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Name of the University : IEOR @ IIT Bombay Industrial Engineering & Operations Research Indian Institute Of Technology Bombay
Exam : M.Tech. Admissions Test
Document Type : Model Question Paper
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IEOR – IITB M.Tech. Admissions Test Model Question Paper

** Following are some model questions for admissions-tests.
** The pattern and contents may be updated ocassionally.

Related : Industrial Engineering & Operations Research Bombay Ph.D. Admissions Entrance Test Question Paper :

** These question papers may be used for guidance but cannot be considered as a reference for the pattern, breadth and scope of the tests.


** No clarications on questions should be sought during the examination.
** Answer as many questions as you can. There are a total of NN questions. Duration MM minutes.

** Write the answer in the space provided on the right side of the question. Answers written in the marked space only will be evaluated.
** Each correct answer will be awarded two marks.

** For multiple choice questions, you have to mention all the right choices for full marks; one mark will be deducted for wrong or incomplete solution.
** There is no negative marking for questions other than multiple-choice questions.

** Use of calculator is allowed. Mobile phones, tablets and other electronic items are not allowed.

Disclaimer about this document :
** This question paper is a model for the admissions-test to IEOR department at IIT Bombay.
** Some of these questions may have appeared in the previous years’ tests.

** The actual test may have a dierent number of questions and questions of dierent types.
** This paper is meant only to provide an idea of the kind of questions that may be asked in the test.

Sample Question

1. A manufacturing facility has four stages in series (i.e. every product has to go through each stage in sequence), A-B-C-D with processing rates of 4 units per hour, 5 units per hour, 4 units per hour and 6 units per hour respectively. The maximum achievable throughput is?

2. Consider the manufacturing facility given in the previous question. If you have to invest in any stage to improve the processing rate, so as to achieve higher throughput which stage(s) will you invest initially: stage A, B, C or D?

3. In designing a health facility (e.g. a diagnostic centre), there could be many objectives. One such objective is Maximize `Utilization of the personnel in the facility’. Identify the objective(s) which are perhaps con icting with the above objective.
A. Minimizing the average waiting time of customers
B. Minimizing the average number of customers waiting
C. Minimizing the number of customers who wait beyond some time (e.g. two hours)
D. Maximize the total revenue of the hospital

4. We flip a fair coin 10 times. What is the probability of getting exactly 5 heads?

5. Consider a group of children: 3 boys and x girls. We pick 2 children at random, and the probability that both are boys is 1 2 . How many girls are there in the group?
A. 1
B. 2
C. 3
D. 4

6. Consider the algorithm given below. Let the inputs be A=4, 6, 8 and n=3. What is the nal output of the algorithm?
1. Create array B of size n
2. number: s
4. for i 1 to n
5. s A[1]
6. for j 2 to i
7. s s + A[j]
8. next j
9. B[i] s / i
10. next i
11. output: array B
A. f4; 6; 8g
B. f4; 6; 7g
C. f4; 5; 7g
D. f4; 5; 6g

7. The condition \U is true if V is true” is captured in which of the following constraints (if we follow the convention that 0=false and 1=true)?
A. V U
B. U V
C. U = V
D. U + V = 1

8. The function f(x) = x4 over the real numbers always satises f(x) 0. At point x = 0, we have
f(x) = 0; f0(x) = 0 and f00(x) = 0. This illustrates the fact that
A. f0(x) = 0 and f00(x) 0 are necessary conditions for x to be a minimum point of f.
B. f0(x) = 0 and f00(x) = 0 are necessary conditions for x to be a minimum point of f.
C. f0(x) = 0 and f00(x) 0 are sucient conditions for x to be a minimum point of f.
D. f0(x) = 0 and f00(x) = 0 are sucient conditions for x to be a minimum point of f.

9. Consider the LP: maximize 3×1 ?? x2, subject to x1 ?? 2×2 0; x1 2; x2 0. The LP has
A. bounded feasible region
B. unbounded feasible region
C. unique optimum solution
D. unbounded objective value

10. The following frequency table gives the values obtained in 40 rolls of a die.
Value 1 2 3 4 5 6
Frequency 9 8 5 5 6 7
The sample median of the above data is?

11. Consider the data given in the previous question. The sample mode of the data is?
12. A `basic feasible solution’ in the context of linear programming is:
A. An optimal solution.
B. An optimal solution that is a candidate for being a feasible solution.
C. A feasible solution that is a candidate for being an optimal solution.
D. A solution that satises all the constraints.

13. A country has n cities, each of which is connected by road to every other city. A tourist wants to tour the country in such a way that starting from city 1, she visits each city exactly once, and returns to city 1. In how many ways can she do this?

14. A cook-book gives a recipe (instructions) to bake a cake of 8 inches diameter and of a certain height. If you want to use the recipe to bake a cake of the same height but of 12 inches diameter, by what factor should you multiply the recipe ingredients?

15. Most of the fast growing jobs in today’s economy need a college degree but require knowledge other than that gained from earning the degree. Good basic skills in reading, communication and mathematics play an important role in getting a job and developing one’s career. From the above paragraph it can be validly concluded that:
A. New jobs being created do not require knowledge gained from earning a degree
B. If a job is a fast growing job then it would need a college degree
C. Communication skills play a valuable role in getting a job
D. Getting a job and earning a degree are two different things

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