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 161-170 of 575 questions.
What is the slope of the boundary line of \(y\le -2x+7\)?
C. (-2)
सीमा रेखा (y=-2x+7) है और (x) का गुणांक ढाल होता है। ढाल देखकर रेखा की दिशा समझें। / The boundary line is (y=-2x+7), and the coefficient of (x) is the slope. Use the slope to understand the line direction.
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What is the (y)-intercept of the boundary line of \(y\ge \frac{1}{2}x-3\)?
B. (-3)
सीमा रेखा \(y=\frac{1}{2}x-3\) है। इसमें (y)-अवरोध (-3) है। / The boundary line is \(y=\frac{1}{2}x-3\). Its (y)-intercept is (-3).
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C. (\left\(\frac{8}{3},\frac{8}{3}\right\))
दोनों तिरछी रेखाओं को हल करने पर \(x=y=\frac{8}{3}\) मिलता है। यह संयुक्त क्षेत्र का अंदरूनी शीर्ष है। / Solving the two oblique lines gives \(x=y=\frac{8}{3}\). This is an inner vertex of the common region.
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If the solution region of a system is only a line segment, what type of solution is it?
B. एक-आयामी सीमित हलone-dimensional bounded solution
रेखाखंड में अनंत बिंदु होते हैं लेकिन वह क्षेत्रफल वाला द्वि-आयामी भाग नहीं होता। इसे सीमित रैखिक हल माना जाता है। / A line segment has infinitely many points but not a two-dimensional area. It is considered a bounded linear solution.
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What is the common solution of \(x\ge 2\) and \(x\le 2\)?
A. रेखा (x=2)line (x=2)
दोनों शर्तें मिलकर (x=2) देती हैं। जब \(\ge\) और \(\le\) एक ही संख्या पर हों तो बराबरी मिलती है। / Both conditions together give (x=2). When \(\ge\) and \(\le\) occur at the same number, equality is obtained.
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What is the common solution of (y>1) and (y<1)?
C. रिक्त समुच्चयempty set
एक ही (y) मान (1) से बड़ा और छोटा दोनों नहीं हो सकता। इसलिए कोई संयुक्त हल नहीं है। / The same (y)-value cannot be both greater than and less than (1). Therefore there is no common solution.
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In the first quadrant, what is the (y)-intercept of the triangle formed by \(x+3y\le 12\)?
B. ((0,4))
(x=0) रखने पर (3y=12) इसलिए (y=4)। इसलिए (y)-अक्ष पर शीर्ष ((0,4)) है। / Putting (x=0) gives (3y=12), so (y=4). Hence the vertex on the (y)-axis is ((0,4)).
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In the first quadrant, what is the (x)-intercept of the region formed by \(4x+y\le 20\)?
C. ((5,0))
(y=0) रखने पर (4x=20) इसलिए (x=5)। यह (x)-अक्ष पर बनने वाला शीर्ष है। / Putting (y=0) gives (4x=20), so (x=5). This is the vertex on the (x)-axis.
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What is the position of the origin ((0,0)) for \(x+2y\le 0\)?
A. हल में शामिल और सीमा परincluded in solution and on boundary
((0,0)) रखने पर \(0\le 0\) सत्य है और बराबरी भी है। इसलिए मूल बिंदु सीमा रेखा पर शामिल है। / Substituting ((0,0)) gives \(0\le 0\), which is true with equality. So the origin is included on the boundary line.
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Which inequality is obtained by simplifying (2x+2y<10)?
A. (x+y<5)
पूरी असमानता को (2) से भाग देने पर (x+y<5) मिलता है। धनात्मक संख्या से भाग देने पर चिन्ह नहीं बदलता। / Dividing the whole inequality by (2) gives (x+y<5). Dividing by a positive number does not change the sign.
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