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 331-340 of 600 questions.
If \(f:A\to B\) and \(f=\{(a,1),(b,2),(c,1),(d,3)\}\), what is (A)?
A. \({a,b,c,d})
domain ordered pairs के first components का set है। यहां \(A=\{a,b,c,d\}\) है। / The domain is the set of first components of ordered pairs. Here \(A=\{a,b,c,d\}\).
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Which relation from \(A=\{1,2,3\}\) to \(B=\{1,2,3\}\) is neither a function nor an empty relation?
A. \(R=\{(1,1),(1,2),(2,3)\}\)
यह empty नहीं है, लेकिन (1) की दो images हैं और (3) की image missing है। hard MCQ में दोनों conditions अलग-अलग जांचें। / It is not empty, but (1) has two images and (3) has no image. In hard MCQs, check both conditions separately.
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A. (2)
(x=2) पर denominator (0) हो जाता है, इसलिए (f(2)) defined नहीं है। rational function में denominator zero न हो, यह जरूरी है। / At (x=2), the denominator becomes (0), so (f(2)) is not defined. In a rational function, the denominator must not be zero.
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If \(f:{1,2,3}\to{1,2,3,4,5}\) by (f(x)=x-2), is (f) a valid function?
A. नहीं, क्योंकि \(f(3)=9\notin{1,2,3,4,5}\)No, because \(f(3)=9\notin{1,2,3,4,5}\)
output unique तो है, लेकिन (f(3)=9) codomain में नहीं है। function के लिए image codomain के अंदर भी होनी चाहिए। / The output is unique, but (f(3)=9) is not in the codomain. For a function, every image must also lie in the codomain.
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If \(f:{0,1,2}\to{0,1,2,3,4}\) by (f(x)=x-2), what is the graph of (f) as ordered pairs?
A. \({(0,0),(1,1),(2,4)})
\(0^2=0\), \(1^2=1\), और \(2^2=4\)। function का graph finite case में ordered pairs का set है। / \(0^2=0\), \(1^2=1\), and \(2^2=4\). In a finite case, the graph of a function is the set of ordered pairs.
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A student called \(R=\{(1,a),(2,b),(2,c),(3,d)\}\) a function. What is the mistake?
A. (2) की दो different images (b) और (c) हैं(2) has two different images (b) and (c)
एक input (2) दो outputs से जुड़ा है, इसलिए यह function नहीं है। function check में repeated first coordinate पर सबसे पहले ध्यान दें। / One input (2) is related to two outputs, so it is not a function. In function checks, first notice repeated first coordinates.
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A. \({2,4})
(f(x)=0) even inputs (2) और (4) पर मिलता है। preimage हमेशा domain के elements का set होता है। / (f(x)=0) occurs for even inputs (2) and (4). A preimage is always a set of domain elements.
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A. identity में \(x\mapsto x\), constant में हर \(x\mapsto 1\)In identity, \(x\mapsto x\); in constant, every \(x\mapsto 1\)
identity input को उसी पर map करती है, जबकि constant function हर input को same value पर भेजता है। दोनों valid functions हो सकते हैं। / Identity maps each input to itself, while a constant function sends every input to the same value. Both can be valid functions.
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If \(R=\{(x,y):y=|x-2|,\ x\in{0,1,2,3,4}\}\), what is the range of (R)?
A. \({0,1,2})
outputs (2,1,0,1,2) हैं, इसलिए distinct range ({0,1,2}) है। set में order और repetition important नहीं होते। / The outputs are (2,1,0,1,2), so the distinct range is ({0,1,2}). In a set, order and repetition are not important.
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If \(f=\{(1,4),(2,8),(3,12)\}\), what is the simplest rule for (f(x))?
A. (f(x)=4x)
हर pair में second coordinate first coordinate का (4) times है। rule पहचानने के लिए सभी given values पर verify करें। / In every pair, the second coordinate is (4) times the first coordinate. To identify a rule, verify it on all given values.
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