Mathematics - Set Theroy , Relations & Mappings

Question - 1

In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers, is 

  • A at least 30
  • B almost 20
  • C exactly 25
  • D None of these

Question - 2

Of the member of three athletic teams in a certain school, 21 are on the basketball team, 26 on the hockey team and 29 on the football team.14 play hockey and basket ball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. Then the total number of members in the team is

  • A 35
  • B 43
  • C 60
  • D 72

Question - 3

Let \(A=\left\{ \theta :2\quad { cos }^{ 2 }\theta +sin\theta \le 2 \right\} \) and B=\(\left\{ \theta :\frac { \pi }{ 2 } \le \theta \le \frac { 3\pi }{ 2 } \right\} \) then \(A\cap B\),equals

  • A \(\left\{ \theta :\frac { 5\pi }{ 6 } \le \theta \le \frac { 3\pi }{ 2 } \right\} \)
  • B \(\left\{ \theta :\frac { \pi }{ 2 } \le \theta \le \frac { 5\pi }{ 6 } \right\} \)
  • C \(\left\{ \theta :\frac { \pi }{ 2 } \le \theta \le \frac { 5\pi }{ 6 } or\pi \le \theta \le \frac { 3\pi }{ 2 } \right\} \)
  • D \(\left\{ \theta :\pi \le \theta \le \frac { 3\pi }{ 2 } \right\} \)

Question - 4

If A and B are two sets, then \(A\cap (A\cup B)'\quad\)equals, where' stands for the complement of a set,

  • A A
  • B B
  • C \(A'\cap B\)
  • D \(\varphi \)

Question - 5

If X and Y are two sets, then \((X\sim Y)\cup (Y\sim X)\)equals 

  • A \(X\cup Y\)
  • B \(X\cap Y\)
  • C \((X\cup Y)\sim (X\cap Y)\)
  • D none of these

Question - 6

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

  • A 8
  • B 7
  • C 6
  • D 5

Question - 7

The set having only one subset is

  • A {}
  • B {)}
  • C {!}
  • D none of these

Question - 8

For any two sets A and B, the set \((A\sim B)\cup (B\sim A)\cup (A\cap )\)

  • A \(A\cap B\)
  • B \(A\cup B\)
  • C \(A\sim B\)
  • D \(B\sim A\)

Question - 9

The set \(A=(x:x\in R,{ x }^{ 2 }=16\quad and\quad 2x=6)\)equals

  • A {-4,3,4}
  • B {4}
  • C {3}
  • D \(\varphi \)

Question - 10

Given A={2,B,3} where B={4,5} which of the following statements is true?

  • A \(4\in A\)
  • B \(5\in A\)
  • C \(\{ 4,5\} \in A\)
  • D \( 4,5\ \in A\)
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