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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If (lx+11y=44) and (10x+22y=91) have no solution then what will be the value of (l)?
C. (5)
कोई हल नहीं के लिए (l/10=11/22) और (44/91) अलग होना चाहिए। इसलिए (l=5)। / For no solution (l/10=11/22) and (44/91) must be different. Hence (l=5).
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Which statement is correct by observing (12x+5y=41) and (24x+10y=82)?
B. रेखाएं एक ही हैंLines are the same
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं। / The second equation is (2) times the first. Therefore both lines are the same.
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What is the correct conclusion by observing (14x-10y=36) and (7x-5y=19)?
A. कोई हल नहींNo solution
यहां (14/7=(-10)/(-5)) लेकिन (36/19) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (14/7=(-10)/(-5)) but (36/19) is different. Therefore the lines are parallel and distinct.
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What is the correct solution status for (17x+6y=52) and (8x+3y=25)?
C. एक अद्वितीय हलOne unique solution
यहां \(17/8 \ne 6/3\) इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है। / Here \(17/8 \ne 6/3\) so the lines will intersect. Hence there is one unique solution.
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What is the correct condition on (t) for (3x+4y=22) and (9x+12y=t) to be inconsistent?
B. \(t \ne 66\)
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(t \ne 66\) सही है। / The first two ratios are equal so the constant ratio must be different for inconsistency. Hence \(t \ne 66\) is correct.
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What will be the value of (a) for (4x+ay=36) and (12x+21y=108) to have infinitely many solutions?
C. (7)
अनंत हल के लिए (4/12=a/21=36/108) होना चाहिए। इसलिए (a=7) मिलता है। / For infinitely many solutions (4/12=a/21=36/108) must hold. Therefore (a=7).
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Which condition is correct for (5x+2y=18) and (15x+ky=54) to have a unique solution?
B. \(k \ne 6\)
अद्वितीय हल के लिए \(5/15 \ne 2/k\) होना चाहिए। इसलिए \(k \ne 6\) सही शर्त है। / For a unique solution \(5/15 \ne 2/k\) must hold. Therefore \(k \ne 6\) is the correct condition.
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What is the correct solution status for (6x-7y+13=0) and (18x-21y+40=0)?
C. कोई हल नहींNo solution
यहां (6/18=(-7)/(-21)) लेकिन (13/40) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (6/18=(-7)/(-21)) but (13/40) is different. Therefore the lines are parallel and distinct.
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A. एक अद्वितीय हलOne unique solution
यहां \(2/5 \ne 7/16\) इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है। / Here \(2/5 \ne 7/16\) so the lines intersect at one point. Such a pair has one unique solution.
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Which statement is correct about the graph of (7x+9y=43) and (14x+18y=86)?
B. एक ही रेखाSame line
दूसरा समीकरण पहले का (2) गुना है। इसलिए ग्राफ में दोनों समीकरण एक ही रेखा दिखाते हैं। / The second equation is (2) times the first. Therefore both equations show the same line in the graph.
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