isical.ac.in M.TECH CS ISI Admission Test Sample Questions Paper : 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 : M.TECH(CS)
Year : 2016
Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-MTech-CS.html
Download Sample/Previous Years’ Questions :
MMA 2016 : https://www.pdfquestion.in/uploads/11346-MMA-2016-Even.pdf
PCB 2016 : https://www.pdfquestion.in/uploads/11346-PCB-2016.pdf
MMA 2015 : https://www.pdfquestion.in/uploads/11346-MMA-2015-Even.pdf
PCB 2015 : https://www.pdfquestion.in/uploads/11346-PCB-2015.pdf
MMA 2014 : https://www.pdfquestion.in/uploads/11346-MMA-2014-Even.pdf
PCB 2014 : https://www.pdfquestion.in/uploads/11346-PCB-2014.pdf
CS 2009 : https://www.pdfquestion.in/uploads/11346-MTech(CS)2009.pdf
M.TECH(CS) ISI Admission Sample Questions Paper :
Test Code : CS
Session :L Afternoon
Time : 2 HOURS
Max Score :
Group A : 30
Group B : 70
Instruction :
** Write your Name, Registration Number, Test Center, Test Code and the Booklet No. in the appropriate places on the answer-booklet.
** The questions are divided into two groups, A and B. Group B consists of five sections.
Related : Indian Statistical Institute MS QMS ISI Admission Sample Questions Paper : www.pdfquestion.in/11343.html
** Answer All Questions In Group A And Five Questions
** From Only One Of The Five Sections In Group B.
** The figures inside the square brackets [ ] following each question denote the marks allotted to it.
** In Answering Questions, All Necessary Steps Should Be Clearly Shown.
** Write Neatly And Indicate In A Separate Line The Final Answer Of Each Question.
** All Rough Work Must Be Scratched Through.
1. Suppose a; b; c > 0 are in geometric progression and ap = bq = cr 6= 1. Which one of the following is always true?
(A) p; q; r are in geometric progression
(B) p; q; r are in arithmetic progression
(C) p; q; r are in harmonic progression
(D) p = q = r
2. How many complex numbers z are there such that jz+1j = jz+ij and jzj = 5?
(A) 0
(B) 1
(C) 2
(D) 3
3. If a; b; c and d satisfy the equations
a + 7b + 3c + 5d = 16
8a + 4b + 6c + 2d = -16
2a + 6b + 4c + 8d = 16
5a + 3b + 7c + d = -16
Then (a + d)(b + c) equals
(A) -4
(B) 0
(C) 16
(D) -16
5. Find the centroid of the triangle whose sides are given by the following equations
4x – y = 19
x – y = 4
x + 2y = ??11
(A) 11/3 7/3
(B) 5/3 7/3
(C) – 11/3 7/3
(D) -5/3 7/3
5. Suppose X and Y are two independent random variables both following Poisson distribution with parameter t. What is the value of E(X – Y )2?
(A)
(B) 2
(C) 2
(D) 42
6. Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability 4/5 and with water it would die with probability 3/20. The probability that Ravi’s neighbor would remember to water the plant is 9/10. If the plant actually died, what is the probability that Ravi’s neighbor forgot to water the plant?
(A) 4/5
(B) 27/43
(C) 16/43
(D) 2/25
7. Suppose there are n positive real numbers such that their sum is 20 and the product is strictly greater than 1. What is the maximum possible value of n?
(A) 18
(B) 19
(C) 20
(D) 21
8. Which one of the following statements is correct regarding the elements and subsets of the set f1; 2; f1; 2; 3gg?
(A) f1; 2g 2 f1; 2; f1; 2; 3gg
(B) f1; 2g f1; 2; f1; 2; 3gg
(C) f1; 2; 3g f1; 2; f1; 2; 3gg
(D) 3 2 f1; 2; f1; 2; 3gg
9. The number of positive integers n for which n2+96 is a perfect square is
(A) 0
(B) 1
(C) 2
(D) 4
10. Suppose a 6 digit number N is formed by rearranging the digits of the number 123456. If N is divisible by 5, then the set of all possible remainders when N is divided by 45 is
(A) f30g
(B) f15; 30g
(C) f0; 15; 30g
(D) f0; 5; 15; 30g
TEST CODE: PCB
Instruction :
** Write your Registration Number, Test Centre, Test Code and the Booklet No. in the appropriate places in the answer-book.
** The questions are divided into two groups, A and B.
** Answer ALL questions in GROUP A.
** Answer questions from ONLY ONE SECTION in GROUP B.
GROUP B consists of the following FIVE sections :
I. Computer Science
II. Engineering and Technology
III. Mathematics
IV. Physics
V. Statistics
Section I : Computer Science
Answer any FIVE questions :
C1. (i) Consider the array A = [20; 13; 19; 8; 3; 5; 4] that represents a heap. Draw the heap after removing the element 20.
(ii) List all distinct integer keys k such that, when k is inserted in the Binary Search Tree of Figure 1, its height increases. Note that you are not allowed to insert an already existing key again. Justify your answer.
C2. (i) Consider sending a large le of 360,000 bits from Host A to Host B, connected through a router, as shown in Figure 2. Assume that there is no queuing and propagation delay, and the router has sucient buer space. Host A splits the le into segments of S bits each and adds 36 bits of header to ach segment, forming packets of (36 + S) bits. Each link has a transmission rate of R bps. Find the value of S thatminimizes the time needed to move the le from Host A to Host B.
(ii) The CPU of a system having an execution rate of 1 million instructions per second needs 4 machine cycles on an aver age for executing an instruction. On an average, 50% of the cycles use memory bus. For execution of the programs, the system utilizes 90% of the CPU time. For block data transfer, an I/O device is attached to the system, while the CPU executes background programs continuously.
Determine the maximum I/O transfer rate for each of the two cases :
(a) programmed I/O, (b) cycle-stealing DMA (in transparent mode). You may assume that transferring one byte involves 4 operations: in-status, check-status, branch and read/write in memory, each requiring one machine cycle. [7+ (3+4) = 14]