isical.ac.in M.Mathematics 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.Mathematics
Year : 2016
Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-MMath.html
Download Sample/Previous Years’ Questions :
2016 MMA : https://www.pdfquestion.in/uploads/11328-MMAEven2016.pdf
2016 PMB : https://www.pdfquestion.in/uploads/11328-MMathPMB-2016.pdf
2015 MMA : https://www.pdfquestion.in/uploads/11328-MMAEven2015.pdf
2015 PMB : https://www.pdfquestion.in/uploads/11328-MMathPMB-2015.pdf
2014 MMA : https://www.pdfquestion.in/uploads/11328-MMAEven2014.pdf
2014 PMB : https://www.pdfquestion.in/uploads/11328-MMathPMB-2014.pdf
M.Mathematics 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 B.Mathematics ISI Admission Sample Questions Paper : www.pdfquestion.in/11319.html
** This test contains 30 questions in all. For each of the 30 questions, there are four suggested answers. Only one of the suggested answers is correct.
** You will have to identify the correct answer in order to get full credit for that question.
** Indicate your choice of the correct answer by darkening the appropriate oval”, completely on the answersheet.
You will get :
** 4 marks for each correctly answered question,
** 0 marks for each incorrectly answered question and
** 1 mark for each unattempted question.
** All Rough Work Must Be Done On This Booklet Only.
** You Are Not Allowed To Use Calculator.
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
4. Suppose X and Y are two independent random variables both following Poisson distribution with parameter . What is the value of E(X – Y )2?
A)
(B) 2
(C) 2
(D) 42
5. 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
6. 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
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. Let f : (0;1) ! (0;1) be a strictly decreasing function. Consider Which one of the following is always true?
(A) h is strictly decreasing
(B) h is strictly increasing
(C) h is strictly decreasing at first and then strictly increasing
(D) h is strictly increasing at first and then strictly decreasing
9. An integer is said to be a palindrome if it reads the same forward or backward. For example, the integer 14541 is a 5-digit palindrome and 12345 is not a palindrome. How many 8 digit palindromes are prime?
(A) 0
(B) 1
(C) 11
(D) 19
10. A club with n members is organized into four committees so that each member belongs to exactly two committees and each pair of committees has exactly one member in common. Then
(A) n = 4
(B) n = 6
(C) n = 8
(D) n cannot be determined from the given information
TEST CODE : PMB
Session : Afternoon
Duration of test : 2 hours
Instruction :
** Write your registration number, test code, booklet no., etc. in the appropriate places on your ANSWER BOOKLET.
** This test has questions arranged in two groups.
** Each group consists of 6 questions.
** You need to answer 4 questions FROM EACH GROUP.
** Each question carries 10 marks. Total marks = 80.
Note :
** All Rough Work Must Be Done On This Booklet And/Or On Your Answer Booklet.
** Calculators Are Not Allowed
Group A :
1. (a) Show that there exists X 2 (0; 1) such that for all n e 2,
(b) Prove that limn!1 xn exists and find its value.
2. Examine, with justification, whether the following limit exists If the limit exists, then find its value.
3. Does there exist a continuous function f : R -> R that takes every real value exactly twice? Justify your answer.
4. Let S17 be group of all permutations of 17 distinct symbols. How many subgroups of order 17 does S17 have? Justify your answer
5. Suppose that H and K are two subgroups of a group G. Assume that [G : H] = 2 and K is not a subgroup of H. Show that HK = G.