www.drmgrdu.ac.in PhD Entrance Exam Mathematics Model Question Paper : Dr MGR University

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Dr.M.G.R Educational and Research Institute University,
Chennai – 95.
Department of Mathematics
Sample questions for Ph.D admission entrance examination in Mathematics

Model Question List : http://www.drmgrdu.ac.in/Enterence%2...for%20Ph.D.htm
Model Question Paper : http://www.drmgrdu.ac.in/Enterence%2...athematics.pdf


Objective type questions(1 mark for each question): (10x1=10)Marks
1. The function ( ) f x x = , (x is real) is
(a) Not differentiable at any point
(b) Differentiable at all points
(c) Differentiable only at x=0
(d) Not differentiable at x=0

2. If X has the variance 9 and Y has the variance 5 then Var(2X+Y-5) is equal to
(a) 18
(b) 23
(c) 41
(d) 32

3. A: Every optimal solution is feasible solution in L.P.P
B: Every feasible solution is optimal solution in L.P.P
(a) A & B both true
(b) A is true
(c) B is true
(d) Both A & B false

Subjective type questions (Five Marks) (6x5=30) Marks

1. If V is a finite dimensional vector space, with direct sum of its subspaces, U and W then show that dim(U+W) = dim(U) + dim(W).

2. Solve ''' cos(2 1) y y x + = - .

3. Do the Mathematical formulation of the following problem:
A Manufacturer of leather belts makes three types of belts, A, B, and C which are processed on three Machines M1, M2 and M3. Belt A requires 2 hours on Machine M1and 3 hours on Machine M3. Belt B requires 3 hours on Machine M1, 2 hours on Machine M2 and 2 hours on Machine M3, and Belt C requires 5 hours on Machine M2 and 4 hours on Machine M3. There are 8 hours of time per day available on Machine M1, 10 hours of time per day available on Machine M2 and 15 hours of time per day available on Machine M3. The profit gained from belt A is Rs.3 per unit, from belt B is Rs.5 per unit, from belt C is Rs.4 per unit.