Properties of Set Operation

Q.

Show that for any sets A and B, $A=(A\cap B)\cup (A-B)$ and $A\cup (B-A)=(A\cup B).$

Q. If A, B and C are any three sets, then $A-(B\cup C)$ is equal to

1. $(A-B)\cap (A-C)$
2. $(A-B)\cup C$
3. $(A-B)\cap C$
4. $(A-B)\cup (A-C)$

Q. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
(i) the number of people who read at least one of the newspapers.
(ii) the number of people who read exactly one newspaper.

Q.

The derivative of log [log(logx)]w.r.t x is:

1. $\frac{1}{xlogxlog\left(logx\right)}$

2. $\frac{1}{logxlog\left(logx\right)}$

3. $\frac{1}{logxlog\left(logx\right)}$

4. $\frac{1}{xlogxlog\left(logx\right)}$

Q. Using properties of sets show that (i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.

Q.

Let A, B and C be the sets such that $A\cup B=A\cup C$ and $A\cap B=A\cap C.$ Show that $B=C.$

Q.

In how many ways can two 10-paise coins, two 20-paise coins, three 25-paise coins and one 50-paise coin be distributed among 8 children so that each child gets only one coin?

1. 1400

2. 1450

3. 1325

4. 1680

Q. Among a group of students, $50$ played cricket, $50$ played hockey and $40$ played volley ball. $15$ played both cricket and hockey, $20$ played both hockey and volley ball, $15$ played cricket and volley ball and $10$ played all three. If every student played at least one game, then

1. The sum of the number of students who played only cricket, only hockey and only volley ball is $70$
2. The sum of the number of students who played only cricket, only hockey and only volley ball is $75$
3. The number of students who played only cricket is $30$
4. The number of students who played only volley ball is $15$

Q. In a town of 10, 000 families it was found that $40\%$ family buy newspaper A, $20\%$ buy newspaper B and $10\%$ families buy newspaper C, $5\%$ families buy A and B, $3\%$ buy B and C and $4\%$ buy A and C. If $2\%$ families buy all the three newspapers, then number of families which buy A only is

1. 3100
2. 3300
3. 2900
4. 1400

Q.

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

1. At most 20

2. At least 30

3. Exactly 25

4. None of these

Q. In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics?

Q. 7. A batsman scored 35 runs fewer in hi second innings than in his first inning total score in the two innings of the match was 207 . Find his score in each the two innings.

Q. If A, B and C are any three sets, then $A\times (B\cap C)$ is equal to

1. $(A\times B)\cap (A\times C)$
   
2. $Noneofthese$
3. $(A\times B)\cup (A\times C)$
   
4. $(A\cup B)\times (A\cup C)$
   

Q. In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?

Q. The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
(a) 4! × 3!
(b) 4!
(c) 3! × 3!
(d) none of these.

Q. Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
(a) 60
(b) 20
(c) 15
(d) 125

Q. If A, B and C are any three sets, then $A\times (B\cap C)$ is equal to

1. $(A\times B)\cup (A\times C)$
   
2. $(A\cup B)\times (A\cup C)$
   
3. $(A\times B)\cap (A\times C)$
   
4. $Noneofthese$

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. Then

1. $n=1$
2. $n=23$
3. number of people who like facebook is $69$
4. number of people who like facebook is $72$

Q.

Let A, B and C be the sets such that $A\cup B=A\cup C$ and $A\cap B=A\cap C$. Show that B = C

Or

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all three sports? How many received medals in exactly two of the three sports?

Q.

Out of 120 farmers 93 farmers grows vegetables, 63 grows flowers, 45 grows sugarcane, 45 grows vegetables flowers, 24 grows flowers sugarcane, 27 grows vegetables sugarcane find how many farmers grows all the three?

Q.

In a class 6 students have to be arranged for a photograph. If the prefect and the vice must occupy the positions at either ends, how many ways the students can be arranged?

1. 48

2. 64

3. 58

4. 32

Q. Solve the
$2\frac{1}{5}-\frac{-1}{3}$

Q. For any two sets $A$ and $B,$ $A-(A\cap B)$ = ___.

1. $A^{\prime }\cap B$
2. $A\cap B^{\prime }$
3. $A^{\prime }\cap B^{\prime }$
4. $(A\cup B{)}^{\prime }$

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. From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

Q. Let $A=\{p,q,r,4,5\}$ and $B=\{p,q,r\},$ then

1. $n\left(A\right)=n\left(B\right)$
2. $A=B$
3. $A\ne B$
4. None of these.

Q.

To fill 3 vacancies there are 25 candidates of which five are from scheduled caste. If all 3 of the vacancies are reserved for scheduled caste, then the number of ways in which the selection can be made __________.

1. 

2. 

3. 

4. 

Q. In how many ways can five children stand in a queue?

Q. Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. show that B = C.

Q.

There are 21 people in an orientation group. Each person shakes hands with every other person exactly once. How many handshakes are there in total?