Intersection of Sets

Q.

Question 4 (d)
Find
d) $75\%of1kg$

Q.

If $A=\{x:x\text{is a prime number}\}$ and

$B=\{x:x\le 10,x\in N\}$, then $A\cap B$ is ________ .

1. {1, 3, 5, 7}
2. {3, 5, 7}
3. {2, 3, 5, 7}
4. {1, 2, 3, 5, 7}

Q. Let A = {x : x is a natural number and a factor of 18}

B = {x : x is a natural number and less than 6}

Find A ∪ B and A ∩ B.

1. A ∩ B = {1, 2, 3}
2. A ∪ B = {1, 2, 3, 4, 5, 6, 9, 18}
3. A ∩ B = {1, 2, 4}
4. A ∪ B = {1, 1, 2, 2, 3, 3, 4, 5, 6, 9, 18}

Q.

If $P\left(A\right)=0.25,P\left(B\right)=0.50$, and $P(A\cap B)=0.14$, then$P(A\cap B)$ is equal to

1. $0.61$

2. $0.39$

3. $0.48$

4. None of these

Q. Two coins are tossed once. Find the probability of getting:
i) 2 heads
ii) at least 1 tail
[3 MARKS]

Q.

Given $U$ is the set of natural numbers between 11 and 19.

$A=\{x:x\text{is divisible by 3}\}$

$B=\{12,14,15,16\}$

Find $A\cap B$.

1. $\{14,16\}$

2. $\{2,14\}$

3. $\{12,15\}$

4. $\left\{15\right\}$

Q. Question 37(ii)
A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square?

Q. The probability of a man hitting the target is $\frac{1}{4}$. The number of times atleast must he fire so that the probability of his hitting the target atleast once is greater than $\frac{2}{3}$ is

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

Q. how to solve probability related to weeks and days

Q. A coin is tossed $5$ times. The probability of $2$ heads and $3$ tails is:

1. $\frac{11}{16}$
2. $\frac{5}{32}$
3. $\frac{5}{16}$
4. $\frac{11}{32}$

Q.

Represent the given set in Roster form.

A = {x: x is a prime number, $\frac{5}{2}$ < x < $\frac{11}{2}$}

1. {-3, -2, -1, 0, 1, 2, 3, 4, 5}

2. {-1, 0, 1, 2, 3, 4, 5, 6}

3. {-1, 0, 1, 2, 3, 4, 5}

4. {-2, -1, 0, 1, 2, 3, 4, 5}

Q. Let A = {x : x is a natural number and a factor of 15}

B = {x : x is a natural number and less than 5}

Find A ∪ B and A ∩ B.

1. A ∩ B = {1, 3}
2. A ∪ B = {1, 2, 3, 4, 5, 15}
3. A ∩ B = {1, 2, 4}
4. A ∪ B = {1, 1, 2, 2, 3, 3, 4, 5, 6, 9, 18}

Q.

Question 164(ii)

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use
$(\times 1)$ machines.

Q.

If A = {1, 4, 9}, B = {1, 2, 3} and C = {1, 3, 5}, find A $\cap$ (B $\cap$ C).

Q. A king, queen and jack of spades are removed from a deck of 52 playing cards and then well shuffled one card is selected from the remaining cards find the probability to getting (1) a spade (2) a king

Q. If set A = {4, 8, 12, 16} and set B = {8, 16, 24, 32}, then the cardinality of the set $A\cap B$ is ______.

1. 4
2. 6
3. 8
4. 2

Q.

Question 164(iii)

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use
$(\times 1)$ machines.

Q. Using the given Venn diagram, find $A\cap B$. [ 2 marks ]

Q.

Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two Is do not come together ?

Q. Given $P=\{x:n\in N,x=2n\}$
$Q=\{x:n\in N,x=4n\}$ where N is a set of natural numbers.
Then, $(P-Q)\cap (Q-P)$ is:

1. P
2. Q
3. $P\cap Q$
4. {}

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

1. {5}
2. {2, 4, 5, 6}
3. {1, 2, 3, 4, 5, 6, 7, 8}
4. {1, 3, 5, 7, 8}

Q. A coin is tossed three tiimes. Find the probability of getting exactly two heads.

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

Q.

If A = {1, 2, 3, 4, 5},

B= {4, 5, 6, 7, 8} and C= {7, 8, 9, 10, 11}

Find :

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

(iii) $B\cup C$

Q.

If $A=\{x:x=n,nϵN,5\le n<10\}$ and $B=\{3,4,5,6\}$, then $A\cup B$ is ______.

1. {3, 4, 5, 6}
2. {5, 6, 7, 8}
3. {5, 6}
4. {3, 4, 5, 6, 7, 8, 9}

Q. If A = {0}, then $A\cap A$ is:

1. 0
2. { }
3. A
4. None of the above

Q. Box A contains $3$ red and $2$ blue marbles while box $B$ contains $2$ red and $8$ blue marbles. A fair coin is tossed. If the coin turns up heads, a marbles is drawn from $A$, if it turns up tails, a marble is drawn from bag $B$. the probability that a red marble is chosen, is

1. $\frac{1}{5}$
2. $\frac{2}{5}$
3. $\frac{3}{5}$
4. $\frac{1}{2}$

Q.

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two digit number (ii) a perfect square number (iii) a number divisible by 5.

Q. The probability of getting an ace from a well-shuffled deck of 52 cards is ____.

1. 1/13

2. 1/52

3. 4/13

4. 1/4

Q. Stephany is trying to solve a puzzle but in unable to find the missing block.

Pick out the correct block from the given options.

1. 
2. 
3. 
4. 

Q. If $\overrightarrow{a}=2\hat{i}-\hat{j}-2\hat{k}$ and $\overrightarrow{b}=7\hat{i}+2\hat{j}-3\hat{k}$, then express $\overrightarrow{b}$ in the form of $\overrightarrow{b}=\overrightarrow{b_1}+\overrightarrow{b_2}$, where $\overrightarrow{b_1}$ is parallel to $\overrightarrow{a}$ and $\overrightarrow{b_2}$ is perpendicular to $\overrightarrow{a}$.