বিষয় : গণিত (Mathematics)
বিষয় কোড : ৪১৪
পূর্ণমান : ১০০
Algebra (including Trigonometry):
a. Inequalities: Order properties of
real number, Inequalities involving different types of means, Inequalities of
Cauchy, C'hebyshev. Weierstrass.
b. Complex numbers and Demoiver's
theorem with applications.
c. Summation of algebraic and
trigonometric series.
d. Theory of equations: Relations
between roots and co-efficients, Symmetric functions of roots, Simple
transformations.
e. Linear algebra with vector spaces,
Eigenvalues and Eignevectors.
f. Set theory: Set and subsets, Set
operations, Cartesion product of two sets, Operations on family of sets.
g. Functions, One-one function, Onto
function, Inverse functions, Domain and Range.
Geometry (Analytical Geometry of two
and three dimensions)
a. Pair of straight lines.
b. General equation of the second
degree: Reduction of standard forms, Properties of parabola, Ellipse,
Hyperbola.
c. Planes and straight lines in three
dimensions, Shortest distance between two straight lines.
d. Vectors in three dimensional space
with applications to geometry.
Diferential Calculas:
a. Limit & Continuity
b. Differentiation (including
successive differentiation)
c. Means Value theorem, Taylor's
theorem.
d. Maxima and Minima.
e. Tangents and Normals.
Intigral Calculas (Including
differential equations):
a.
Techniques of indefinite integration
b.
Definite integrals:
c.
Determination of areas
d.
Defferential equation's: Equations of first order and first degree, Linear
equations with constant co-efficents.
The
paper will consist of four parts, having 3 questions of equal value in each
part. Candidates will be required to answer six questions in all, taking at
least one question from each part but not more than two questions from any one
part.