# IIT Madras MS Written Test Questions - CSE

30 April 2019
Gate score - 762, AIR- 388, Category - General

IIT Madras for MS in CSE conducts written test and those who get shortlisted in written are selected for Interviews. Around 250+ candidates were called for test. Test syllabus was entire gate syllabus. There were 30 questions to be solved in 2 hrs and each question carried 2 marks. There was 0.5 negative marking for each incorrect answer. Level of questions were same as that for Gate. Few questions which I remember were :

1. Which of the following are hard problems- Finding shortest path between a pairs of vertices, Finding longest pair between a pair of vertices?
2. Arrange in ascending order by Asymptotic time complexity: 100^n, 2^n, n^2, 2^{\sqrt{n}}$100^n, 2^n, n^2, 2^{\sqrt{n}}$
3. Let P and Q be two sets, let P be the set having n element, Q have k element, Q is subset of P, among all the subsets of P, how many subsets are there which have intersection with Q As exactly 1 element?
4. Let P and Q be 2 subsets of a set S, find the no of pairs (P, Q) such that P intersection Q is \Phi$\Phi$?
5. Which among the given was ambiguous grammar? Find L attributed and S attributed grammar
6. A DFA was given and asked to give the regular language
7. If L1 is not regular, L2 is not regular, which statement are true? S1: L1 intersection L2 is not regular, S2: L1 union L2 is not regular
8. To solve Priority inversion problem in OS, which is true? S1: Assign the highest priority to any process which is currently executing, S2: Incrementally keep increasing the priority of process which is executing till it exits the critical section
9. CN- Question on find the window size
10. DBMS- A question on usage of ‘having’ and ‘group by’
11. Signal system- Find Fourier transform co efficient
12. PL- Complete the code, find the output
13. DS- Loneliness ratio=no of lone nodes/ total nodes, Lone node is the one which has parent but no sibling. Give the tightest bound on the Loneliness ratio- 0.25, 0.5, 0.75, 1
14. No of different words which can be formed from the word Science such that vowels are always together
15. 2 dice are rolled, if the sum is strictly less than 7, then output is min of 2 numbers, if the sum is greater than or equal to 7, output is max of 2 numbers, then what is the probability that the output is 5?
16. Which of the following infinite sets have same cardinality- Real numbers, Natural numbers, rational numbers, even numbers
17. K map based question on Digital Logic
18. CO- A question based on carry save adder
19. If P and Q work together, they can do a work in 7.5 days, if P works alone he can finish half of the work, and Q alone can finish the rest of the half in 20 days, if P is more efficient than Q, in how many days Q alone can do the work- 20 days, 40 days, 36 days, 30 days
20. Which of the following is largest if n is 73, (n^2)^3, n^{2^3}, 2^{n^3}, 3^{n^2}$(n^2)^3, n^{2^3}, 2^{n^3}, 3^{n^2}$

After this there was a Subjective test for 30 mins. There were 2 questions:

1. They had asked to write the pseudo code for this problem- Maximum sum such that no two elements are adjacent
2. Why you want to do Research at IIT Madras? The marks of this test were not included for shortlisting for interviews, but it was supposed to be used for discussions during interviews. (However they didn’t ask anything from this test during interviews)

Suggestions:
IIT Madras made sure to cover all topics in test, 2–3 questions were put from every subject like Dbms, OS, Algo, DS, Maths, Calculus, TOC, Compiler, CO, Signal systems also. So to maximize your chance of getting selected be prepared in all subjects.

Thanks for reading guys, and if you liked my post, don’t forget to Upvote it and share among your friends for whom this may be helpful. Cheers!