Cardinal Number

Q.

Find the cardinality of the given set:

$A=\left\{a,e,i,o,u\right\}$.

Q. Let $A_1,A_2,...,A_m$ be non-empty subsets of $\{1,2,3,...,100\}$ satisfying the following conditions:
(1) the numbers $|A_1|,|A_2|,...,|A_m|$ are distinct ;
(2) $A_1,A_2,...,A_m$ are pairwise disjoint.
(Here $|A|$ denotes the number of elements in the set $A$).
Then the maximum possible value of $m$ is

1. $13$
2. $14$
3. $15$
4. $16$

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.

In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The no. of newspaper is

1. At least 30

2. At most 20

3. Exactly 25

4. None of these

Q.

What are elements and cardinality?

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.

Write the cardinal number for the set $E=\left\{e,r,m\right\}$.

Q. If $A=\left\{\right(a,b):a^2+b^2=25\text{and}a,b\in N\}$ then $n\left(A\right)=$

1. $1$
2. $2$
3. $4$
4. $12$

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. The cardinal number of the set $A=\{1,2,2,3,4,5,5,6,6,7,7,8\}$ is .

1. $8$
2. $7$
3. $12$

Q. Let $A_1,A_2,...,A_m$ be non-empty subsets of $\{1,2,3,...,100\}$ satisfying the following conditions:
(1) the numbers $|A_1|,|A_2|,...,|A_m|$ are distinct ;
(2) $A_1,A_2,...,A_m$ are pairwise disjoint.
(Here $|A|$ denotes the number of elements in the set $A$).
Then the maximum possible value of $m$ is

1. $13$
2. $14$
3. $15$
4. $16$

Q. If $A=\{x,x\in Z\text{and}|x^2+5x-6|=6-5x-x^2\}$, then cardinality of set $A$ is

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 $A=\{x:x$ is a letter in the word 'QUARANTINE'$\}$, then the cardinality of $A$ is

1. $5$
2. $6$
3. $7$
4. $8$

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

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

Q.

State the cardinality of the given set:

A = the set of letters in the word ‘SATELLITE’.

Q. If $I$ is the set of all integers greater than $0,$ then $n\left(I\right)=$, and the set is

1. $\infty$
2. an infinite set
3. $10$
4. a finite set

Q. If $A=\{x:x$ is a letter in the word 'QUARANTINE'$\}$, then the cardinality of $A$ is