JRF Computer Science Sample Questions for ISI Admission Test 2017 : Indian Statistical Institute

Name of the University : Indian Statistical Institute
Exam : ISI Admission Test
Document Type : Sample/Previous Year Question Paper
Name of the Subject : Computer Science
Year : 2016

Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-Jrf-CS.html
Download Sample/Previous Years’ Questions :
CSB 2017 : https://www.pdfquestion.in/uploads/11366-JRF-CSB-2017.pdf
MMA 2016 : https://www.pdfquestion.in/uploads/11366-MMA-2016.pdf
CSB 2016 : https://www.pdfquestion.in/uploads/11366-JRF-CSB-2016.pdf
MMA 2015 : https://www.pdfquestion.in/uploads/11366-MMA-2015.pdf
CSB 2015 : https://www.pdfquestion.in/uploads/11366-JRF-CSB-2015.pdf
MMA 2014 :  https://www.pdfquestion.in/uploads/11366-MMA-2014.pdf
CSB 2014 :  https://www.pdfquestion.in/uploads/11366-JRF-CSB-2014.pdf

JRF Computer Science Sample Questions for ISI Admission Test :

Test Code :CSB (Short Answer Type) 2017
** Junior Research Fellowship (JRF) in Computer Science

Related : Indian Statistical Institute JRF Quantitative Economics Sample Questions for ISI Admission Test : www.pdfquestion.in/11360.html 

The CSB test booklet will have two groups as follows :
GROUP A :
** A test of aptitude for Computer Science for all candidates in the basics of computer programming and mathematics, as indicated in the syllabus.
GROUP B :
** A test, divided into ve sections in the following areas at M.Sc./M.E./M.Tech.

Level :
** Mathematics,
** Statistics,
** Physics,
** Electrical and Electronics Engineering, and
** Computer Science.

** A candidate has to answer questions from only one of these sections in GROUP B, according to his/her choice.
** Group A carries 40 marks and Group B carries 60 marks.
** The syllabi and sample questions of the CSB test are given overleaf.

Sample Questions :
Note that all questions in the sample set are not of same marks and same level of diculty.

Group A :
A1. The king’s minter keeps mn coins in n boxes each containing m coins. Each box contains 2 false coins out of m coins. The king suspects the minter and randomly draws 1 coin from each of the n boxes and has these tested. What is the probability that the minter’s dishonest actions go undetected?

A2. Consider the pseudo-code given below.
Input: Integers b and c.
1. a0 max(b; c), a1 min(b; c).
2. i 1.
3. Divide ai??1 by ai . Let qi be the quotient and ri be the remainder.
4. If ri = 0 then go to Step 8.
5. ai+1 ai-1 – qi – ai.
6. i- i + 1.
7. Go to Step 3.
8. Print ai . What is the output of the above algorithm when b = 28 and c = 20? What is the mathematical relation between the output ai and the two inputs b and c?

A3. Consider the sequence an = an??1 an??2 +n for n 2, with a0 = 1 and a1 = 1. Is a2011 odd? Justify your answer.

A4. Given an array of n integers, write pseudo-code for reversing the contents of the array without using another array. For example, for the array 10 15 3 30 3 the output should be 3 30 3 15 10. You may use one temporary variable.

A5. The integers 1, 2, 3, 4 and 5 are to be inserted into an empty stack using the following sequence of push() operations push(1) push(2) push(3) push(4) push(5) Assume that pop() removes an element from the stack and outputs the same. Which of the following output sequences can be generated by inserting suitable pop() operations into the above sequence of push() operations? Justify your answer.
(a) 5 4 3 2 1
(b) 1 2 3 4 5
(c) 3 2 1 4 5
(d) 5 4 1 2 3.

A6. Derive an expression for the maximum number of regions that can be formed within a circle by drawing n chords.

A7. Given A = f1; 2; 3; : : : ; 70g, show that for any six elements a1, a2, a3, a4, a5 and a6 belonging to A, there exists one pair ai and aj for which jai ?? aj j 14 (i 6= j).

A8. The function RAND() returns a positive integer from the uniform distribution lying between 1 and 100 (including both 1 and 100). Write an algorithm (in pseudo-code) using the given function RAND() to return a number from the binomial distribution with parameters (100; 1=4).

A9. Calculate how many integers in the set f1; 2; 3; : : : ; 1000g are not divisible by 2, 5, or 11.
A10. Let M be a 4-digit positive integer. Let N be the 4-digit integer obtained by writing the digits of M in reverse order. If N = 4M, then nd M. Justify your answer.