Sample QuestionsPART - 1 CH - 1 Sets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Out of 300 students of a college, each student reads five newspapers and each newspaper is read by 60 students, then the number of newspapers will be :
Answer: A.
View full solution →If $A , B$ are two sets, then $( A \cup B )^{\prime}$ is equal to :
Answer: C.
View full solution →Which of the following is a infinite set?
- ✓
$\{x: x \in N$ and $x \geq 10\}$
- B
$\{x: x \in N$ and $x<10\}$
- C
$\{x: x \in N$ and $10 \leq x \leq 100\}$
- D
$\{x: x \in N$ and $x<1000\}$
Answer: A.
View full solution →If $U =\{1,2,3,4,5,6\}$ and $A =\{1,2,3,4,5,6\}$, then $A ^{\prime}$ is equal to :
- A
$\{0\}$
- B
$\{1,2,3\}$
- ✓
$\phi$
- D
$\{4,5,6\}$
Answer: C.
View full solution →Which of the following is a finite set :
- A
$\{x: x \in N\}$
- B
$\{x: x>10 x \in N\}$
- ✓
$\{x: x<10, x \in N\}$
- D
$\{x: x=2 n, n \in N\}$
Answer: C.
View full solution →For disjoint sets, $A \cap B =\phi$
View full solution →If $A =\{1,2,3\}$ and $B =\{3\}, A - B =\{1,2\}$
View full solution →The set of real numbers is represented by $R$.
View full solution →If $[a, b]=a \leq x \leq b, x \in R$
View full solution →If $A$ and $B$ are two sets, then $\left(A \cup B^{\prime}\right)^{\prime} \cap\left(A^{\prime} \cup B\right)^{\prime}=\{\phi\}$
View full solution →Write true/false for the following sets?
(i) $\phi \in \phi$
(ii) $0 \in \phi$
(iii) $\phi=\{0\}$
View full solution →Write the distributive law for any three sets A, B and C.
Write the association law for any three sets A, B and C.
Write the following set in the set-builder form:
$B=\{1,5,10,15, \ldots .\}$
View full solution →Write the following set in the set-builder form :
$A=\left\{1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \ldots \ldots\right\}$
View full solution →Prove that the sets $A$ and $B , A - B = B ^{\prime}- A ^{\prime}$ as true.
View full solution →Prove $\left( A ^{\prime}\right)^{\prime}= A$ for an empty set $A$.
View full solution →If $A =\{1,2,3\}, B =\{2,3,4\}$ and $C =\{3,4,5,6\}$ then find $(A \cap B)-C$.
View full solution →If $A =\{x: x=2 n, n$ is a positive integer $\}$ and B $=\{x: x=3 n, n$ is a positive integer $\}$, then find the value of $A \cap B$.
View full solution →If $A =\{1,2,6,9\}, B=\{2,4,6,8\}$ and $C=\{3,4,9\}$ then prove that $A \cup(B \cap C)=(A$ $\cup$ B) $\cap(A \cup C)$.
View full solution →Write the following set of real numbers in a set - builder form :
(a) $\left\{x: x^2-9 x+20=0\right\}$
(b) $\left\{x: x^3+1=0\right\}$
(c) $\left\{x: x^2-2=10\right\}$
(d) $\{x: x$ is a prime number, $x \leq 11\}$
View full solution →Which of the following collections does not represent a set :
(a) $A =\{x: x$ is a tall student of class XI $\}$
(b) $B=\{x: x$ is a student of class XII whose height is more than 5 feets?
(c) $C =\{x: x$ is a good player of cricket $\}$
(d) $D =\{x: x$ is a player of cricket, who made more than five thousand runs in test cricket$\}$
View full solution →Every set is subset of _________.
$A \subset B$ and $A \neq B$, then A is called _________ of B.
View full solution →If there is only one element in the set A, then A is called _______ set.
If every element of A is also an element of set B, then A is called the _________ of B.
A set which does not have even single element is called a _________ set.
If $A =\{p, q, r, s\}, B =\{q, s, u\}$ and $C =\{r, s, t, u\}$, then prove the following :
(i) $(A-B) \cup(A-C)=A-(B \cap C)$
(ii) $A \cap(B \cup C)=(A \cap B) \cup(A \cap C)$
(iii) $A \cup(B \cap C)=(A \cup B) \cap(A \cup C)$
View full solution →