Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
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What kind of pair is (13x+5y=22) and (26x+10y=45)?
C. असंगतInconsistent
यहां (13/26=5/10) लेकिन (22/45) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (13/26=5/10) but (22/45) is different. Therefore the lines are parallel and distinct.
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What is the correct solution status for (4x-7y=3) and (8x-13y=6)?
B. एक अद्वितीय हलOne unique solution
यहां (4/8 \ne (-7)/(-13)) इसलिए रेखाएं कटती हैं। अतः एक अद्वितीय हल है। / Here (4/8 \ne (-7)/(-13)) so the lines intersect. Hence there is one unique solution.
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Choose the correct statement for (15x+10y=5) and (3x+2y=1).
C. अनंत हल हैंThere are infinitely many solutions
पहला समीकरण दूसरे का (5) गुना है। इसलिए दोनों समीकरण एक ही रेखा दर्शाते हैं। / The first equation is (5) times the second. Therefore both equations represent the same line.
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Which conclusion is correct for (16x-8y=24) and (2x-y=4)?
C. कोई हल नहींNo solution
यहां (16/2=(-8)/(-1)) लेकिन (24/4) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (16/2=(-8)/(-1)) but (24/4) is different. Therefore the lines are parallel and distinct.
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Which option is correct for (6x+11y=7) and (3x+5y=4)?
C. रेखाएं एक बिंदु पर कटती हैंLines intersect at one point
यहां \(6/3 \ne 11/5\) इसलिए रेखाएं समानांतर नहीं हैं। वे एक बिंदु पर कटती हैं। / Here \(6/3 \ne 11/5\) so the lines are not parallel. They intersect at one point.
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If (2) equations have \(a_1/a_2=b_1/b_2\) and \(c_1/c_2\) is also the same then what happens?
C. अनंत हलInfinitely many solutions
तीनों अनुपात बराबर होने पर समीकरण समान रेखा बनाते हैं। इसलिए हल अनंत होते हैं। / When all three ratios are equal the equations make the same line. Therefore the solutions are infinite.
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If (2) equations have \(a_1/a_2=b_1/b_2\) but \(c_1/c_2\) is different then what happens?
C. रेखाएं अलग समानांतर होती हैंLines are distinct parallel
पहले दो अनुपात बराबर और तीसरा अलग हो तो रेखाएं समानांतर रहती हैं। इसलिए कोई हल नहीं होता। / When the first two ratios are equal and the third is different the lines remain parallel. Therefore there is no solution.
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State the correct solution status for (17x+4y=29) and (9x+2y=16).
C. एक अद्वितीय हलOne unique solution
यहां \(17/9 \ne 4/2\) इसलिए रेखाएं एक बिंदु पर मिलेंगी। इसलिए एक अद्वितीय हल है। / Here \(17/9 \ne 4/2\) so the lines will meet at one point. Therefore there is one unique solution.
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What is the correct conclusion for (18x+6y=12) and (3x+y=2)?
C. अनंत हलInfinitely many solutions
पहला समीकरण दूसरे का (6) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं में अनंत हल होते हैं। / The first equation is (6) times the second so both lines are coincident. Coincident lines have infinitely many solutions.
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What will be the number of solutions for (5x+10y=25) and (x+2y=6)?
C. कोई हल नहींNo solution
यहां (5/1=10/2) लेकिन (25/6) अलग है इसलिए रेखाएं समानांतर और अलग हैं। ऐसी रेखाओं का कोई सामान्य हल नहीं होता। / Here (5/1=10/2) but (25/6) is different so the lines are parallel and distinct. Such lines have no common solution.
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