Cardinality of Sets

Q.

What is the cardinality of set?

Q.

If $A,B,C$ be three sets such that $A\cup B=A\cup C$ and $A\cap B=A\cap C$, then

1. $A=B$

2. $B=C$

3. $A=C$

4. $A=B=C$

Q. Write a pair of integers whose product is -12 and which has seven integers between them

Q.

If A and B are disjoint sets, then the value of $n(A\cap B)$ = ____.

1. 2

2. 0

3. 1

4. 3

Q. Choose the pair of integer whose sum is -3

1. -2, -2
2. -2, -1
3. -5, 3
4. 4, -1

Q.

Let $x=\{n\in N:1\le n\le 50\}$. If $A=\{n\in x:n$ is a multiple of $2$} and $B=\{n\in x:n$ is a multiple of $7$}, then the number of elements in the smallest subset of ‘$x$’ containing both A & B is

Q. on the first day of the month of september , jeevan noticed just one lotus flower in the pond near his house . the next day he noticed that the pond had two flowers . on the third day he noticed four flowers . on the fourth day he noticed that the pond had eight flowers . and this pattern continued everyday . on the 10th of september , his pond was half full . on what date will the pond be full of lotus flowers ? express the number of flowers in exponential form when it is full.

Q. If A : B = 3 : 5 and B : C = 4 : 7 , find A: B : C

Q.

Sets having the same cardinal number and same elements are called _________ sets.

1. equal

2. null

3. disjoint

4. universal

Q.

Cardinal number of the set A = { x: x is even prime number} is ____.

1. 2

2. Infinite

3. 0 (Zero)

4. 1

Q.

Question 118 (ii)

Language Application
Given below are few mathematical terms.
Find
The percentage of consonants in each of the terms.

Q.

If A = {set of integers between -2 and 4}, then n(A) = ___.

1. 5

2. 4

3. 7

4. 6

Q. If $A\cup B=\{1,2,3,5,6,7,9\},B=\{2,5,7,9\},A\cap B=\{2,5\}$, then represent $A,B$ in Venn-diagrams and verify the relation $n(A\cup B)+n(A\cap B)=n\left(A\right)+n\left(B\right)$.

Q.

Find the number whose $25\%$ is $36$.

Q.

Find the number whose $35\%$ is $42$.

Q.

If $a=p^l.q^m.r^n$ and $b=p^x.q^y.r^z$ where p, q, r are primes and p<q<r and l, m, n, x, y, z are all natural numbers. Given HCF = $p^2$.$q^3$.r and LCM = $p^3$.$q^4$.$r^3$, which one of the following is NOT true?

1. l + x = 5

2. m + y = 7

3. n + z = 4

4. l + m + n = x + y + z

Q. lies between 7 and 8.

1. $\frac{12}{5}$
2. $\frac{12}{8}$
3. $\frac{32}{5}$
4. $\frac{30}{4}$

Q.

The cardinal number of the set A = {Present Prime minister of India} is

1. n (A) = 2

2. n (A) = 0

3. n (A) = 1

4. n (A) = 3

Q.

The set A = {0}. Then n(A)___.

Q. A survey show that $73$% of the indians like apples, where as $65$% like oranges. What percentage of indian like both apples and oranges?

Q.

Aju scored 70 in 1st test and 85 in 2nd test of Mathmatics out of 100. What is percentage increase in marks scored by him?
[3 MARKS]

Q.

Find the number whose $68\%$ is $34$.

Q.

Answer the following from the adjoining venn diagram$.$

Are $A$ and $B$ disjoint sets$.$

Q. Consider the set of all determinants of order $3$ with entries $0$ or $1$ only, Let $B$ be the subset of $A$ consisting of all determinants with value $1$. Let $C$ be the subset of the set of all determinants with value $-1$. Then

1. $C$ is empty
2. $B$ has as many elements as $C$
3. $B$ has twice as many elements as $C$.
4. $A=B\cup C$

Q. Let U be the universal set containing 700 elements . if A, B are sub-sets of U such that n (A) =200, n (B) = 300 and n $(A\cap B)=100,n(A\cup B)=$

1. 400
2. 600
3. 300
4. none of these

Q.

Cardinal number of the set A = { x: x is neither prime nor composite number} is ____.

1. Infinite

2. 0 (Zero)

3. 1

4. 2

Q.

For any two sets $A$ and $B$ if $A\cap X=B\cap X=\varphi$ and $A\cup X=B\cup X$ for some set $X$, then

1. $A–B=A\cap B$

2. $A=B$

3. $B–A=A\cap B$

4. None of these

Q. Let $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$. Then, $n(A^c\cap B^c)=$

1. $600$
2. $300$
3. $200$
4. $400$

Q.

If A = {5, 6, 7, 8} B = {7, 8, 9, 11}, A $\cup$ B =

1. {5, 6, 7, 8, 9, 10, 11}

2. {5, 6, 7, 8, 9, 11}

3. {9, 11}

4. {5, 6, 7, 8}

Q.

How many numbers (integers) are found in between the numbers -8 and 3?

1. 8

2. 7

3. 10

4. 9