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 561-570 of 600 questions.
What is the range of (f(x)=|3x+2|-6)?
A. \( [-6,\infty\) )
\(|3x+2|\ge 0\), इसलिए सबसे छोटा मान (-6) है। यह तब मिलता है जब (3x+2=0)। / Since \(|3x+2|\ge 0\), the least value is (-6). It occurs when (3x+2=0).
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What is the domain of (f(x)=\frac{1}{|x-4|-1})?
A. \( \mathbb{R}\setminus{3,5} \)
हर शून्य नहीं होना चाहिए, इसलिए \(|x-4|-1\ne 0\)। इससे \(|x-4|\ne 1\), अतः \(x\ne 3,5\)। / The denominator must not be zero, so \(|x-4|-1\ne 0\). This gives \(|x-4|\ne 1\), hence \(x\ne 3,5\).
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What is the domain of (f(x)=\frac{x-2-16}{x-4})?
A. \( \mathbb{R}\setminus{4} \)
मूल हर (x-4) है, इसलिए (x=4) स्वीकार्य नहीं है। सरलीकरण के बाद भी हटे बिंदु को प्रांत में न जोड़ें। / The original denominator is (x-4), so (x=4) is not allowed. Even after simplification, do not add the removed point to the domain.
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What is the range of (f(x)=\frac{x-2-16}{x-4})?
A. \( \mathbb{R}\setminus{8} \)
\(x\ne 4\) पर फलन (x+4) के बराबर है। (x=4) से आने वाला मान (8) परिसर में नहीं आएगा। / For \(x\ne 4\), the function equals (x+4). The value (8), which would come from (x=4), will not be in the range.
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If the domain of (f(x)=\sqrt{x+b}) is \([-6,\infty\)), what is the value of (b)?
A. (6)
\(\sqrt{x+b}\) के लिए \(x+b\ge 0\), यानी \(x\ge -b\)। दिए गए प्रांत से (-b=-6), इसलिए (b=6)। / For \(\sqrt{x+b}\), \(x+b\ge 0\), so \(x\ge -b\). Comparing with the given domain, (-b=-6), hence (b=6).
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If the domain of (f(x)=\frac{1}{x-2-k}) is \(\mathbb{R}\setminus{-5,5}\), what is (k)?
A. (25)
हर शून्य तब होगा जब \(x^2=k\)। हटे हुए मान \(\pm 5\) हैं, इसलिए (k=25)। / The denominator becomes zero when \(x^2=k\). The excluded values are \(\pm 5\), so (k=25).
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If the range of (f(x)=ax-2-3) is (\(-\infty,-3]\), which condition on (a) is correct?
A. (a<0)
नीचे खुलने वाला परवलय ही (-3) को अधिकतम बनाता है। इसलिए (a<0) होना चाहिए। / Only a downward-opening parabola makes (-3) the maximum. Therefore (a<0) is required.
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If the range of (f(x)=x-2-8x+20) is \([m,\infty\)), what is (m)?
A. (4)
(x-2-8x+20=(x-4)2+4), इसलिए न्यूनतम (4) है। अतः (m=4) होगा। / Since (x-2-8x+20=(x-4)2+4), the minimum is (4). Therefore (m=4).
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If (f(x)=-x-2+6x-5), what is the range of (f)?
A. ( \(-\infty,4] \)
(f(x)=-(x-3)2+4), इसलिए अधिकतम (4) है। \(नीचे खुलने वाले परवलय का परिसर ((-\infty\),अधिकतम]) होता है। \(/ Here (f(x)=-(x-3)^2+4), so the maximum is (4). A downward-opening parabola has range ((-\infty\),maximum]).
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What is the range of (f(x)=\frac{1}{x-2+4x+8})?
A. ( \(0,\frac{1}{4}] \)
हर ((x+2)2+4\ge 4) है, इसलिए अधिकतम मान \(\frac{1}{4}\) है। हर असीम होने पर मान (0) के पास जाता है। / The denominator ((x+2)2+4\ge 4), so the maximum value is \(\frac{1}{4}\). As the denominator grows, the value approaches (0).
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