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Class 12MathematicsRelations and FunctionsFunctionsHard
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If (A) has (4) elements and (B) has (4) elements, how many functions from (A) to (B) are both one-one and onto?

Answer and explanation

Correct answer: (24)

Step 1: For finite sets of equal size, functions that are one-one and onto are permutations. Step 2: The number of permutations of (4) elements is (4!=24). Step 3: Use (n!) directly in such bijection counting questions.

Related tags

BijectionCounting FunctionsFinite SetsFunctionsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1If (f:A\to B) is a function, what condition is necessary for every element of (A)?
  2. 2If (f(x)=2x+3), what is the value of (f(4))?
  3. 3In a function (f:A\to B), what is (A) called?
  4. 4In a function (f:A\to B), what is (B) called?
  5. 5If (f={(1,2),(2,4),(3,6)}), what is the domain of (f)?
  6. 6If (f={(1,2),(2,4),(3,6)}), what is the range of (f)?
  7. 7Which of the following relations from (A={1,2}) to (B={3,4}) is a function?
  8. 8If (f(x)=x^2) and the domain is ({-2,-1,0,1,2}), what is the range?
  9. 9For the function (f:R\to R), (f(x)=x+5), what is (f(0))?
  10. 10If f(x) = 3x − 1, what is the value of f(2) + f(0)?
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