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)=\sqrt{x-3}), what is (x) when (f(x)=5)?
A. (28)
\(\sqrt{x-3}=5\) से (x-3=25), इसलिए (x=28)। परीक्षा में वर्ग करने के बाद original equation में जांच लें। / \(\sqrt{x-3}=5\) gives (x-3=25), so (x=28). In exams check the answer in the original equation after squaring.
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If (f(x)=|x+6|), what values can (x) have when (f(x)=9)?
A. (x=3) या (x=-15)(x=3) or (x=-15)
(|x+6|=9) से (x+6=9) या (x+6=-9) मिलता है। परीक्षा में modulus equation की दोनों शाखाएं लें। / (|x+6|=9) gives (x+6=9) or (x+6=-9). In exams take both branches of a modulus equation.
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If (f(x)=x-2+3x-2), what is (f(-2))?
A. (-4)
(f(-2)=(-2)2+3(-2)-2=-4) है। परीक्षा में ऋणात्मक input डालते समय brackets लगाएं। / (f(-2)=(-2)2+3(-2)-2=-4). In exams use brackets while substituting a negative input.
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If (f(x)=\frac{x-3}{x+2}), what is (f(1))?
A. \(-\frac{2}{3}\)
(f(1)=\frac{1-3}{1+2}=-\frac{2}{3}) है। परीक्षा में numerator और denominator अलग-अलग सावधानी से रखें। / (f(1)=\frac{1-3}{1+2}=-\frac{2}{3}). In exams handle the numerator and denominator separately with care.
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If (f(x)=\sqrt{x-2-16}), what is (f(-5))?
A. (3)
(f(-5)=\sqrt{25-16}=\sqrt{9}=3) है। परीक्षा में वर्गमूल की principal value non-negative होती है। / (f(-5)=\sqrt{25-16}=\sqrt{9}=3). In exams the principal value of square root is non-negative.
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If (f(x)=x-2-12) and the real domain is \(\mathbb{R}\), what is the range?
A. \([-12,\infty\))
क्योंकि \(x^2\ge0\), इसलिए \(x^2-12\ge-12\)। परीक्षा में square function की minimum value (0) याद रखें। / Since \(x^2\ge0\), \(x^2-12\ge-12\). In exams remember the minimum value of the square function is (0).
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If \(f:\mathbb{R}\to\mathbb{R}\) and (f(x)=x-2+7), which statement is correct?
A. रेंज \([7,\infty\)) है और codomain \(\mathbb{R}\) हैRange is \([7,\infty\)) and codomain is \(\mathbb{R}\)
दिए गए notation में दूसरा समुच्चय codomain \(\mathbb{R}\) है, जबकि वास्तविक outputs \([7,\infty\)) हैं। परीक्षा में range और codomain अलग रखें। / In the given notation, the second set is the codomain \(\mathbb{R}\), while actual outputs are \([7,\infty\)). In exams keep range and codomain separate.
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If \(A=\{-3,-1,2\}\), \(f:A\to\mathbb{R}\), and (f(x)=x-2-1), what is the range?
A. ({0,3,8})
(f(-3)=8), (f(-1)=0), और (f(2)=3) हैं। परीक्षा में set में repeated output हो तो एक बार ही लिखें। / (f(-3)=8), (f(-1)=0), and (f(2)=3). In exams write a repeated output only once in a set.
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If \(A=\{2,5,10,17\}\) and \(f:A\to\mathbb{R}\), (f(x)=\sqrt{x-1}), what is the range?
A. ({1,2,3,4})
दिए गए inputs पर (f(2)=1), (f(5)=2), (f(10)=3), और (f(17)=4) हैं। परीक्षा में finite domain में केवल दिए गए inputs लें। / For the given inputs, (f(2)=1), (f(5)=2), (f(10)=3), and (f(17)=4). In exams use only the given inputs in a finite domain.
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What is the domain of (f(x)=\sqrt{\frac{x+3}{x-1}})?
A. ((-\infty,-3]\cup\(1,\infty\))
वर्गमूल के अंदर \(\frac{x+3}{x-1}\ge0\) और \(x\ne1\) चाहिए। संकेत तालिका से ((-\infty,-3]\cup\(1,\infty\)) मिलता है। / The expression inside the square root must satisfy \(\frac{x+3}{x-1}\ge0\) and \(x\ne1\). A sign table gives ((-\infty,-3]\cup\(1,\infty\)).
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