Intersection of Sets

Q.

In an election between 2 candidates A and B, A got 65%of total votes cast and won the election by 2748 votes more than B , find the total of votes cast if no vote is declared invalid.????

Q.

A football team won $10$ matches out of the total number of matches they played. If their win percentage was $40$, then how many matches did they play in all?

Q.

If $A$ and $B$ are two sets, then $(AUB)U(A\cap B)$ is equal to

1. $A$

2. $A$

3. $B$

4. None of these

Q.

$IfA\bigcap B=B,then$

1. $A\subset B$

2. $B\subset A$

3. $A=ɸ$

4. $B=ɸ$

Q.

In a school, $38\%$ of the students are girls. If the number of boys is $1023.$ Find the total strength of the school.

Q.

Where would the number $\sqrt{5}$ lie on the number line?

1. between 1 and 2

2. None of the above

3. between 0 and 1

4. between 2 and 3

Q.

Asha got 86.875% marks in the annual examination. If she got 695 marks, find the total number of marks of the examination.

Q. Sets having no element in common are called:

1. Equal sets
2. Joint sets
3. Equivalent sets
4. Disjoint sets

Q.

There are 800 students in a school, out of which 560 are girls. The percentage of boys students in the school is ______

1. 35%

2. 20%

3. 30%

4. 25%

Q.

If $N_a=\{an:n\in N\}$ , then $N_3\cap N_4$ =

1. $N_7$

2. $N_{12}$

3. $N_3$

4. $N_4$

Q.

Classify the set of even numbers as finite or infinite set.

Q.

In an examination a candidate attempts 90% of the questions. Out of these 70% of his answers are correct. Each questions carries 3 marks for the correct answers and -1 mark for the wrong answer. If the marks secured by the candidate is 243, what is the total number of questions?

Q.

In a mathematics class, 20 children had forgotten their rulers and 17 forgotten their pencils. "Go and borrow them from someone at once”, said the teacher. If 24 children left the room, then the number of children who had forgotten both is ____.

1. 11

2. 12

3. 13

4. 14

Q.

Which of the following represent a function?

1. 

2. 

3. 

4. 

Q.

A sum of$Rs700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $Rs20$ less than its preceding prize, find the value of each of the prizes.

Q. 30% passengers got down from a train at station X . 70% of the remaining got down at station Y. If there are still 1050 passengers in the train how many passengers were there before station X. ( note no one boarded the train in station X and Y)

Q.

60% of a class are girls. The number of boys is 20. So, the strength of the class is 45.

1. True
2. False

Q. In a company out of total strength of 600 employees 15% are men and rest are women. If 30%of men and 10%womens are south Indian find the total number and percentage of South Indian employees in the company.

Q.

In a school, $30\%$ of students play chess, $60\%$ play carrom and the rest play other games. If the total number of students in the school is $900$, find the exact number of students who play each game.

Q.

If A = $\{5,6,7,8,9\}$, B = $\{x:3<x<8andx\in W\}$ and C= $\{x:x\le 5andx\in N\}$. Find:

(i)$A\cup Band(A\cup B)\cup C$

(ii) $B\cup CandA\cup (B\cup C)$

(iii) $A\cap Band(A\cup B)\cap C$

(iv) $B\cap CandA\cap (B\cap C)$

Is $(A\cup B)\cup$ C = A $\cup (B\cup C)$ ?

Is $(A\cap B)\cap C$ = A $\cap (B\cap C)$ ?

Q. If $f\left(x\right)+2f\left(\frac{1}{x}\right)=3x,x\ne 0andS=xϵR:f\left(x\right)=f(-x)$; then S

1. contains more than two elements
2. is an empty set
3. contains exactly one element
4. contains exactly two elements

Q.

Using the given Venn diagram, find $A\cap B$.

1. $\{a,b,c,e,g\}$

2. $\{c,e\}$

3. $\{d,f\}$

4. $\{a,b,g\}$

Q.

If A = set of whole numbers and B = set of natural numbers, then the set of elements belonging to A and B is _____ .

1. phi

2. {phi}

3. A

4. B

Q.

If A = {x : x is a natural number}

B = {x : x is an even natural number}

C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

1. C

2. B

3. A

4. A ∩ B

Q.

In a class of 40 students, 20% are selected for a trip to Goa. Find the number of students going for the trip.

1. 8

2. 20

3. 12

4. 4

Q. Let $A,B$ be two sets such that $A\cap B=\varphi$, then $A=\varphi$ and $B=\varphi$?

1. True
2. False

Q.

B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.

1. A = {x, y, z}, B = {a, b, c}

2. A = {a, b, c}, B = {x, y, z}

3. A = {a, x, y}, B = {b, c, z}

4. A = {b, z, x}, B = {c, b, y}

Q.

If A = $A=\{x\in W:5<x<10\},B=\{3,4,5,6,7\}andC=\{x=2n;n\in Nandn\le 4\}$. Find :

(i) $A\cap (B\cup C)$

(ii) $(B\cup A)\cap (B\cup C)$
(iii) $B\cup (A\cap C)$
(iv) $(A\cap B)\cup (A\cap C)$

Name the sets which are equal

Q.

Let $n(A-B)=25+x,n(B-A)=2x$ and $n(A\cap B)=2x.$ If $n\left(A\right)=2\left(n\right(B\left)\right),$ then $x$ = ___.

1. 4

2. 7

3. 5

4. 6

Q.

Given A = $\{0,1,2,3,4,5\},B=\{0,2,4,6,8\}andC=\{0,3,6,9\}$. Show that

(i) $A\cup (B\cup C)=(A\cup B)\cup C$ i.e. the union of sets is associative.

(ii)$A\cap (B\cap C)=(A\cap B)\cap C$ i.e. the intersection of sets is associative.