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- Question
- 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
- Correct Answer
- 13
ExplanationGiven 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. - 1. 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
- 2. 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
- 3. 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
- 4. 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 Discuss
- 5. 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
- 6. 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
- 7. The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be?
Options- A. 25m2
- B. 28 m2
- C. 30m2
- D. None of these Discuss
- 8. The length of a rectangle is double while its breadth is halved. What is the percentage change in area?
Options- A. 50
- B. 75
- C. No change
- D. None of these Discuss
- 9. The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is?
Options- A. 6 meters
- B. 8 meters
- C. 9 meters
- D. 12 meters Discuss
- 10. If the side of a square is increased by 25%, then how much percent does its area get increased?
Options- A. 125
- B. 156.25
- C. 50
- D. 56.25 Discuss
Sets and Functions problems
Search Results
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: 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: (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: 19
Explanation:
Let 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.
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: 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
Correct Answer: 30m2
Explanation:
Altitude = ?(13)2 - (5)2
= ?144 = 12m
? Area of the triangle = (5 x 12 ) / 2 m2
= 30m2
Correct Answer: No change
Explanation:
Let length = l and breadth = b
Then, area = lb
New length = 2l
And new breadth = b/2
? New area = ( 2l ) x (b/2) = lb
So, there is no change in area .
Correct Answer: 6 meters
Explanation:
Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
? Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
Correct Answer: 56.25
Explanation:
Let area 100 m2
Then, side = 10 m
New side = 125 % of 10
= (125/100) x 10
= 12.5 m
New area = 12.5 x 12.5 m2
=(12.5)2 sq. m
? Increase in area = (12.5)2 - (10)2 m2
= 22.5 x 2.5 m2
=56.25 m2
% Increase = 56.25 %
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