Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Choose the correct solution status for (10x+5y=30) and (2x+y=7).
B. कोई हल नहींNo solution
यहां (10/2=5/1) लेकिन (30/7) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (10/2=5/1) but (30/7) is different. Therefore the lines are parallel and distinct.
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Which option is correct for (11x+3y=17) and (22x+7y=35)?
C. एक अद्वितीय हलOne unique solution
यहां \(11/22 \ne 3/7\) इसलिए रेखाएं कटेंगी। इससे एक अद्वितीय हल मिलेगा। / Here \(11/22 \ne 3/7\) so the lines will intersect. This gives one unique solution.
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What is the correct conclusion for (x-5y=1) and (2x-10y=2)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों समीकरण समान रेखा दर्शाते हैं। / The second equation is (2) times the first. Therefore both equations represent the same line.
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What kind of pair is (12x+4y=16) and (3x+y=5)?
C. असंगतInconsistent
यहां (12/3=4/1) लेकिन (16/5) अलग है। इसलिए यह असंगत युग्म है। / Here (12/3=4/1) but (16/5) is different. Therefore this is an inconsistent pair.
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Which statement is correct for (13x+2y=19) and (4x+5y=11)?
C. रेखाएं एक बिंदु पर कटती हैंLines intersect at one point
यहां \(13/4 \ne 2/5\) इसलिए रेखाएं समानांतर नहीं हैं। वे एक बिंदु पर कटेंगी और एक हल देंगी। / Here \(13/4 \ne 2/5\) so the lines are not parallel. They will intersect at one point and give one solution.
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If two lines have the same slope and the same intercept then how many solutions will there be?
C. अनंत हलInfinitely many solutions
समान ढाल और समान अवरोध से दोनों रेखाएं एक ही हो जाती हैं। इसलिए अनंत हल मिलते हैं। / Same slope and same intercept make both lines identical. Therefore infinitely many solutions are obtained.
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If two lines have the same slope but different intercepts then what type of pair will it be?
B. असंगतInconsistent
समान ढाल और अलग अवरोध से रेखाएं समानांतर और अलग होती हैं। इसलिए कोई सामान्य हल नहीं होता। / Same slope and different intercepts make the lines parallel and distinct. Therefore there is no common solution.
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If two lines have different slopes then how many solutions will the pair have?
C. एक अद्वितीय हलOne unique solution
अलग ढाल वाली रेखाएं एक ही बिंदु पर मिलती हैं। इसलिए युग्म संगत और स्वतंत्र होता है। / Lines with different slopes meet at exactly one point. Therefore the pair is consistent and independent.
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Choose the correct statement for (15x+9y=6) and (5x+3y=2).
C. अनंत हल हैंThere are infinitely many solutions
पहला समीकरण दूसरे का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / The first equation is (3) times the second. Therefore both lines are coincident and have infinitely many solutions.
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What is the correct solution status for (14x-7y=28) and (2x-y=3)?
C. कोई हल नहींNo solution
यहां (14/2=(-7)/(-1)) लेकिन (28/3) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (14/2=(-7)/(-1)) but (28/3) is different. Therefore the lines are parallel and distinct.
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