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 261-270 of 600 questions.
If (f(x)=x-2) and (g(x)=3x), which (x) satisfies ((f-g)(x)=0)?
A. (x=0) या (x=3)(x=0) or (x=3)
((f-g)(x)=x-2-3x=x(x-3)), इसलिए (x=0) या (x=3)। शून्य गुणनफल नियम याद रखें। / ((f-g)(x)=x-2-3x=x(x-3)), so (x=0) or (x=3). Remember the zero product rule.
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If (f(x)=x+4) and (g(x)=2x-1), which equation is formed for ((f+g)(x)=(fg)(x))?
B. \(2x^2+7x-4=3x+3\)
((f+g)(x)=3x+3) और ((fg)(x)=(x+4)(2x-1)=2x-2+7x-4)। पहले दोनों पक्ष अलग लिखें। / ((f+g)(x)=3x+3) and ((fg)(x)=(x+4)(2x-1)=2x-2+7x-4). Write both sides separately first.
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If (f(x)=\frac{x+1}{x-2}) and (g(x)=x-2-4), what is the domain of ((fg)(x))?
A. \(\mathbb{R}-{2}\)
(g(x)) सभी वास्तविक (x) पर परिभाषित है, पर (f(x)) में \(x-2\ne 0\) चाहिए। गुणन में भी साझा डोमेन लेते हैं। / (g(x)) is defined for all real (x), but (f(x)) needs \(x-2\ne 0\). For product also, take the common domain.
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If (f(x)=x-1) and (g(x)=x+1), what is the domain of (\left\(\frac{f}{g}\right\)(x))?
A. \(\mathbb{R}-{-1}\)
भाग में (g(x)\ne 0) चाहिए, इसलिए \(x+1\ne 0\) और \(x\ne -1\)। अंश शून्य हो सकता है। / In division, (g(x)\ne 0), so \(x+1\ne 0\) and \(x\ne -1\). The numerator may be zero.
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If (f(x)=2x-2-3) and (g(x)=x-2+5), what is ((f-g)(x))?
A. \(x^2-8\)
((f-g)(x)=2x-2-3-\(x^2+5\)=x-2-8)। पूरा (g(x)) घटाया जाता है। / ((f-g)(x)=2x-2-3-\(x^2+5\)=x-2-8). The whole (g(x)) is subtracted.
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If (f(x)=3) and (g(x)=x-2-2x), what is ((fg)(x))?
A. \(3x^2-6x\)
स्थिर फलन (3) पूरे (g(x)) से गुणा होगा। इसलिए ((fg)(x)=3\(x^2-2x\)=3x-2-6x)। / The constant function (3) multiplies the whole (g(x)). Thus ((fg)(x)=3\(x^2-2x\)=3x-2-6x).
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If (f(x)=|x|) and (g(x)=x), what is ((f+g)(-4))?
A. (0)
(f(-4)=|-4|=4) और (g(-4)=-4), इसलिए योग (0) है। मापांक हमेशा अऋणात्मक होता है। / (f(-4)=|-4|=4) and (g(-4)=-4), so the sum is (0). Modulus is always non-negative.
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If (f(x)=\frac{1}{x}) and (g(x)=x-2), simplify ((fg)(x)).
A. (x), \(x\ne 0\)
((fg)(x)=\frac{1}{x}\cdot x-2=x), पर मूल डोमेन में \(x\ne 0\) रहेगा। सरल करने से हटे प्रतिबंध वापस नहीं आते। / ((fg)(x)=\frac{1}{x}\cdot x-2=x), but the original domain keeps \(x\ne 0\). Restrictions do not disappear after simplification.
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If (f(x)=x-2+2x) and (g(x)=x-2-2x), what is ((f-g)(x))?
A. (4x)
समान \(x^2\) पद कट जाते हैं और (2x-(-2x)=4x)। ऋण चिह्न के कारण दूसरा पद बदलता है। / The \(x^2\) terms cancel and (2x-(-2x)=4x). The minus sign changes the second term.
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If (f(x)=2x+1) and (g(x)=x-2-1), what is ((f+g)(2))?
A. (8)
(f(2)=5) और (g(2)=3), इसलिए ((f+g)(2)=8)। मान निकालते समय (x) की जगह (2) रखें। / (f(2)=5) and (g(2)=3), so ((f+g)(2)=8). Substitute (2) for (x) carefully.
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