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 401-410 of 633 questions.
If \(x\in\mathbb{Z}\) and (|x-1|<4), which set will appear on the number line?
A. ({-2,-1,0,1,2,3,4})
(|x-1|<4) से (-3<x<5), इसलिए पूर्णांक (-2) से (4) तक हैं। परीक्षा में strict boundary को शामिल न करें।
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Which is the number line solution of \(\frac{7-2x}{4}\ge -3\)?
A. \(x\le\frac{19}{2}\), \(\frac{19}{2}\) पर बंद बिंदु और बाईं ओर\(x\le\frac{19}{2}\), closed dot at \(\frac{19}{2}\) shaded left
\(7-2x\ge -12\) से \(-2x\ge -19\), इसलिए \(x\le\frac{19}{2}\)। परीक्षा में ऋणात्मक से भाग देने पर चिन्ह पलटें। / \(7-2x\ge -12\) gives \(-2x\ge -19\), so \(x\le\frac{19}{2}\). In exams, reverse the sign when dividing by a negative.
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B. (\(-\infty,-10\)\cup\(-3,\infty\))
खुले सिरों के कारण (-10) और (-3) शामिल नहीं हैं और बाहर के दो भाग लिए जाते हैं। परीक्षा में बाहर छायांकन का अर्थ दो अलग किरणें होता है। / Because the endpoints are open, (-10) and (-3) are excluded, and two outer parts are taken. In exams, outer shading means two separate rays.
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Which ray represents \(\frac{x+1}{2}<\frac{3x-5}{6}\) on the number line?
B. (x>4), (4) पर खुला बिंदु और दाईं ओर(x>4), open dot at (4) shaded right
(6) से गुणा करने पर (3x+3<3x-5) बनता है, जो असंभव है। परीक्षा में समान (x) पद कटने पर स्थिर संख्याओं की तुलना करें। / Multiplying by (6) gives (3x+3<3x-5), which is impossible. In exams, when (x)-terms cancel, compare the constants.
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What is the result of \([3,\infty\)\cap\(-\infty,12]\) on the number line?
B. ([3,12])
साझा भाग (3) से (12) तक है और दोनों सिरे शामिल हैं। परीक्षा में दो बंद सीमाएँ common भाग में closed interval देती हैं। / The common part is from (3) to (12), and both endpoints are included. In exams, two included boundaries give a closed interval in the common region.
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Which interval represents ((-\infty,2]\setminus(-4,0]) on the number line?
A. ((-\infty,-4]\cup(0,2])
हटाया गया भाग (-4) को नहीं हटाता पर (0) को हटाता है। परीक्षा में हटाए गए interval के खुले और बंद सिरे उलटकर सोचें। / The removed part does not remove (-4), but it removes (0). In exams, think carefully about the open and closed endpoints of the removed interval.
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Which is the correct representation of (|x-7|>2) on the number line?
C. (\(-\infty,5\)\cup\(9,\infty\))
(|x-7|>2) में (x<5) या (x>9) मिलता है। परीक्षा में (>) वाले modulus में बाहर के खुले भाग बनते हैं। / (|x-7|>2) gives (x<5) or (x>9). In exams, modulus with (>) gives open outer regions.
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If (A=(-2,4]) and (B=[1,9)), what is \(A\cup B\) on the number line?
A. ((-2,9))
दोनों intervals overlap करते हैं और (-2) से (9) तक बिना gap के जाते हैं। परीक्षा में union में पूरा covered भाग लें। / The two intervals overlap and cover from (-2) to (9) without a gap. In exams, take the entire covered region for a union.
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If (A=(-12,-5]) and (B=[-7,1)), what is \(A\cap B\) on the number line?
B. ([-7,-5])
साझा भाग (-7) से (-5) तक है और दोनों सिरे शामिल हैं। परीक्षा में intersection में केवल overlapping segment चुनें। / The common part is from (-7) to (-5), and both endpoints are included. In exams, choose only the overlapping segment for intersection.
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Which is the number line solution of (2(4-x)\ge 3x-7)?
B. \(x\le3\), (3) पर बंद बिंदु और बाईं ओर\(x\le3\), closed dot at (3) shaded left
\(8-2x\ge3x-7\) से \(15\ge5x\), इसलिए \(x\le3\)। परीक्षा में चर को एक ओर और संख्याओं को दूसरी ओर रखें। / \(8-2x\ge3x-7\) gives \(15\ge5x\), so \(x\le3\). In exams, keep variables on one side and constants on the other.
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