1.Let A denotes the set of quadrilaterals having two diagonals equal and bisecting each other. Let B denotes the set of quadrilaterals having diagonals bisecting each other at 90. Then, A ∩ B denotes
(a) the set of parallelograms
(b) the set of rhombuses
(c) the set of squares
(d) the set of rectangles
Ans: c
A= diagonal equal and bisecting each other.
A is square or rectangle. And B diagonal bisecting each other at 90°.
So, A ∪ B = the set of square
2. Out of 105 students taking an examination English and Mathematics, 80 students pass in English, 75 students fail students in both the subjects. How many students pass in only one subject?
(a) 26
(b) 30
(c) 35
(d) 45
Ans: d
Number of students failing in Mathematics= 105-75=30
Number of students tailing in English= 105-80=25
Number of students failing in 1 subject= (25+30) – 10= 45
3.If A and B are any two non-empty subsets of a set E, then what is A ∪ (A ∩ B) equal to?
(a) A ∩ B
(b) A ∪ B
(c) A
(d) B
Ans: C
Since, A and B are non-empty subsets of E.
∴A∪(A ∩ B) = A ∪( Shaded portion)= A
4. If A is a non- empty subset of a set E, then what is E∪(A ∩ Ø) – (A – Ø) equal to? E ∪(A∩Ø) equal to?
(a) A
(b) Complement of A
(c) Ø
(d) E
Ans: c
E ∪[(A ∩Ø) – ( A -Ø)]⇒E ∪[ Ø- A ] [Because (A ∩ Ø ) = fand (A – Ø)= A]
Here, A cannot be subtracted from f
5. Consider the following statements
Set of points of a given line is a finite set.
Intelligent students in a class is a set.
Good books in a school library is a set.
Which of the above statement(s) is/are not correct?
(a) Only I
(b) Both ll and III
(c) Both I and II
(d) I, II and III
Ans: d
The set of points of a given line is not a finite set
Here, we cannot decide, which students are intelligent
Here, we cannot decide, which books are good a school library
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