isical.ac.in JRF Physics 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 : Physics
Year : 2016

Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-Jrf-Physics.html
Download Sample/Previous Years’ Questions :
MMA 2016 : https://www.pdfquestion.in/uploads/11373-MMA-2016.pdf
PHB 2016 : https://www.pdfquestion.in/uploads/11373-JRF-PHB-2016.pdf
MMA 2015 :  https://www.pdfquestion.in/uploads/11373-MMA-2015.pdf
PHB 2015 : https://www.pdfquestion.in/uploads/11373-JRF-PHB-2015.pdf
MMA 2014 : https://www.pdfquestion.in/uploads/11373-MMA-2014.pdf
PHB 2014 : https://www.pdfquestion.in/uploads/11373-JRF-PHB-2014.pdf

JRF Physics Questions for ISI Admission Test 2017 :

Test code : PHB
Session : Afternoon
Questions : 6+8+8
Time : 2 hours
** On the answer-booklet write your Registration Number, Test Code, Number of this booklet, etc. in the appropriate places.

Related : JRF Quality Reliability & Operations Research Sample Question for ISI Admission Test : www.pdfquestion.in/11370.html

Attention :
** Please read the following very carefully before answering the test.

** There are three parts. Part I is compulsory for all candidates and carries a credit of 30% of the total. Besides, each candidate has to choose only one of the Parts II & III and answer from that part as per instructions.

** The credit for each of these parts is 70% of the total.
** All rough work must be done on this booklet and/or on the answer-booklet.
** You are not allowed to use calculators.

Part I :
Mathematical and Logical Reasoning :
** Answer all questions. All questions carry equal marks.

1. For any real x, let f(x) = min{vx, x2}. Compute f(x) dx.

2. A ray of light traveling along the line y = 2, in the direction of the positive x-axis, falls on a convex mirror in the form of a parabola. The equation of the parabola is y2 = 4x. Find the equation of the line along which it will be reflected.

3. Find all possible real functions f(x) such that, for x = 0
4. A particle describes a curve r = aekµ under a central force P, where a and k are positive constants. Show that the force law will be the following P 1/r3

5. At time t = 0 an object having mass m is released from rest at a height y0 above the ground. Let g represent the constant gravitational acceleration. Derive an expression for the impact time (the time at which the object strikes the ground). What is the velocity with which the object strikes the ground?

Part II :
Mathematics :
Answer any five questions :
1. (a) Show that the escape velocity V for a satellite of the earth moving under the central force µ r2 (r being the radial distance) per unit mass is given by V = q 2µ R , where R is the radius of the earth and µ is a constant.

(b) A solid circular cylinder of radius a rotating about its axis is placed gently with its axis horizontal on a rough plane, whose inclination to the horizon is a. Initially, the friction acts up the plane and the coefficient of friction is µ. Show that the cylinder will move upwards if µ > tan

c. Also show he time that elapses before rolling commence is where ? is the initial angular velocity of the cylinder.

TEST CODE : PHB
Session : Afternoon
Questions : 6+8+8
Time : 2 hours
** On the answer-booklet write your Registration Number, Test Code, Number of this booklet, etc. in the appropriate places.

Attention :
** Please read the following very carefully before answering the test.
** There are three parts. Part I is compulsory for all candidates and carries a credit of 30% of the total.

** Besides, each candidate has to choose only one of the Parts II & III and answer from that part as per instructions.
** The credit for each of these parts is 70% of the total.

1. A ray of light traveling along the line y = 2, in the direction of the positive x-axis, falls on a convex mirror in the form of a parabola. The equation of the parabola is y2 = 4x. Find the equation of the line along which it will be reflected.

2. At time t = 0 an object having mass m is released from rest at a height y0 above the ground. Let g represent the constant gravitational acceleration. Derive an expression for the impact time (the time at which the object strikes the ground). What is the velocity with which the object strikes the ground?

3. A solid circular cylinder of radius a rotating about its axis is placed gently with its axis horizontal on a rough plane, whose inclination to the horizon is a. Initially, the friction acts up the plane and the coefficient of friction is µ. Show that the cylinder will move upwards if µ > tan

a. Also show the time that elapses before rolling commence is where w is the initial angular velocity of the cylinder.

4. Show that for any real or complex square matrix A, there is an a such that aI + A is non-singular, where I denotes the identity matrix.