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.
Showing 171-180 of 575 questions.
What is the boundary-line form of \(-x+y\le 3\)?
B. (-x+y=3)
सीमा रेखा पाने के लिए असमानता चिन्ह को (=) से बदलते हैं। इसलिए (-x+y=3) सही है। / To get the boundary line, replace the inequality sign by (=). Hence (-x+y=3) is correct.
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Which point is not in the region formed by \(x\ge 0\), \(y\ge 0\), \(x+y\le 6\), and \(x\le 4\)?
D. ((5,0))
((5,0)) पर \(x\le 4\) असत्य है। सभी शर्तों को अलग-अलग जांचना जरूरी है। / At ((5,0)), \(x\le 4\) is false. It is necessary to check every condition separately.
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C. \(x+y\ge 5\)
रेखा (x+y=5) है और मूल बिंदु \(0\ge 5\) को संतुष्ट नहीं करता। ठोस रेखा होने से बराबरी शामिल होगी। / The line is (x+y=5), and the origin does not satisfy \(0\ge 5\). Since the line is solid, equality is included.
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What type of common region is formed by \(x\ge 0\), \(y\ge 0\), \(x+2y\ge 6\), and \(2x+y\ge 6\)?
B. असीमित क्षेत्रunbounded region
प्रथम चतुर्थांश में दोनों रेखाओं के ऊपर का क्षेत्र अनंत तक फैलता है। इसलिए हल क्षेत्र असीमित है। / In the first quadrant, the region above both lines extends infinitely. Therefore the solution region is unbounded.
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Which point is a vertex of the region formed by \(y\ge 0\), \(x\le 6\), and \(y\le x-2\)?
B. ((2,0))
(y=0) और (y=x-2) को मिलाने पर (x=2) मिलता है। इसलिए ((2,0)) क्षेत्र का एक शीर्ष है। / Solving (y=0) with (y=x-2) gives (x=2). Hence ((2,0)) is one vertex of the region.
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What are the intercepts of the boundary line for \(3x+y\le 15\)?
D. ((5,0)) और ((0,15))((5,0)) and ((0,15))
सीमा रेखा (3x+y=15) है। (y=0) पर (x=5) और (x=0) पर (y=15) मिलता है। / The boundary line is (3x+y=15). At (y=0), (x=5), and at (x=0), (y=15).
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Using the origin test relative to the line (2x-3y=12), which conclusion is correct for (2x-3y<12)?
B. मूल बिंदु वाली ओर शेड होगीside containing origin is shaded
((0,0)) रखने पर (0<12) सत्य है। इसलिए मूल बिंदु वाली ओर का अर्ध-समतल हल है। / Substituting ((0,0)) gives (0<12), which is true. Hence the half-plane containing the origin is the solution.
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Which statement about the boundary line and shading is correct for (x+4y>8)?
C. टूटी रेखा और मूल बिंदु के विपरीत ओरdashed line and opposite to origin
चिन्ह (>) होने से रेखा टूटी होगी। ((0,0)) रखने पर (0>8) असत्य है इसलिए विपरीत ओर शेड होगा। / The sign (>) makes the boundary dashed. Substituting ((0,0)) gives (0>8), false, so shade the opposite side.
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Which point on the line (x+2y=10) is included in the solution of \(x+2y\le 10\)?
A. ((4,3))
((4,3)) रखने पर (4+6=10) मिलता है। \(\le\) में सीमा रेखा शामिल होती है। / Substituting ((4,3)) gives (4+6=10). The boundary line is included with \(\le\).
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Where is the solution region of \(y\le -3x+9\)?
D. रेखा के नीचे सहितbelow the line including it
\(y\le -3x+9\) में (y) रेखा के मान से कम या बराबर है। इसलिए रेखा के नीचे का भाग सीमा सहित हल है। / In \(y\le -3x+9\), (y) is less than or equal to the line value. Therefore the region below the line including the boundary is the solution.
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