lines intersect at one point
Step 1
Concept
Here \(13/4 \ne 2/5\) so the lines are not parallel. They will intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point. Here \(13/4 \ne 2/5\) so the lines are not parallel. They will intersect at one point and give one solution.
Step 3
Exam Tip
यहां \(13/4 \ne 2/5\) इसलिए रेखाएं समानांतर नहीं हैं। वे एक बिंदु पर कटेंगी और एक हल देंगी।
Here \(7/5 \ne 2/4\) so the lines meet at one point. One intersection means one unique solution.
Step 2
Why this answer is correct
The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(7/5 \ne 2/4\) so the lines meet at one point. One intersection means one unique solution.
Step 3
Exam Tip
यहां \(7/5 \ne 2/4\) इसलिए रेखाएं एक बिंदु पर मिलती हैं। एक intersection का अर्थ एक अद्वितीय हल है।
Here \(1/2 \ne 7/9\) 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 है / There is one unique solution. Here \(1/2 \ne 7/9\) so the lines intersect at one point. Different coefficient ratios give one unique solution.
Step 3
Exam Tip
यहां \(1/2 \ne 7/9\) इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग गुणांक अनुपात एक अद्वितीय हल देते हैं।
C. रेखाएं एक बिंदु पर कटती हैं/Lines intersect at one point
Step 1
Concept
Here \(2/3 \ne 5/7\), so the lines intersect at one point. This means there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point. Here \(2/3 \ne 5/7\), so the lines intersect at one point. This means there is one unique solution.
Step 3
Exam Tip
यहां \(2/3 \ne 5/7\), इसलिए रेखाएं एक बिंदु पर कटती हैं। इसका मतलब एक अद्वितीय हल है।
A. वे एक बिंदु पर कटेंगी/They will intersect at one point
Step 1
Concept
Here \(5/10 \ne 2/3\), so the lines will intersect. Intersecting lines give one unique solution.
Step 2
Why this answer is correct
The correct answer is A. वे एक बिंदु पर कटेंगी / They will intersect at one point. Here \(5/10 \ne 2/3\), so the lines will intersect. Intersecting lines give one unique solution.
Step 3
Exam Tip
यहां \(5/10 \ne 2/3\), इसलिए रेखाएं कटेंगी। कटती रेखाएं एक अद्वितीय हल देती हैं।
Here \(1/2 \ne 3/5\), so the lines will meet at one point. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(1/2 \ne 3/5\), so the lines will meet at one point. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(1/2 \ne 3/5\), इसलिए रेखाएं एक बिंदु पर मिलेंगी। इसलिए एक अद्वितीय हल है।
Different ratios indicate different slopes, so the lines intersect. Intersecting lines give one solution.
Step 2
Why this answer is correct
The correct answer is C. कटती हुई / Intersecting. Different ratios indicate different slopes, so the lines intersect. Intersecting lines give one solution.
Step 3
Exam Tip
अलग अनुपातों के कारण ढालें अलग होती हैं, इसलिए रेखाएं कटती हैं। कटती रेखाओं से एक हल मिलता है।
Here \(3/6 \ne 2/5\), so the lines intersect at one point. Different (a) and (b) ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here \(3/6 \ne 2/5\), so the lines intersect at one point. Different (a) and (b) ratios give a unique solution.
Step 3
Exam Tip
यहां \(3/6 \ne 2/5\), इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग (a) और (b) अनुपात अद्वितीय हल देते हैं।
For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is B. (5x-2y=11), (x+y=7). For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 3
Exam Tip
(5x-2y=11) और (x+y=7) में \(\frac{5}{1}\neq\frac{-2}{1}\), इसलिए रेखाएं प्रतिच्छेदी हैं। अलग गुणांक अनुपात अद्वितीय समाधान देता है।
The coefficient ratios are not equal, so the lines meet at one point. This is the case of a unique solution.
Step 2
Why this answer is correct
The correct answer is A. प्रतिच्छेदी / Intersecting. The coefficient ratios are not equal, so the lines meet at one point. This is the case of a unique solution.
Step 3
Exam Tip
गुणांक अनुपात बराबर नहीं हैं, इसलिए रेखाएं एक बिंदु पर मिलती हैं। यह अद्वितीय समाधान की स्थिति है।
For (3x-y=6) and (x+y=4), \(\frac{3}{1}\neq\frac{-1}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is B. (3x-y=6), (x+y=4). For (3x-y=6) and (x+y=4), \(\frac{3}{1}\neq\frac{-1}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 3
Exam Tip
(3x-y=6) और (x+y=4) में \(\frac{3}{1}\neq\frac{-1}{1}\), इसलिए रेखाएं प्रतिच्छेदी हैं। अलग गुणांक अनुपात अद्वितीय समाधान देता है।
C. ठीक (1) हल होता है/There is exactly (1) solution
Step 1
Concept
When coefficient ratios are unequal, the lines intersect at one point. Therefore the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. ठीक (1) हल होता है / There is exactly (1) solution. When coefficient ratios are unequal, the lines intersect at one point. Therefore the pair is consistent and independent.
Step 3
Exam Tip
असमान गुणांक अनुपात होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए युग्म संगत और स्वतंत्र होता है।
Unequal coefficient ratios mean the lines intersect at one point. Therefore the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. ठीक (1) हल / Exactly (1) solution. Unequal coefficient ratios mean the lines intersect at one point. Therefore the pair is consistent and independent.
Step 3
Exam Tip
असमान गुणांक अनुपात का अर्थ है कि रेखाएँ एक बिंदु पर कटेंगी। इसलिए युग्म संगत और स्वतंत्र होगा।
In (x+3y=10) and (3x+y=10), coefficient ratios are not equal. Hence the lines intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. (x+3y=10) और (3x+y=10) / (x+3y=10) and (3x+y=10). In (x+3y=10) and (3x+y=10), coefficient ratios are not equal. Hence the lines intersect at one point.
Step 3
Exam Tip
(x+3y=10) और (3x+y=10) में गुणांक अनुपात समान नहीं हैं। इसलिए रेखाएँ एक बिंदु पर कटेंगी।
C. एक बिंदु पर प्रतिच्छेदी/Intersecting at one point
Step 1
Concept
Unequal ratios mean the lines will intersect at one point. Such a pair has exactly (1) solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर प्रतिच्छेदी / Intersecting at one point. Unequal ratios mean the lines will intersect at one point. Such a pair has exactly (1) solution.
Step 3
Exam Tip
असमान अनुपात का अर्थ है कि रेखाएँ एक बिंदु पर कटेंगी। ऐसे युग्म का ठीक (1) हल होता है।
In (x+2y=7) and (2x+y=8), the coefficient ratios are not equal. Hence the lines will intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. (x+2y=7) और (2x+y=8) / (x+2y=7) and (2x+y=8). In (x+2y=7) and (2x+y=8), the coefficient ratios are not equal. Hence the lines will intersect at one point.
Step 3
Exam Tip
(x+2y=7) और (2x+y=8) में गुणांक अनुपात समान नहीं हैं। इसलिए रेखाएँ एक बिंदु पर कटेंगी।
Unequal coefficient ratios make the lines intersect at one point. Therefore the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is B. ठीक (1) हल / Exactly (1) solution. Unequal coefficient ratios make the lines intersect at one point. Therefore the pair is consistent and independent.
Step 3
Exam Tip
असमान गुणांक अनुपात से रेखाएँ एक बिंदु पर कटती हैं। इसलिए युग्म संगत और स्वतंत्र होता है।
C. जब रेखाएँ एक बिंदु पर कटें/When lines intersect at one point
Step 1
Concept
Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 2
Why this answer is correct
The correct answer is C. जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point. Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 3
Exam Tip
ठीक एक हल तब मिलता है जब दोनों रेखाएँ एक ही बिंदु पर कटती हैं। वही बिंदु दोनों समीकरणों का सामान्य हल होता है।
C. जब रेखाएँ एक बिंदु पर कटें/When lines intersect at one point
Step 1
Concept
Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 2
Why this answer is correct
The correct answer is C. जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point. Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 3
Exam Tip
ठीक एक हल तब मिलता है जब दोनों रेखाएँ एक ही बिंदु पर कटती हैं। यही बिंदु दोनों समीकरणों का सामान्य हल है।
A. एक बिंदु पर कटेंगी/They will intersect at one point
Step 1
Concept
The two equations give different lines with unequal slopes. Hence, they will have one unique intersection point.
Step 2
Why this answer is correct
The correct answer is A. एक बिंदु पर कटेंगी / They will intersect at one point. The two equations give different lines with unequal slopes. Hence, they will have one unique intersection point.
Step 3
Exam Tip
दोनों समीकरण अलग-अलग रेखाएँ देते हैं जिनकी ढाल समान नहीं है। इसलिए उनका एक अद्वितीय प्रतिच्छेद बिंदु होगा।
One intersection point means the equations have exactly one solution. Remember, intersecting lines are consistent and independent.
Step 2
Why this answer is correct
The correct answer is A. (1) अद्वितीय हल / (1) unique solution. One intersection point means the equations have exactly one solution. Remember, intersecting lines are consistent and independent.
Step 3
Exam Tip
एक प्रतिच्छेद बिंदु होने पर समीकरणों का एक ही हल होता है। याद रखें, कटती हुई रेखाएँ संगत और स्वतंत्र होती हैं।
