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 221-230 of 600 questions.
What is the vertical asymptote of (f(x)=\frac{1}{(x+2)2})?
A. (x=-2)
हर ((x+2)2) शून्य होने पर फलन परिभाषित नहीं रहता। इसलिए (x=-2) ऊर्ध्व आसिम्प्टोट है। / The function is not defined when ((x+2)2) is zero. So (x=-2) is the vertical asymptote.
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What is the range of (f(x)=\frac{2}{(x-1)2}-3)?
A. (\(-3,\infty\))
(\frac{2}{(x-1)2}) हमेशा धनात्मक है लेकिन (0) नहीं होता। इसलिए फलन (-3) से बड़ा रहता है। / (\frac{2}{(x-1)2}) is always positive but never (0). Therefore the function remains greater than (-3).
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What is the range of (f(x)=-\frac{3}{(x+1)2}+2)?
A. (\(-\infty,2\))
(-\frac{3}{(x+1)2}) हमेशा ऋणात्मक होता है और (0) नहीं बनता। इसलिए (f(x)) हमेशा (2) से कम है। / (-\frac{3}{(x+1)2}) is always negative and never becomes (0). So (f(x)) is always less than (2).
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For (f(x)=\operatorname{sgn}(3x-12)), what is the value when (x>4)?
A. (1)
यदि (x>4), तो (3x-12>0)। इसलिए साइनम मान (1) है। / If (x>4), then (3x-12>0). Therefore the signum value is (1).
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For (f(x)=\operatorname{sgn}(2-x)), what is the value when (x>2)?
A. (-1)
यदि (x>2), तो (2-x<0)। इसलिए (\operatorname{sgn}(2-x)=-1) है। / If (x>2), then (2-x<0). Hence (\operatorname{sgn}(2-x)=-1).
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At which (x)-value does (f(x)=\operatorname{sgn}(x+7)) become zero?
A. (x=-7)
साइनम फलन शून्य तब होता है जब अंदर की राशि शून्य हो। (x+7=0) से (x=-7) मिलता है। / The signum function is zero when the inside expression is zero. From (x+7=0), we get (x=-7).
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What is the value of (f(x)=\lfloor x-3\rfloor) at (x=5.9)?
A. (2)
(x-3=2.9) और \(\lfloor 2.9\rfloor=2\)। पहले अंदर का मान निकालें। / Here (x-3=2.9), and \(\lfloor 2.9\rfloor=2\). First find the inside value.
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What is the value of (f(x)=\lfloor 3x\rfloor) at (x=-0.4)?
A. (-2)
(3x=-1.2) और \(\lfloor -1.2\rfloor=-2\)। ऋणात्मक दशमलव में नीचे की ओर पूर्णांक लें। / Here (3x=-1.2), and \(\lfloor -1.2\rfloor=-2\). For negative decimals, take the lower integer.
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What is the value of (f(x)=\left\lfloor\frac{x+2}{3}\right\rfloor) at (x=7.4)?
A. (3)
\(\frac{7.4+2}{3}=\frac{9.4}{3}\), जो (3) से बड़ा और (4) से छोटा है। इसलिए ग्रेटेस्ट इंटीजर (3) है। / \(\frac{7.4+2}{3}=\frac{9.4}{3}\), which is greater than (3) and less than (4). So the greatest integer is (3).
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In the graph of (f(x)=\lfloor x\rfloor), what is the value of (y) for \(x\in[-3,-2\))?
A. (y=-3)
हर \(x\in[-3,-2\)) के लिए \(\lfloor x\rfloor=-3\)। इसलिए उस चरण पर (y=-3) है। / For every \(x\in[-3,-2\)), \(\lfloor x\rfloor=-3\). So on that step, (y=-3).
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