BIT - Birla Institute of Technology - Online Entrance Test for M.Sc. |
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(40
questions – objective type)
Algebra and Trigonometry:
Simple inequalities,
Relations between roots and
Co-efficient of a polynomial
equation, Cardon’s method
for solving a cubic
equation. Summation of
series, Hyperbolic
functions.
Abstract and Linear Algebra:
Groups, Subgroups, cyclic
groups, normal subgroups.
Elementary ideas of rings,
integral domains and fields
with examples. Rank of a
matrix, Solution of a system
of linear equations by rank
method, consistency and
inconsistency of a system of
linear equations. Cayley
Hamilton’s theorem.
Real Analysis:
Convergences and Divergences
of an infinite series. Tests
for convergence. Comparison
tests, radical tests, ratio
and higher ratio tests
(Raabe’s test, Gauss’s test,
log test and higher log
tests). Continuity and
Differentiability.
Geometry:
Polar equation of conics.
Equations of cylinder, cone
and central conicoids.
Calculus:
Successive Differentiation,
Leibnitz’s Theorem, Taylor’s
and Maclaurin’s theorems.
Pedal equations Curvature,
asymptotes. Maxima and
Minima for a function of two
variables. Method of
Undetermined multipliers.
Partial Differentiation,
Euler’s Theorem, change of
variables, Taylor’s series
for two variables,
envelopes. Reduction
Formulae, Definite
Integrals. Applications in
finding length, areas,
volumes and surfaces.
Complex Analysis:
Continuity,
differentiability and
analyticity of a function of
a complex variable, Cauchy
Riemann equation, harmonic
functions. Milne Thomson’s
method’ to construct
analytic function.
Differential Equations:
Higher order differential
equations with constant
Co-efficients, complementary
function and particular
integrals. Cauchy
homogeneous forms, Solution
by change of independent
variables. Variation of
parameters.
Vectors and Mechanics:
Scalar and vector point
functions, gradient,
divergence and curl,
conservative field,
solenoidal and irrotational
vectors. directional
derivatives. Common
Catenary, Parabolic motion,
Differential equation of a
central orbit in polar and
pedal forms.
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