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 581-590 of 600 questions.
For (f(x)=\lfloor x \rfloor), what is (f(-4))?
A. (-4)
जब (x) स्वयं पूर्णांक हो तो \(\lfloor x \rfloor=x\) होता है। इसलिए \(\lfloor -4 \rfloor=-4\) है। / When (x) itself is an integer, \(\lfloor x \rfloor=x\). Hence \(\lfloor -4 \rfloor=-4\).
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What is (f(2.6)) for (f(x)=\lfloor x+0.5 \rfloor)?
A. (3)
(2.6+0.5=3.1) है और \(\lfloor 3.1 \rfloor=3\)। पहले अंदर का मान निकालें। / (2.6+0.5=3.1), and \(\lfloor 3.1 \rfloor=3\). First calculate the inside value.
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What is the set of values of (f(x)=\lfloor 2x \rfloor) for \(x\in[1,1.5\))?
A. ({2})
\(x\in[1,1.5\)) से \(2x\in[2,3\)) है। इस पूरे अंतराल पर \(\lfloor 2x \rfloor=2\) होता है। / From \(x\in[1,1.5\)), \(2x\in[2,3\)). On this whole interval \(\lfloor 2x \rfloor=2\).
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What is (g(-2.2)) for the ceiling function (g(x)=\lceil x \rceil)?
A. (-2)
\(\lceil x \rceil\) (x) से बड़ा या बराबर सबसे छोटा पूर्णांक देता है। (-2.2) के लिए वह (-2) है। / \(\lceil x \rceil\) gives the smallest integer greater than or equal to (x). For (-2.2), it is (-2).
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What is the value of (f(x)=\operatorname{sgn}(5-x)) at (x=7)?
A. (-1)
(x=7) पर (5-x=-2) ऋणात्मक है। साइनम फलन ऋणात्मक इनपुट पर (-1) देता है। / At (x=7), (5-x=-2), which is negative. The signum function gives (-1) for a negative input.
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For which (x) values is (f(x)=\operatorname{sgn}\(x^2-4\)) equal to (0)?
A. (x=-2,2)
साइनम फलन (0) तब देता है जब अंदर की अभिव्यक्ति (0) हो। \(x^2-4=0\) से \(x=\pm2\) है। / The signum function gives (0) when the inside expression is (0). From \(x^2-4=0\), \(x=\pm2\).
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At which point is the corner of the graph (y=\max(x,3))?
A. ((3,3))
दोनों नियम (y=x) और (y=3) तब मिलते हैं जब (x=3)। इसलिए कोना ((3,3)) पर है। / The two rules (y=x) and (y=3) meet when (x=3). Hence the corner is at ((3,3)).
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At which point is the corner of (y=\min(x,-3))?
A. ((-3,-3))
नियम (y=x) और (y=-3) (x=-3) पर मिलते हैं। इसलिए कोना ((-3,-3)) है। / The rules (y=x) and (y=-3) meet at (x=-3). Therefore the corner is ((-3,-3)).
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For \(x\ge 2\), which line represents (y=|x-2|+x)?
A. (y=2x-2)
\(x\ge 2\) पर (|x-2|=x-2) होता है। इसलिए (y=x-2+x=2x-2) है। / For \(x\ge 2\), (|x-2|=x-2). Hence (y=x-2+x=2x-2).
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At which (x) values do \(y=x^2\) and (y=3x+4) meet?
A. (x=-1,4)
प्रतिच्छेद के लिए \(x^2=3x+4\) रखें। \(x^2-3x-4=0\) से (x=-1,4) है। / For intersection set \(x^2=3x+4\). From \(x^2-3x-4=0\), (x=-1,4).
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