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 592 questions.
What is the correct interval for (x\in(-\infty,3]\cap\(0,\infty\)) on the number line?
A. ((0,3])
समान भाग (0) से बड़ा और (3) तक है। (0) शामिल नहीं है लेकिन (3) शामिल है। / The common part is greater than (0) and up to (3). (0) is excluded but (3) is included.
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Which number line interval represents (2(x-1)\le x+4)?
A. (\(-\infty,6]\)
हल करने पर \(2x-2\le x+4\) और \(x\le 6\) मिलता है। \(\le\) होने से (6) शामिल है। / Solving gives \(2x-2\le x+4\) and \(x\le 6\). Since \(\le\) is present, (6) is included.
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Which is the correct number line form for (3(x+2)>2x-1)?
B. (\(-7,\infty\))
हल करने पर (3x+6>2x-1) और (x>-7) मिलता है। कठोर असमता होने से (-7) खुला रहेगा। / Solving gives (3x+6>2x-1) and (x>-7). Since the inequality is strict, (-7) remains open.
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Which interval shows (5-2(x+1)\ge 1) on the number line?
A. (\(-\infty,1]\)
सरल करने पर \(3-2x\ge 1\), फिर \(-2x\ge -2\) और \(x\le 1\) मिलता है। ऋणात्मक से भाग देने पर चिह्न बदलता है। / Simplifying gives \(3-2x\ge 1\), then \(-2x\ge -2\), and \(x\le 1\). The sign reverses when dividing by a negative.
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C. (2) और (9) दोनों शामिल नहीं हैंBoth (2) and (9) are not included
खाली वृत्त सीमा को समाधान से बाहर रखता है। इसलिए दोनों अंतिम बिंदु शामिल नहीं होंगे। / Open circles keep boundary points out of the solution. Therefore both endpoints are not included.
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After removing (0) from the interval ([-3,7]), which form appears on the number line?
A. ([-3,0)\cup(0,7])
(0) हटाने का अर्थ है (0) पर खाली वृत्त लगाना। बाकी (-3) और (7) शामिल रहेंगे। / Removing (0) means placing an open circle at (0). The endpoints (-3) and (7) remain included.
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If \(x\in[-10,-4\)\cup[-4,2]), what is the combined number line interval?
A. ([-10,2])
दूसरा अंतराल (-4) को शामिल करता है इसलिए बीच में कोई खाली जगह नहीं बचती। संयुक्त अंतराल ([-10,2]) है। / The second interval includes (-4), so no gap remains in the middle. The combined interval is ([-10,2]).
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What is the result of \(x\in(-2,6)\cap[1,8]\) on the number line?
A. ([1,6))
समान भाग (1) से शुरू होकर (6) से पहले तक है। (1) शामिल है और (6) शामिल नहीं है। / The common part starts at (1) and goes up to but not including (6). (1) is included and (6) is excluded.
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If (x) is a real number and \(x\notin[2,5]\), which interval is correct on the number line?
A. (\(-\infty,2\)\cup\(5,\infty\))
([2,5]) में (2) और (5) शामिल हैं इसलिए बाहर का भाग उन्हें शामिल नहीं करेगा। इसलिए दोनों सीमाएँ खुली रहेंगी। / Since ([2,5]) includes (2) and (5), the outside part will not include them. Thus both boundaries are open.
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If (x) is a real number and \(x\notin(-1,4)\), what is the correct number line representation?
B. (\(-\infty,-1]\cup[4,\infty\))
((-1,4)) में (-1) और (4) शामिल नहीं हैं इसलिए पूरक में दोनों शामिल होंगे। अतः बाहरी भाग बंद सिरों के साथ होगा। / ((-1,4)) does not include (-1) and (4), so the complement includes both. Hence the outside regions have closed endpoints.
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