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 241-250 of 600 questions.
If (f(x)=2x+1) and (g(x)=x-2), what is ((3f+2g)(x))?
A. (8x-1)
((3f+2g)(x)=3(2x+1)+2(x-2)=8x-1)। गुणांक को पूरे फलन से गुणा करें। / ((3f+2g)(x)=3(2x+1)+2(x-2)=8x-1). Multiply the coefficient by the whole function.
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If (f(x)=x-2+6x+9) and (g(x)=x+3), what is (\left\(\frac{f}{g}\right\)(0)) for \(x \neq -3\)?
A. (3)
(\frac{x-2+6x+9}{x+3}=\frac{(x+3)2}{x+3}=x+3), अतः (x=0) पर मान (3) है। पूर्ण वर्ग पहचान उपयोगी है। / (\frac{x-2+6x+9}{x+3}=\frac{(x+3)2}{x+3}=x+3), hence the value at (x=0) is (3). The perfect square identity is useful.
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If (f(x)=\frac{1}{\sqrt{x-1}}) and (g(x)=x), what is the domain of ((f+g)(x))?
A. (x>1)
हर में \(\sqrt{x-1}\) है, इसलिए (x-1>0) होना चाहिए। अतः प्रांत (x>1) है। / The denominator has \(\sqrt{x-1}\), so (x-1>0) is required. Hence the domain is (x>1).
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If (f(x)=x-2+1) and (g(x)=x-2-1), what is ((f-g)(5))?
A. (2)
((f-g)(x)=\(x^2+1\)-\(x^2-1\)=2), इसलिए किसी भी (x) पर मान (2) है। पहले सरल करने से गणना कम होती है। / ((f-g)(x)=\(x^2+1\)-\(x^2-1\)=2), so at any (x) the value is (2). Simplifying first reduces calculation.
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If (f(x)=2x) and (g(x)=\frac{1}{2}x), what is ((fg)(x))?
A. \(x^2\)
((fg)(x)=2x\cdot \frac{1}{2}x=x-2)। संख्यात्मक गुणांकों को पहले गुणा करें। / ((fg)(x)=2x\cdot \frac{1}{2}x=x-2). Multiply numerical coefficients first.
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If (f(x)=x-2+x+1) and (g(x)=x-2-x+1), what is ((f-g)(x))?
A. (2x)
((f-g)(x)=x-2+x+1-\(x^2-x+1\)=2x)। कोष्ठक खोलकर चिह्न सावधानी से बदलें। / ((f-g)(x)=x-2+x+1-\(x^2-x+1\)=2x). Open brackets and change signs carefully.
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If (f(x)=\frac{x+2}{x-3}) and (g(x)=x-3), what is ((fg)(4))?
A. (6)
((fg)(x)=\frac{x+2}{x-3}(x-3)=x+2), जहाँ \(x \neq 3\)। (x=4) पर मान (6) है। / ((fg)(x)=\frac{x+2}{x-3}(x-3)=x+2), where \(x \neq 3\). At (x=4), the value is (6).
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If (f(x)=\sqrt{x}) and (g(x)=\sqrt{x}), what are ((fg)(x)) and its domain?
A. \(x, x \geq 0\)
((fg)(x)=\sqrt{x}\cdot\sqrt{x}=x), लेकिन दोनों वर्गमूलों के लिए \(x \geq 0\)। सरल रूप से प्रांत नहीं बदलता। / ((fg)(x)=\sqrt{x}\cdot\sqrt{x}=x), but both square roots require \(x \geq 0\). The simplified form does not change the original domain.
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If (f(x)=x-2-3x+2) and (g(x)=x-1), what is (\left\(\frac{f}{g}\right\)(3)) for \(x \neq 1\)?
A. (1)
(\frac{x-2-3x+2}{x-1}=\frac{(x-1)(x-2)}{x-1}=x-2), अतः (x=3) पर मान (1) है। गुणनखंडन से भाग सरल होता है। / (\frac{x-2-3x+2}{x-1}=\frac{(x-1)(x-2)}{x-1}=x-2), so at (x=3) the value is (1). Factorisation makes division simple.
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If (f(x)=x+4) and (g(x)=4-x), what is ((fg)(x)) equal to?
A. \(16-x^2\)
((fg)(x)=(x+4)(4-x)=16-x-2)। इसे ((4+x)(4-x)) के रूप में देखें। / ((fg)(x)=(x+4)(4-x)=16-x-2). View it as ((4+x)(4-x)).
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