### Sets and Relations JEE Mains:

## Sets Relations and Functions JEE Mains Questions

Question 1 |

Let

*R*be an equivalence relation on a finite set*A*having*n*elements. Then the number of ordered pairs in*R*isLess than or equal to n | |

Greater than or equal to n | |

Less than n | |

None of these |

Question 2 |

The relation

*R*= {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set*A*= {1, 2, 3} isNeither symmetric nor transitive | |

Reflexive but not transitive | |

Reflexive but not symmetric | |

Symmetric and Transitive |

Question 3 |

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is

Reflexive only | |

Reflexive and transitive only | |

An equivalence relation | |

Reflexive and symmetric only |

Question 4 |

Let

*S*be the set of all real numbers. Then the relation*R*= {(*a*,*b*) : 1 +*ab*> 0} on*S*is**Related:** Trigonometry Ratios Sample Paper

Symmetric, transitive but not reflexive | |

Reflexive and symmetric but not transitive | |

Reflexive and transitive but not symmetric | |

Reflexive, transitive and symmetric |

Question 5 |

Let

*R*= {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set*A*= {1, 2, 3, 4}. The relation*R*isA function | |

Transitive | |

Not symmetric | |

Reflexive |

Question 6 |

Let

*A*and*B*be two non-empty subsets of a set*X*such that*A*is not a subset of*B*, thenA and B are always disjoint | |

B is always a subset of A | |

A and the complement of B are always non-disjoint | |

A is always a subset of the complement of B |

Question 7 |

In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is

22 | |

45 | |

10 | |

33 |

Question 8 |

If A = {1, 2, 3, 4, 5}, then the number of proper subsets of

*A*is30 | |

120 | |

32 | |

31 |

Question 9 |

The relation “less than” in the set of natural numbers is

**Related:** JEE Mains Mathematics Practice Paper

Only reflexive | |

Only transitive | |

Equivalence relation | |

Only symmetric |

Question 10 |

The relation "is subset of" on the power set

*P*(*A*) of a set*A*isAnti-symmetric | |

Symmetric | |

Equivalency relation | |

None of these |

Question 11 |

The relation

*R*defined on the set of natural numbers as {(*a*,*b*) :*a*differs from*b*by 3}, is given by{(4, 1), (5, 2), (6, 3),.....} | |

{(1, 3), (2, 6), (3, 9),..} | |

{(1, 4, (2, 5), (3, 6),.....} | |

None of these |

Question 12 |

Two finite sets have

*m*and*n*elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of*m*and*n*are**Related:** UPSEE Mathematics Sample Paper

7, 6 | |

5, 1 | |

8, 7 | |

6, 3 |

Question 13 |

The number of non-empty subsets of the set {1, 2, 3, 4} is

15 | |

17 | |

14 | |

16 |

Question 14 |

Let

*A*and*B*be two non-empty subsets of a set*X*such that*A*is not a subset of*B*, thenB is always a subset of A | |

A is always a subset of the complement of B | |

A and the complement of B are always non-disjoint | |

A and B are always disjoint |

Question 15 |

Let

*L*be the set of all straight lines in the Euclidean plane. Two lines l_{1}and l_{2}are said to be related by the relation*R*i is parallel to l_{2}. Then the relation*R*isReflexive and Symmetric | |

Reflexive | |

Transitive and Equivalence | |

all |

Question 16 |

Two finite sets have

*m*and*n*elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of*m*and*n*are8, 7 | |

5, 1 | |

7, 6 | |

6, 3 |

Question 17 |

Let

*A*= {*a, b, c*} and*B*= {1, 2}. Consider a relation*R*defined from set*A*to set*B*. Then*R*is equal to setB | |

A x B | |

B x A | |

A |

Question 18 |

x

^{2}= xy is a relation which isNone of these | |

Reflexive | |

Symmetric | |

Transitive |

Question 19 |

Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is

128 | |

240 | |

216 | |

160 |

Question 20 |

The number of proper subsets of the set {1, 2, 3} is

6 | |

5 | |

7 | |

8 |

Question 21 |

Given the relation

*R*= {(1, 2), (2, 3)} on the set*A*= {1, 2, 3}, the minimum number of ordered pairs which when added to*R*make it an equivalence relation is6 | |

8 | |

7 | |

5 |

Question 22 |

In a certain town 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:

- 10% families own both a car and a phone
- 35% families own either a car or a phone
- 40,000 families live in the town

1 and 3 | |

1, 2 and 3 | |

1 and 2 | |

2 and 3 |

There are 22 questions to complete.

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