Cardinal Number

Q. The number of elements in a set is called

1. total number
2. number set
3. roster notation
4. cardinal number

Q.

In boolean algebra, the unit element $1$

1. has two values

2. is unique

3. has atleast two values

4. None of these

Q. Fill in the blanks:

(iii) The empty set is a _______ of every set.

Q. In a college of $300$ students, every student reads $5$ newspapers. If every newspaper is read by $60$ students, then the number of newspaper is

1. at least $30$
2. at most $20$
3. exactly $25$
4. exactly $50$

Q. Let $\bigcup _{i=1}^{50}{X}_i=\bigcup _{i=1}^n{Y}_i=T,$ where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s, then $n$ is equal to

1. $15$
2. $30$
3. $50$
4. $45$

Q.

What is the rule that gives the number of matchsticks required in terms of number of ?

Q. The cardinal number of a set $A=\{2,3,6,7\}$ is $4.$

1. False
2. True

Q. Fill in the blanks:

(ii) Every set is a_______ of itself.

Q. If $A=\{x:x$ is a letter of the word 'RAMANA'$\}$,
$B=\{x:x$ is a letter of the word 'MISSISSIPPI'$\}$,
$C=\{x:x$ is a letter of the word 'NOOKBOOK'$\}$,
Then relation between cardinality of sets $A,B$ and $C$ is

1. $n\left(A\right)=n\left(B\right)=n\left(C\right)$
2. $n\left(A\right)=2,n\left(B\right)=n\left(C\right)$
3. $n\left(A\right)+n\left(C\right)=n\left(B\right)$
4. $n\left(B\right)>n\left(A\right)>n\left(C\right)$

Q. Find the cardinal number of the following sets:
$A_2=\{x:x\in Nand3\le x<7\}$

Q. The number of elements in the set
$S=\left\{\right(a,b):2a^2+3b^2=35;a,b\in Z\},$ where $Z$ is the set of all integers, is

Q. If the set A is defined as A = {x : x is a factor of 42 and is a prime number}. Then the number of elements in set A is

1. 4
2. 3
3. 6
4. 5

Q. If $A=\{x,x\in R\text{and}{x}^2-4x+1=0\}$, then $n\left(A\right)=$

Q. Suppose $A_1,A_2,....,A_{30}$ are thirty sets, each having 5 elements and $B_1,B_2,.....,B_n$ are n sets, each with 3 elements.
Let ${\bigcup }_{i=1}^{30}{A}_i={\bigcup }_{i=1}^n{B}_j=S$. Each element of S belongs to exactly 10 of the $A_{i}s$ and exactly 9 of the $B_{i}s$. Then n is equal to

1. 15
2. 3
3. 45
4. 50

Q. If a set $Y$ is a singleton set, then $n\left(Y\right)=$

1. $0$
2. $1$
3. $\infty$

Q. Let $a,b\in N$ with $2\le a\le 2020$ and $2\le b\le 2020$.
$P,Q,R$ are three sets defined as
$P=\left\{\right(a,b):{\log }_{a}b+6{\log }_{b}a=5\}$
$Q=\left\{\right(a,b):b=a^2\}$
$R=\left\{\right(a,b):b=a^3\}.$
Then which of the following is (are) correct?

1. $n\left(P\right)=54$
2. $n(P\cap Q)=44$
3. $n(P\cap R)=11$
4. $n(P\cup Q\cup R)=54$

Q. Out of $60$ students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, $16$ do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. Then the range of cardinal number of students who could have done only chemistry is

1. $[0,40]$
2. $[0,44]$
3. $[2,28]$
4. $[2,38]$

Q. The Set $K=\{k:0\le k\le 1,k\in R\},$ where $R$ is the set of all real numbers is

1. an infinite set
2. a finite set
3. a singleton set

Q. If $A=\{x,x\in N\text{and}16-x^2\ge 0\}$, then cardinality of set $A$ is

Q. In a survey it was found that, the number of people who like only What’s app, only Facebook, both What’s app and Facebook and neither of them are $2n,3n,\frac{69}{n},\frac{69}{3n}$
respectively. What is the number of people who like facebook?

1. $49$
2. $36$
3. $72$
4. $23$

Q. For a set $A$, if $n\left(A\right)=\infty$, then the $A$ is a finite set.

1. False
2. True

Q. The Set $K=\{k:0\le k\le 1,k\in R\},$ where $R$ is the set of all real numbers is

1. an infinite set
2. a finite set
3. a singleton set

Q. Two sets $A\&B$ such that $A=\varphi$ and $B=\left\{A\right\}$, then $n\left(B\right)=$

1. $0$
2. $1$
3. $2$

Q. Two sets $A\&B$ such that $A=\varphi$ and $B=\left\{A\right\}$, then $n\left(B\right)=$

1. $0$
2. $1$
3. $2$