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 291-300 of 600 questions.
If (f(x)=x-2) and (g(x)=x+1), what is ((f+g)(a))?
A. \(a^2+a+1\)
((f+g)(x)=x-2+x+1), इसलिए (x=a) रखने पर \(a^2+a+1\)। चर बदलने पर नियम वही रहता है। / ((f+g)(x)=x-2+x+1), so putting (x=a) gives \(a^2+a+1\). The rule stays the same when the variable changes.
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If (f(x)=2x-3) and (g(x)=x-2+1), what is ((3f+g)(x))?
A. \(x^2+6x-8\)
(3f(x)=6x-9), फिर \(6x-9+x^2+1=x^2+6x-8\)। स्थिर पदों को सही जोड़ें। / (3f(x)=6x-9), then \(6x-9+x^2+1=x^2+6x-8\). Add constant terms correctly.
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If (f(x)=x-2-5x+6) and (g(x)=x-2), what is (\left\(\frac{f}{g}\right\)(x)) for \(x\ne 2\)?
A. (x-3)
(x-2-5x+6=(x-2)(x-3)), इसलिए भागफल (x-3) है। गुणनखंड बनाना भागफल में मदद करता है। / (x-2-5x+6=(x-2)(x-3)), so the quotient is (x-3). Factorisation helps in quotient problems.
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If (f(x)=x+1) and (g(x)=\frac{1}{x+1}), which statement about ((fg)(x)) is correct?
A. ((fg)(x)=1), \(x\ne -1\)
गुणनफल (1) है, पर (g(x)) के हर के कारण \(x\ne -1\)। सरल रूप के साथ डोमेन लिखना जरूरी है। / The product is (1), but \(x\ne -1\) because of the denominator of (g(x)). It is important to write the domain with the simplified form.
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If (f(x)=x-2+2) and (g(x)=2x-2-1), what is ((g-f)(x))?
A. \(x^2-3\)
((g-f)(x)=2x-2-1-\(x^2+2\)=x-2-3)। क्रम बदलने से घटाव का उत्तर बदल सकता है। / ((g-f)(x)=2x-2-1-\(x^2+2\)=x-2-3). Changing the order can change the subtraction result.
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If (f(x)=\frac{x-2}{x+3}) and (g(x)=\frac{x+3}{x-2}), what is the domain of ((fg)(x))?
A. \(\mathbb{R}-{-3,2}\)
गुणनफल (1) बनता है, पर मूल हरों से \(x\ne -3,2\) है। डोमेन हमेशा मूल फलनों से तय करें। / The product becomes (1), but original denominators give \(x\ne -3,2\). Always decide the domain from the original functions.
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If (f(x)=x-2+x) and (g(x)=x-2-x), what is ((f+g)(x))?
A. \(2x^2\)
(x) और (-x) कट जाते हैं, इसलिए ((f+g)(x)=2x-2)। विपरीत पद पहचानें। / (x) and (-x) cancel, so ((f+g)(x)=2x-2). Identify opposite terms.
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If (f(x)=\sqrt{4-x}) and (g(x)=\frac{1}{x}), what is the domain of ((f+g)(x))?
A. (\(-\infty,4]-{0}\)
वर्गमूल के लिए \(4-x\ge 0\), यानी \(x\le 4\), और हर के लिए \(x\ne 0\)। दोनों शर्तें साथ लें। / The square root needs \(4-x\ge 0\), i.e. \(x\le 4\), and the denominator needs \(x\ne 0\). Take both conditions together.
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If (f(x)=2x+1) and (g(x)=3x-4), what is ((fg)(-1))?
A. (7)
(f(-1)=-1) और (g(-1)=-7), इसलिए गुणनफल (7) है। दो ऋणात्मक संख्याओं का गुणन धनात्मक होता है। / (f(-1)=-1) and (g(-1)=-7), so the product is (7). The product of two negative numbers is positive.
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A. (1-x)
(f(x)=(x-1)2) और (g(x)=-(x-1)), इसलिए भागफल (-(x-1)=1-x) है। चिह्न पर विशेष ध्यान दें। / (f(x)=(x-1)2) and (g(x)=-(x-1)), so the quotient is (-(x-1)=1-x). Pay special attention to the sign.
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