__APPLIED MATHEMATICS__

**Max Marks : 40 Marks**

**ALGEBRA**

**DETERMINANTS. 1 X 2 = 2M**

Definition, Order,
Expansion of 2

^{nd}& 3^{rd}order Determinants by means of examples. Problems on finding unknown quantity in a 2^{nd}& 3^{rd}determinant using expansion. Solving simultaneous linear equations by determinant method ( Cramer’s rule).**MATRICES. 1 X 3 = 3M**

Determinant value of a
square matrix. Singular and non singular matrices. Minor and co factor of an
element of a matrix. Adjoint of a matrix. Inverse of a matrix. Characteristics
equations of a square matrix and its roots, problems.

**BINOMIAL THEOREM. 1 X 2 = 2M**

Meaning of

^{n}Cr and its value. Binomial theorem for (x + a)^{n}, where n is a positive integer. Expansion. Finding constant term, co-efficient of x^{n}, particular term and middle term(s).**VECTOR ALGEBRA. 1 X 3 = 3M**

Definition of vector.
Magnitude of a vector. Position vector. Addition and subtraction of vector.
Product of vectors, scalar and vector product. Geometrical meaning of scalar
and vector product. Applications of dot(scalar) and cross(vector) product:
Projection of a vector on another vector. Area of parallelogram and area of
triangle. Work done by a force and moment of force, problems

**TRIGONOMETRY**

**TRIGONOMETRIC RATIOS OF AN ACUTE ANGLE. 1 X 2 = 2M**

Defination of Trigonometric ratios in terms
of sides of a triangle for an acute angle. Trigonometric identities.
Trigonometric ratios of standard angles: The numerical value of trigonometric
ratios of standard angles like 0

^{0}, 30^{0}, 45^{0}, 60^{0}and 90^{0}, problems**ALLIED ANGLES. 1 X 2 = 2M**

Angle of any magnitude,
sign of the trigonometric ratios. Meaning of allied angles. Trigonometric
ratios of allied angles in terms of θ. Complimentary angles and relation
between trigonometric ratios of complimentary angles, problems.

**COMPOUND ANGLES. 1 X 2 = 2M**

Recall Sin( A + B) and
Cos(A + B). Find Tan( A + B) using
Sin( A + B) and Cos (A + B). Write the
formulae for Sin( A - B), Cos(A - B) and tan( A - B), problems.

Write ratios of multiple
angles of 2A and 3A and sub multiple angle formulae, problems.

**TRANSFORMATION FORMULAE. 1 X 1 = 1M**

Express sum or difference
of Sine and Cosine of an angles in to product form. Express product of Sine and
Cosine of angles in to sum or difference form, simple problems.

**INVERSE TRIGONOMETRIC FUNCTIONS. 1 X 1 = 1M**

Definition. Principle
values of inverse trigonometric functions. Results like sin

^{-1}x + cos^{-1}x =Л/2 = tan^{-1}x + cot^{-1}x = cosec^{-1}x + sec^{-1}x, tan^{-1}x + tan^{-1}y = tan^{-1}[(x+y)/(1-xy)] etc., problems.**ANALYTICAL GEOMETRY**

**BASIC CONCEPTS OF ANALYTICAL GEOMETRY. 1 X 3 = 3M**

Defination of a point in a
plane, Specification of a point using co-ordinate system. Points on X-axis and
Y-axis. Distance formula. Section formulae. Co-ordinate of a point which divide
the line internally and externally in the given ratio. Mid point formula.
Centroid, area of a triangle and collinear points, problems.

**STRAIGHT LINES. 1 X 3 = 3M**

Inclination of a line with
horizontal line and its slope. Intercept of a straight line. Slope of a line
parallel to X-axis and Y-axis. Conditions for two lines to be parallel and
perpendicular. Equations of straight
lines y = mx + c, y – y

_{1}= m (x – x_{1}), y – y_{1}= (y_{2}– y_{1}/ x_{2}– x_{1}) (x – x_{1}), (x / a ) + (y / b) = 1. Equation of lines through a point and parallel or perpendicular to a given line. Angle between two lines, problems.**CALCULUS**

**LIMITS. 1 X 2 = 2M**

Variables and Constants.
Definition of function. Concept of x tends to ‘a’. Definition of limit of a
function. Problems on limit of a function by factorization, rationalization
when x tend to ‘0’, when x tend to ‘∞’ and x tend to ‘a’. Algebraic and Trigonometric
limits, problems.

**DIFFERENTIAL CALCULUS. 1 X 4 = 4M**

List of standard
derivatives. Rules of differentiation: Sum, product and quotient of functions.
Derivatives of function of a function(Chain rule). Derivatives of inverse
Trigonometric functions, Hyperbolic functions and inverse of hyperbolic
functions, Implicit functions, Parametric functions. Logarithmic
differentiation. Successive differentiation up to second order, problems.

**APPLICATIONS OF DIFFERENTIATION. 1 X 2 = 2M**

Geometrical meaning of
derivative. Equation of tangent and normal to the curve y = f(x) at a given
point. Derivative as a rate measure. Maxima and minima of a function, problems

**INTEGRAL CALCULUS. 1 X 3 = 3M**

Definition of Integration.
List of standard integrals. Rules of integration (only statement)

Integration by substitution method.
Integration by parts. Rule of integration by parts, problems.

**DEFINITE INTEGRALS. 1 X 2 = 2M**

Definition of Definite
integral. Theorems on definite integrals, problems.

**APPLICATIONS OF DEFINITE INTEGRALS. 1 X 1= 1M**

Find area, volume and r m
s value of a function, problems.

**DIFFERENTIAL EQUATIONS. 1 X 2 = 2M**

Definition, example, order
and degree of differential equation with examples. Formation of differential
equation by eliminating arbitrary constants up to second order. Solution of D E
of first degree and first order by variable separable method. Linear equations
and its solution.