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 361-370 of 633 questions.
Which is the number line solution of (2(1-x)<x+8)?
A. (x>-2), (-2) पर खुला बिंदु और दाईं ओर(x>-2), open dot at (-2) shaded right
(2-2x<x+8) से (-3x<6), इसलिए (x>-2)। परीक्षा में negative coefficient से divide करते समय sign बदलें।
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What is the solution of \(x\in[-5,\infty\)\cap\(-\infty,1\)) on the number line?
A. ([-5,1))
Common भाग (-5) से (1) तक है, जिसमें (-5) शामिल और (1) बाहर है। परीक्षा में intersection में दोनों शर्तें साथ पूरी होनी चाहिए। / The common part is from (-5) to (1), including (-5) and excluding (1). In exams, both conditions must be satisfied in an intersection.
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A. (x<-1) या (x>4)(x<-1) or (x>4)
Open dots endpoints को exclude करते हैं और बाहर shading दो rays देती है। परीक्षा में outer shading को or inequality समझें। / Open dots exclude the endpoints, and outer shading gives two rays. In exams, read outer shading as an or inequality.
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Which number line interval is the union of \(-4\le x\le 0\) and (-1<x<3)?
A. ([-4,3))
दोनों intervals overlap करते हैं और मिलकर (-4) से (3) तक जाते हैं। परीक्षा में overlapping intervals का union एक बड़ा interval बनता है। / The intervals overlap and together extend from (-4) to (3). In exams, the union of overlapping intervals forms one larger interval.
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Which interval represents (\(-\infty,4]\setminus[-1,2\)) on the number line?
A. (\(-\infty,-1\)\cup[2,4])
([-1,2)) हटाने पर (-1) भी हटता है पर (2) बचता है। परीक्षा में set difference में हटाए गए interval के endpoints को ध्यान से जाँचें। / Removing ([-1,2)) removes (-1) but keeps (2). In exams, check endpoints carefully in set difference.
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If \(x\in\mathbb{Z}\) and \(|x|\le 3\), how many points will be marked on the number line?
C. (7)
Points (-3,-2,-1,0,1,2,3) हैं, इसलिए कुल (7) हैं। परीक्षा में integers को गिनते समय दोनों endpoints शामिल करें। / The points are (-3,-2,-1,0,1,2,3), so there are (7) points. In exams, include both endpoints while counting integers.
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Which is the correct number line interval for \(9\le 5-2x<15\)?
A. ((-5,-2])
\(4\le -2x<10\) से negative division के बाद \(-5<x\le -2\) मिलता है। परीक्षा में compound inequality को negative से divide करते समय endpoints भी उलटते हैं।
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What is the union of ((-2,6]) and ([6,10)) on the number line?
A. ((-2,10))
दोनों intervals (6) पर जुड़े हैं और gap नहीं है। परीक्षा में common endpoint शामिल हो तो intervals merge हो जाते हैं। / The intervals join at (6) with no gap. In exams, intervals merge when the common endpoint is included.
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A. \(2\le x<5\)
Common भाग (2) से (5) तक है, जिसमें (2) शामिल और (5) बाहर है। परीक्षा में intersection को simultaneous condition की तरह पढ़ें। / The common part is from (2) to (5), including (2) and excluding (5). In exams, read intersection as a simultaneous condition.
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Which is the number line solution of \(\frac{x+2}{5}\ge \frac{x-4}{3}\)?
B. \(x\le -13\), (-13) पर बंद बिंदु और बाईं ओर\(x\le -13\), closed dot at (-13) shaded left
(15) से गुणा करने पर \(3x+6\ge 5x-20\), इसलिए \(x\le 13\) नहीं बल्कि \(x\le 13\) आता है। परीक्षा में final sign और arithmetic दोबारा जाँचें। / Multiplying by (15) gives \(3x+6\ge 5x-20\), so \(x\le 13\), not \(x\ge 13\). In exams, recheck the final sign and arithmetic.
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