isical.ac.in M.TECH QROR ISI Admission 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 – QROR
Year : 2016
Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-MTech-QROR.html
Download Sample/Previous Years’ Questions :
MMA 2016 : https://www.pdfquestion.in/uploads/11349-MMA-2016.pdf
PQB 2016 : https://www.pdfquestion.in/uploads/11349-PQB-2016.pdf
MMA 2015 : https://www.pdfquestion.in/uploads/11349-MMA-2015.pdf
PQB 2015 : https://www.pdfquestion.in/uploads/11349-PQB-2015.pdf
MMA 2014 : https://www.pdfquestion.in/uploads/11349-MMA-2014.pdf
PQB 2014 : https://www.pdfquestion.in/uploads/11349-PQB-2014.pdf
M.TECH – QROR ISI Admission Sample Questions Paper :
Test Code : MMA
Session : Forenoon
Questions : 30
Time : 2 hours
Instruction :
** Write your Name, Registration Number, Test Centre, Test Code and the Number of this booklet in the appropriate places on the answer sheet.
Related : Indian Statistical Institute MS QMS ISI Admission Sample Questions Paper : www.pdfquestion.in/11343.html
** For each question, there are four suggested answers of which only one is correct.
** For each question indicate your choice of the correct answer by darkening the appropriate oval (c) completely on the answer sheet.
** 4 marks are allotted for each correct answer,
** 0 mark for each incorrect answer and
** 1 mark for each un attempted question.
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
4. 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
5. 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
6. 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
7. The number of positive integers n for which n2+96 is a perfect square is
(A) 0
(B) 1
(C) 2
(D) 4
8. The number of positive integers n for which n3 + (n + 1)3 + (n + 2)3 = (n + 3)3 is
(A) 0
(B) 1
(C) 2
(D) 3
9. Let A be a real 22 matrix. If 5+3i is an eigenvalue of A, then det(A)
(A) equals 4
(B) equals 8
(C) equals 16
(D) cannot be determined from the given information
10. Let f : R ! R be a strictly increasing function. Then which one of the following is always true?
(A) The limits lim x!a+ f(x) and lim x!a- f(x) exist for all real numbers a
(B) If f is differentiable at a then f0(a) > 0
(C) There cannot be any real number B such that f(x) < B for all real x
(D) There cannot be any real number L such that f(x) > L for all real x
TEST CODE: PQB
1. a) Derive the maximum likelihood estimate of y, and hence find an unbiased estimator of y.
(b) Derive an exact 100(1 – y)% confidence interval of y.
2. Management of ABC Fans Limited suspected that background music may improve assembly line productivity of table fans. An industrial engineer is tasked to carry out an experiment to verify the suspicion.
The engineer selects four different music types (Light Hindustani, Light Carnatic, Indian Folk and Hindi Filmi) to study their effects on the productivity. Four different days of a week are selected for study. It is generally believed that assembly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first.
To account for this source of variability, four different assembly time periods, of one hour each, are considered for experimentation.
Now answer the following questions:
(i) To plan this experiment, what type of design do you propose?
Give a design layout for conducting the experiment. Identify the treatments and the block factors.
(ii) Under Gauss-Markov set up, write the linear model for your proposed design, describing the model parameters. (State all the assumptions associated with the model.)
(iii) Derive the normal equations.
(iv) Are all the parametric functions of model parameters estimable? If yes, why? And if not, what type of functions are estimable? (No explicit derivation is required.) [(2+2+1) + 3 + 8 + 4 = 20]
4. (a) Consider a population with N members labelled consecutively from 1 to N. Let X1, X2, …. ,Xn be a random sample drawn with replacement from the population. Find a sufficient statistic for N.
(b) A company procures material from two different suppliers A and B. The lead time to supply are random variables, say, Xa and Xb respectively. Data on lead times are collected for both the suppliers and frequency distributions are constructed.