isical.ac.in B.Mathematics 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 : B.Mathematics
Year : 2016

Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-BMath.html
Download Sample/Previous Years’ Questions :
2016 UGA(Odd) :  https://www.pdfquestion.in/uploads/11319-BMathodd-2016.pdf
2016 UGA(Even) : https://www.pdfquestion.in/uploads/11319-BMatheven-2016.pdf
2015 UGA(Odd) : https://www.pdfquestion.in/uploads/11319-BMathodd-2015.pdf
2015 UGA(Even) : https://www.pdfquestion.in/uploads/11319-BMatheven-2015.pdf
2014 UGA(Odd) : https://www.pdfquestion.in/uploads/11319-BMathodd-2014.pdf
2014 UGA(Even) : https://www.pdfquestion.in/uploads/11319-BMatheven-2014.pdf

B.Mathematics ISI Admission Sample Questions Paper :

TEST CODE : UGA
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 Answersheet.

 Related : Indian Statistical Institute B.Statistics ISI Admission Test Sample Question Paper : www.pdfquestion.in/11316.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. The largest integer n for which n + 5 divides n° 4-5 is
(A) 3115.
(B) 3120.
(C) 3125.
(D) 3130.

2. Let p, q be primes and a, b be integers. If pa is divided by q, then the remainder is 1. If qb is divided by p, then also the remainder is 1. The remainder when pa — qb is divided by pg is
(A) 1.
(B) 0.
(C) –1.
(D) 2.

3. The polynomiala’ + ?” + 1 is divisible by
(A) a.” – a 4 + ?” — a + 1.
(B) a ” + ?4 + 1.
(C) a” + ?” + ?% + a + 1.
(D) arº – a 4 + ?” + a + 1.

4. Let o – 0. If the equation p(a) = a,” –9a,” +26a. – o has three positive real roots, then o must satisfy
(A) o s 27.
(B) o S 81.
(C) 27 × o s 54.
(D) 54 × os 81.

5. The largest integer which is less than or equal to (2 + V3)* is
(A) 192.
(B) 193.
(C) 194.
(D) 195.

6. Consider a circle of unit radius and a chord of that circle that has unit length. The area of the largest triangle that can be inscribed in the circle with that chord as its base is
(A) #
(B) .#
(C) #t
(D)t0

7. Let z = 3 + 4i. If 22 is a complex number such that |z2|=2, then the greatest and the least values of |z1 – 22 are respectively
(A) 7 and 3.
(B) 5 and 1.
(C) 9 and 5.
(D) 4 + V7 and V7.

8. Consider two distinct arithmetic progressions (AP) each of which has a positive first term and a positive common difference. Let S, and T., S be the sums of the first n terms of these AP. Then lim # equals n—roo Tº,
(A) oo or 0 depending on which AP has larger first term.
(B) co or 0 depending on which AP has larger common difference.
(C) the ratio of the first terms of the AP
(D) the ratio of the common differences of the AP

9. Let f(a) = max{cosa, a.”), 0 < a. 3 #. If ao is the solution of the equation cosa. = a,” in (0, ;), then
(A) f is continuous only at a.o.
(B) f is not continuous at aco.
(C) f is continuous everywhere and differentiable only at a 0.
(D) f is differentiable everywhere except at a.o.

10. The set of all real numbers in (–2,2) satisfying 2|+| – |2°–1 – 1 = 2*-1 + 1 is
(A) {-1, 1}.
(B) {-1} U [1,2).
(C) (–2, —1] U [1, 2).
(D) (–2, —1] U {1}.

Test Code : UGA Even
Questions: 30
Time: 2 hours

Instructions :
** Write your Name, Registration Number, Test Centre, Test Code and the Number of this Booklet in the appropriate places on the Answer sheet.

** 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 answer sheet

** You Will Get 4 Marks For Each Correctly Answered Question, 0 Marks For Each Incorrectly Answered Question And 1 Mark For Each Un attempted Question.
** All Rough Work Must Be Done On This Booklet Only.
** You Are Not Allowed To Use Calculator.
** Wait For The Signal To Start.

1. The polynomial a” + æ” + 1 is divisible by
(A) acº — a 4 + æ” — a + 1.
(B) ar” + æ4 + 1.
(C) a ” + æ4 + æ” + a + 1.
(D) arº – a 4 + æ” + a + 1.

2. The largest integer n for which n + 5 divides n° + 5 is
(A) 3115.
(B) 3120.
(C) 3125.
(D) 3130.

3. Let p, q be primes and a, b be integers. If pa is divided by q, then the remainder is 1. If qb is divided by p, then also the remainder is 1. The remainder when pa — qb is divided by pa is
(A) 1.
(B) 0.
(C) –1.
(D) 2.

4. Let a- 0. If the equation p(a) = a “-9a,” +26a. – o has three positive real roots, then o must satisfy
(A) a s 27.
(B) a S 81.
(C) 27 × a s 54.
(D) 54 × a s 81.

5. The largest integer which is less than or equal to (2 + V3)* is
(A) 192.
(B) 193.
(C) 194.
(D) 195