8/9/2019 Syllabus and Model Question Paper for MSc.
Mathmatics
1/2
M. Sc. Programme in Mathematics
Syllabus for the Entrance Examination for M.Sc. in
Mathematics
Differential Equations: Formation of differential equation -
First order and first degree differential
equations- orthogonal trajectories- Linear Differential
Equations with constant coefficients- Variation of
Parameters-Simuitaneous differential equations.
Mathematical Analysis: Real numbers-Sequences-Series-Test Of
convergence-Absolute and conditional
convergence-Limits, Continuity and differentiability-Mean value
theorems -Taylor's and Maclaurin's
expansions-Riemann integration - properties of Riemann
integrals.
Vector Calculus: Vector differentiation - Gradient, Divergence
and Curl- Line, Surface and Volume
integrals -Stokes, Green's and Gauss divergence theorems.
Linear Algebra: Elementary transformation -Rank of-matrix-
Normal form- System of homogeneous and
non - homogeneous linear equations - Eigen Values- Eigen
vectors- Cayley- Hamilton theorem- Vector
space - Subspace - linear dependence and independence- Span of a
set- Basis, Dimension- Linear
Transformation- Rank and nullity -Gram-Schmidt orthogonalisation
-Quadratic forms.
Modern Algebra:-Groups - Subgroups - Lagrange's-Theorem -
Hormomorphism-of groups - Definitions
and elementary properties of Rings and Fields.
Coordinate Geometry of Three Dimensions: Coordinates- Direction
Ratios and Cosines - Angle between
two lines, Angle between planes, Lines- Coplanarity Of lines -
Shortest distance between two lines -
Spheres -tangent planes Polar planes - Conjugate planes and
line.
Probability: Probability, Conditional Probability, -
Independence, Bayes Theorem, Random Variable,
Probability Distributions, Binomial, Poisson and Normal
distributions.
Complex Analysis: Analytical functions, Harmonic functions,
Cauchy's theorem, Cauchy's integral
Formula, Taylor and Laurent expansions, Poles and Residues.
Numerical Analysis: Solution of Algebraic and Transcendental
-equations, Bisection, -Newton Raphson
and fixed point iteration methods, Numerical solutions of system
of linear equations- Interpolation -Newtons-divided difference,
Newtons-backward and 'forward formulae, Numerical solutions of
-ODEs-
Euler and Runge -Kutta Methods.
8/9/2019 Syllabus and Model Question Paper for MSc.
Mathmatics
2/2
Model Questions
1.
The value of k for which the system of equations
x+y+z=0
y+2z=0
kx+z=0
has more than one solution is
(a)
-1 (b) 0 (c)1
2 (d) 1
2. If A is an invertible matrix whose inverse is the matrix 3 45
6
, then A is
(a) 6 45 3 (b) 1/3 4
5 1/6
(c) 3 25/2 3/2 (d)1/3 1/41/5 1/6
3. The function f(x) = |x|- x is
(a) continuous at x = 0 (b) discontinuous at x= 0
(c) differentiable at x = 0 (d) discontinuous at x = 1
4. The solution of the ordinary differential equation x y = x,
satisfying the condition
y(1) = 3 is
(a) y = x log x + 3x (b) y=3+x
(c) y = 3 + log x (d) y = 3x log x
5. Let f(x, y)= (x, y) be a force field acting on a particle
which moves along the unit circle x2+y
2= 1
once. Then the work done is
(a) (b) 1 (c) (d) 0
6. The mean and variance of Binomial distribution b(x; n,p) are
4 and4
3respectively. The probability
of getting 2 successes is
(a)1
20 (b)
20
420 (c)
20
243 (d)
1
243
7. Poles of f(z) = tanz are
(a)[2+12
] (b)2
(c) n (d) n + 2
