Sets- Case Based Type Questions | Mathematics (Maths) Class 11 - Commerce PDF Download

Direction: The given table shows the 10 most famous engineering private colleges of India with their respective fee structure of 4 years Bachelor of Technology course.
Question 1: Ram wants to take admission in a private engineering college but has a budget of 8 lakhs. Which set of colleges can he consider for admission?
(a) {SRM, Birla, LPU, Chandigarh, Kalinga}
(b) {Jaypee, LPU, Chandigarh, Kalinga}
(c) {Manipal, LPU, Thapar, Jaypee, Chandigarh, Kalinga}
(d) {AMITY, Vellore, Chandigarh, Kalinga}

Correct Answer is Option (c)
Ram can afford colleges where the fees are less than or equal to 8 lakhs. These include Manipal, LPU, Thapar, Jaypee, Chandigarh, and Kalinga.

Question 2: If both Sri and Ram want to take admission in the same college with budgets of 4 lakhs and 8 lakhs respectively, which colleges can they both afford?
(a) {Chandigarh, Kalinga}
(b) {Jaypee}
(c) {SRM, LPU}
(d) Ø

Correct Answer is Option (a)
The common colleges within both their budgets (4 lakhs and 8 lakhs) are Chandigarh and Kalinga.

Question 3: Sri has taken an education loan of 3 lakhs, increasing her total budget. Which college can Ram take admission in but Sri cannot?
(a) {Birla, Thapar}
(b) {Thapar}
(c) {SRM}
(d) {Manipal, Thapar}

Correct Answer is Option (b)
With a loan, Sri's budget becomes 7 lakhs, allowing her to afford Manipal, LPU, Jaypee, Chandigarh, and Kalinga. Ram, with 8 lakhs, can afford Thapar as well, which Sri cannot.

Question 4: Sri has a total budget of 4 lakhs and wants to take admission in a well-known college. Can she find a suitable option?
(a) Yes, {SRM, Birla, LPU}
(b) No, {Jaypee, LPU, Kalinga}
(c) Yes, {Chandigarh, Kalinga}
(d) None of the above

Correct Answer is Option (c)
The colleges within Sri's budget of 4 lakhs are Chandigarh and Kalinga.

Question 5: Ram has taken an education loan of 2 lakhs, raising his budget. How many colleges can he now consider for admission?
(a) 4
(b) 9
(c) 7
(d) 6

Correct Answer is Option (b)
With an increased budget of 10 lakhs, Ram can consider 9 colleges: Manipal, LPU, Thapar, Jaypee, Chandigarh, Kalinga, AMITY, SRM, and VIT.

Direction: A survey was conducted to find the career choices of students after intermediate. 100 students chose Engineering, 50 chose Medical, and 100 chose Arts. If 10 students chose both Engineering and Medical, and 3 chose Medical and Arts, with 3 not pursuing further studies, what is the total number of students surveyed?
Question 6: Find the total number of students on which the survey is conducted.
(a) 250
(b) 230
(c) 240
(d) 238

Correct Answer is Option (c)
The total number of students is calculated by adding all those pursuing various courses and considering overlaps, resulting in 240 students.

Question 7: How many students pursued both Medical and Arts?
(a) 5
(b) 2
(c) 3
(d) 4

Correct Answer is Option (c)
The Venn diagram for the survey indicates that 3 students pursued both Medical and Arts.

The region VI shows the student that goes for both Medical and Arts. So, n(B ∩ C) = 3.

Question 8: How many students pursued only engineering courses?
(a) 90
(b) 95
(c) 100
(d) 93

Correct Answer is Option (a)
After accounting for those students who pursued both Engineering and Medical, 90 students pursued only Engineering.

So, the number of students that goes for only engineering course are 90.

Question 9: How many students pursued either Medical or Engineering?
(a) 150
(b) 140
(c) 160
(d) No of the above

Correct Answer is Option (b)
Adding the students who pursued either Medical or Engineering, and considering overlaps, the total is 140.

The region I, II, III, IV, V, and VI shows the student that goes for Engineering or Medical. So, the required number of students is 140.

Question 10: How many students pursued either Engineering or Arts?
(a) 150
(b) 200
(c) 190
(d) 197

Correct Answer is Option (b)
Let A set denotes Engineering, B set denotes Medical and C set denotes Art. Draw the Venn's diagram for the given situation.The total number of students who pursued either Engineering or Arts, based on the Venn diagram, is 200.

The region I, II, IV, IV, V, and VII shows the student that goes for Engineering or Arts. So, the required number of students is 200.