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- Question
- In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
Options- A. 19
- B. 17
- C. 23
- D. 21
- Correct Answer
- 19
ExplanationLet P = set of people who like coffee and Q = set of people like tea.
Then, P ? Q = set of people who like at least one of the two drinks.
And P ? Q = set of people who like both the drinks.
Given in the question,
n(P) = 37, n(Q) = 52, n(P ? Q) = 70.
Use the below formula,
n(P ? Q) = n(P) + n(Q) ? n(P ? Q)
Put the value from the given question,
70 = 37 + 52 ? n(P ? Q)
? n(P ? Q) = 89 ? 70 = 19.
? 19 people like both coffee and tea. - 1. In a town with a population of 5000, 3200 people are egg-eaters, 2500 meat eaters and 1500 eat both egg and meat. How many are pure vegetarians?
Options- A. 600
- B. 800
- C. 900
- D. 850 Discuss
- 2. In a group of 1000 people, there are 750 people who can speak Hindi and 400 who can speak English. How many can speak Hindi only?
Options- A. 600
- B. 650
- C. 750
- D. 800 Discuss
- 3. If A and B are two sets such that A has 40 elements, A ? B has 60 elements and A ? B has 10 elements, how many elements does B have?
Options- A. 40
- B. 30
- C. 45
- D. 50 Discuss
- 4. If X and Y are two sets such that X ? Y has 18 elements, X has 8 elements, and Y has 15 elements, how many elements does X ? Y have?
Options- A. 5
- B. 7
- C. 9
- D. 11 Discuss
- 5. Which of the following pairs of sets are disjoint?
(i) {1, 2, 3, 4 } and { x : x is a natural number and 4 ? x ? 6 }
(ii) { a, e, i, o, u } and { c, d, e, f }
(iii) { x : x is an even integer } and { x : x is an odd integer }.
Options- A. (i)
- B. (ii)
- C. (iii)
- D. None of these Discuss
- 6. If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B ? C) =
Options- A. ?
- B. (A × B) ? (A × C)
- C. (A × B) ? (A × C)
- D. None of these Discuss
- 7. Out of 100 families in the neighborhood, 50 have radios, 75 have TVs and 25 have VCR. Only 10 families have all three and each VCR owner also has a TV. If some families have radio only, how many have only TV?
Options- A. 30
- B. 35
- C. 40
- D. 45 Discuss
- 8. 72% of the students of a certain class took Biology and 44% took Mathematics. If each student took at least one of Biology or Mathematics and 40 students took both of these subjects, the total number of students in the class is:
Options- A. 200
- B. 240
- C. 250
- D. 320 Discuss
- 9. In a class of 50 students, 35 opted for mathematics and 37 opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).
Options- A. 15
- B. 17
- C. 13
- D. 19 Discuss
- 10. Area of a square is 1/2 hectare. The diagonal of the square is?
Options- A. 250 meter
- B. 100 meter
- C. 50? 2 meter
- D. 50 meter Discuss
Sets and Functions problems
Search Results
Correct Answer: 800
Explanation:
Let, E be the set of people who are egg-eaters and M be the set of people who are meat-eaters.
As per given question,
n(E) = 3200, n(M) = 2500, n(E ? M) = 1500.
Use the formula
n(E ? M) = n(E) + n(M) ? n(E ? M)
= 3200 + 2500 ? 1500
= 5700 ? 1500 = 4200.
? Number of pure vegetarians = n(U) ? n(E ? M)
Number of pure vegetarians = 5000 ? 4200 = 800.
Correct Answer: 600
Explanation:
Given in the question,
n(H ? E) = 1000, n(H) = 750, n(E) = 400
Use the below formula,
n(H ? E) = n(H) + n(E) ? n(H ? E)
We get 1000 = 750 + 400 ? n(H ? E)
? n(H ? E) = 1150 ? 1000 = 150.
Number of People who can speak Hindi only
= n(H ? E?) = n(H) ? n(H ? E)
= 750 ? 150 = 600.
Correct Answer: 30
Explanation:
Given in the question ,
n(A) = 40, n(A ? B) = 60 and n(A ? B) = 10.
As we know the formula,
n(A ? B) = n(A) + n(B) ? n(A ? B)
Putting these values in the formula, we get
60 = 40 + n(B) ? 10
? n(B) = 30.
Correct Answer: 5
Explanation:
Given in the question ,
n(X ?Y) = 18, n(X) = 8, n(Y) = 15.
Using the formula
n(X ? Y) = n(X) + n(Y) ? n(X ? Y), we get n(X ? Y) = 8 + 15 ? 18 = 5.
Correct Answer: (iii)
Explanation:
(a) {x: x is a natural number and 4 ? x ? 6} = {4, 5, 6}. Now, {1, 2, 3, 4} and {4, 5, 6} have one element 4 common. Therefore, the given two sets are not disjoint.
(b) The sets {a, e, i, o, u} and {c, d, e, f} have one element e as common. Then, the given two sets are not disjoint.
(c) The sets {x: x is an even integer} and {x: x is an odd integer} have no element as common and therefore they are disjoint sets.
Correct Answer: (A × B) ? (A × C)
Explanation:
As per given question,
(B ? C) = {b, c, e} ? {b, c, f} = {b, c, e, f}
? A × (B ? C) = {a, d} × {b, c, e, f}
= {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)} ?...........(1)
Also, (A × B) = {(a, b), (a, c), (a, e), (d, b), (d, c), (d, e)}
and, (A × C) = {(a, b), (a, c), (a, f), (d, b), (d, c), (d, f)} ?............(2)
? (A × B) ? (A × C) = {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)}
From (1) and (2), we have
A × (B ? C) = (A × B) ? (A × C).
Correct Answer: 35
Explanation:
Let us assume that the N number of people have only TV.
According to question,
? (40 ? P) + P + 10 + 15 + (50 ? P) = 100
? 115 ? 2P + P = 100
? P = 115 ? 100 = 15
? Only TV = 75 ? 15 ? 10 ? 15 = 35
Correct Answer: 250
Explanation:
n(A) = Biology students = 72%
n(B) = Mathematics students = 44%
Total students = n(A ? B) = 100%
? 100% = 72% + 44% - n(A ? B) = 116% - n(A ? B)
? n(A ? B) = 16%
? number of students studying both subjects = 40
? Let the total number of students be P
Now, according to the question,
16P/100 = 40
? P = 250
Correct Answer: 13
Explanation:
Given in the question,
n(M ? B) = 50, n(M) = 35, n(B) = 37, n(M ? B) =?
use the below formula
n(M ? B) = n(M) + n(B) ? n(M ? B)
We get 50 = 35 + 37 ? n(M ? B)
? n(M ? B) = 35 + 37 ? 50 = 72 ? 50 = 22
? 22 students have opted for both Mathematics and Biology.
Again number of students who have opted for only Mathematics = n(M) ? n(M ? B) = 35 ? 22 = 13.
Correct Answer: 100 meter
Explanation:
Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2
Again Area = 1/2 x (Diagonal)2
So 1/2 x (Diagonal)2 = 5000m2
? Diagonal2= 10000
? Diagonal = 100
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