SETS, RELATIONS AND FUNCTIONS
Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.
Top questions
See all →- Let Z be the set of integers. If A = {x ∈ Z : 2(x +2)(x^2 - 5x + 6) = 1} and B {x ∈ Z : -3 < 2x - 1 < 9}, Option 2) 215 is correct 2
- Let S = {1, 2, 3, ... , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is : The correct option (2) 2⁵⁰(2⁵⁰ – 1) Explanation: Product of elements in A is even = (total subjects) – (Number of subject of all whose eleme... 1
- Let X = {n ∈ N : 1 ≤ n ≤ 50}. If A = {n ∈ X : n is multiple of 2} and B = {n ∈ X : n is a multiple of 7}, n(A) = 25 n(B) = 7 n(A ∩ B) = 3 n(A ∪ B) = 25 + 7 - 3 = 29 2
- Let Ui = 1 Xi for i ∈ 50 = Ui = 1 for i ∈ n Yi = T, where each Xi contains 10 elements and each Yi contains 5 elements. Correct answer is 30 EXplaination: n(X_i) = 10. U_(i = 1 )X_i for i ∈ 50 = T, n (T) = 500 each element of T belongs to exactly 20 elements o... 1
- A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. Answer is 36 Note**then x cannot be: C > person like coffee T > Person like Tea n(C)=73 n(T) =65 n(C U T) ≤ 100 n(C)+n(T) -n(C ∩ T) ≤ 100 73... 1
- Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets Correct answer is 28 Explaination: No. of subsets of A=2m No. of subsets of B=2n 2^m=2ⁿ+112 2^m−2ⁿ=112 2ⁿ(2^(m−n)−1)=112 2ⁿ(2^(m−n)−1)=2⁴(2³... 1