Arithmetic, Geometric and Harmonic progression. Permutation and Combination, Application of Binomial Theorem. Exponential and Logarithmic series. Matrix Algebra and Determinants. Trigonometrical problems on height and distance. Complex numbers and their properties.
Statistics : Measures of central Tendency, frequency distribution and probability concept.
Coordinate Geometry
: Straight Line, Circle, Ellipse, Parabola and Hyperbola.
Algebra :
Definition and simple properties of groups and subgroups, permutation groups,
cyclic groups, Cosets, Lagranges theorem on the order of subgroup of finite
group, Morphisms of groups, Cayleys theorem, Normal subgroups and quotient
groups. Fundamental theorem of homomorphism of groups.
Rings : Definiation and examples of ring (integral domain, division rings, fields), Simple properties of rings, subrings and subfields, ring homomorphism and ring isomomorphism.
Vector Space :
Definition and simple properties, subspaces, linear dependence and linear
independence of vector space, dimension of finitely generated vector space,
basic of vector space, dimension of a subspace.
Calculus and Differential
Equations : Successive differentiation, Leibnitz Theorem, Polar tangent, normal
subtangent and subnormal, derivative of an arc (Cartesian and polar). Expansion
of functions by Maclaurins and Taylors series, Indeterminate forms.
Integration of irrational algebraic and trigonometrical functions, Definite
integral. Differential equations of first order and first degree. Linear
differential equations with constant coefficients.
Linear differential
equations of any order, Maxima and Minima of one variables, Partial
differentiation with Eulers theorem and its applications.
Real Analysis :
Description of the real number system as a complete ordered field. Bounded and
unbounded sets of real numbers Supremum and infimum of a bounded set.
Neighbourhood of a point. Real sequences and their convergence, Cauchy sequence,
Cauchys general principle of convergence.
Convergence of series: comparison test, root test, ratio test Alternating series,
Leibnitz test. Continuous functions and their properties.
Verbal and Nonverbal reasoning
Sample Questions
Section A : Mathematics
(a) 0 and 1 (b) 1 and 2 (c) 2 and 3
(d) 3 and 4 (e) none of these
2.A subring of a field is
(a) integral domain (b) Skew field
(c) subring (d) field (e) none of these
3.The straight line x/a +y/b = 1 touches the curve y =bex/a at the point
(a) where it crosses the x-axis (b) where it crosses the y-axis
(c) (0,0) (d) (1,1) (e) none of these
4.Number of diagonals in a n-side polygon are
(a) n(n-1)/2 (b) n(n-3)/2 (c) n(n+3)/2
(d) n(n+1)/2 (e) n2
(a) 21/4 (b) 7/5 (c) -3/14
(d) -14/3 (e) -35/2
(a) 40 (b) 41 (c) 43
(d) 47 (e) 51
2.In a certain code MASTER is written as PDVWHU. Using the same code what is the code word for WINTER ?
(a) ZJQHUW (b) ZQLWHU (c) ZLQWUH
(d) ZQLUWH (e) ZLQWHU
3.Five boys are standing such that they form a circle. Ajay is between Ramesh and Dev, Kant is to the left of Babu, Ramesh is to the left of Kant. Who is to be the right of Ajay?
(a) Babu (b)Remesh (c) Dev
(d) Kant (e) Cannot be determined
4. How many 2s are there in the following sequence, which are preceded by but are not followed by 1?
32312423414323223123243212
(a) 1 (b) 2 (c) 3
(d) 4 (e) 5
5. In the following question find the odd one out
(a) Ant (b) Bee (c) Moth
(d) Mosquito (e) Scorpio