Sets, Relations and Functions

Free Math Problems, Questions, Answers, Shortcuts listed topicwise

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions; one-one, into and onto functions, composition of functions.

List of Sample Problems

1. Question 1: What is the domain of definition for the function ?
   1. (-3, 0) U (1, 3)
   2. (-1, 0) U (1, 3)
   3. (-1, 3)
   4. (-3, -1) U (0, 3)
   Answers & Solution »
   
   
2. Question 2: What is the range of the function ?
   1. [1, 3/2)
   2. (1, 3/2]
   3. [1, 3/2]
   4. [0, 3]
   Answers & Solution »
   
   
3. Question 3: f(x) is defined as , x belongs to the set of natural numbers. For what value of x will f(x) be maximum?
   1. 2
   2. 3
   3. 7
   4. f(x) is a non-decreasing function. It has no definable maximum.
   Answers & Solution »
   
   
4. Question 4: f(x) = x - [x], where [x] is the largest integer lesser than or equal to x, g(x) = x + abs(x), then
   
   
   1. The union of the range of f(x) and g(x) is (0,1)
   2. Neither f(x) nor g(x) can be negative for any x
   3. g(x) + g(-x) = 2x
      
      
   1. All three are true
   2. b and c are true
   3. Only b is true
   4. Only c is true
   Answers & Solution »
   
   
5. Question 5: What is the domain of the function f(x)= ?
   
   1. (3, 5)
   2. [2, 3] U [4, 5]
   3. [3, 4)
   4. (3, 4)
   Answers & Solution »
   
   

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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise

Sets, Relations & Functions		Permutation Combination		Sequences & Series
Limits, Continuity & Differentiability		Statistics & Probability		Trigonometry
Mathematical Reasoning