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 311-320 of 592 questions.
Which interval is correct on the number line for \(x^2<9\)?
A. ((-3,3))
\(x^2<9\) का अर्थ (|x|<3), इसलिए (-3<x<3)। परीक्षा में strict inequality में endpoints खुले रहते हैं।
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How will \(x^2\ge 16\) appear on the number line?
C. (\(-\infty,-4]\cup[4,\infty\))
\(x^2\ge 16\) में \(|x|\ge 4\), इसलिए बाहर के दो closed भाग मिलते हैं। परीक्षा में \(\ge\) होने पर (-4) और (4) शामिल करें। / \(x^2\ge 16\) means \(|x|\ge 4\), giving two closed outer regions. In exams, include (-4) and (4) for \(\ge\).
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Which condition is represented by (\(-\infty,2\)\cup\(2,\infty\)) on the number line?
B. \(x\ne 2\)
यह पूरी संख्या रेखा है लेकिन (2) हटाया गया है। परीक्षा में missing open point को not equal समझें। / This is the whole number line except (2). In exams, treat a missing open point as not equal.
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\(If the solution is ({x:x\le -4\) or \(x>5}), what is the interval notation\)?
A. ((-\infty,-4]\cup\(5,\infty\))
\(\le -4\) बंद endpoint देता है और (>5) खुला endpoint देता है। परीक्षा में infinite side पर हमेशा round bracket लगाएँ। / \(\le -4\) gives a closed endpoint, and (>5) gives an open endpoint. In exams, always use round brackets on the infinite side.
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Which number line representation is equivalent to (7-3x>1)?
A. (x<2), (2) पर खुला बिंदु और बाईं ओर(x<2), open dot at (2) shaded left
(7-3x>1) से (-3x>-6) और (x<2) मिलता है। परीक्षा में negative coefficient हो तो दिशा पलटती है। / (7-3x>1) gives (-3x>-6), hence (x<2). In exams, a negative coefficient reverses the direction.
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What interval is obtained from \([0,3]\cap(2,8)\) on the number line?
A. ((2,3])
Common भाग (2) से (3) तक है, पर (2) शामिल नहीं और (3) शामिल है। परीक्षा में intersection में endpoints की inclusion अलग से जाँचें। / The common part is from (2) to (3), but (2) is excluded and (3) is included. In exams, check endpoint inclusion separately in intersections.
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If a closed ray extends left from (-7) on the number line, what is the inequality?
B. \(x\le -7\)
Closed ray में endpoint शामिल होता है और left ray का मतलब कम या बराबर है। परीक्षा में ray की दिशा और endpoint दोनों देखें। / A closed ray includes the endpoint, and a left ray means less than or equal. In exams, check both ray direction and endpoint.
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What is the number line solution of \(\frac{2x+5}{-3}<1\)?
A. (x>-4), (-4) पर खुला बिंदु और दाईं ओर(x>-4), open dot at (-4) shaded right
(-3) से गुणा करने पर inequality reverse होकर (2x+5>-3) बनती है, इसलिए (x>-4)। परीक्षा में negative denominator हटाते समय चिन्ह पलटें। / Multiplying by (-3) reverses the inequality to (2x+5>-3), so (x>-4). In exams, reverse the sign when removing a negative denominator.
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Which interval correctly shows (x<0) or \(2\le x<5\) on the number line?
A. (\(-\infty,0\)\cup[2,5))
(x<0) में (0) खुला है और \(2\le x<5\) में (2) बंद तथा (5) खुला है। परीक्षा में or को union में बदलें। / In (x<0), (0) is open; in \(2\le x<5\), (2) is closed and (5) is open. In exams, convert or into union.
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If \(x\in\mathbb{N}\) and \(x\le 6\), which points will be marked on the number line?
B. ({1,2,3,4,5,6})
Class (11) में सामान्यतः \(\mathbb{N}={1,2,3,\ldots}\), इसलिए (1) से (6) तक बिंदु होंगे। परीक्षा में domain natural हो तो only natural points mark करें। / Usually in Class (11), \(\mathbb{N}={1,2,3,\ldots}\), so points from (1) to (6) are marked. In exams, if the domain is natural numbers, mark only natural points.
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