The syllabus is divided into sections A,B and C. Section A has to be mandatorily answered by all the candidates. The students will get the option of answering questions from either section B or C.

The Mathematics paper will be of 100 marks and of 3 hours duration.

Section A will have 9 questions in total ( 80 marks). Question no: 1 has to be answered compulsorily. Out of the rest of the 8 questions, the candidate can answer any 5.

From section B/C (20 marks) , the candidates can answer 2 out 3 questions from any of the two sections.

SECTION A

**Determinants and Matrices**

(i) Determinants

- Order.
- Minors.
- Cofactors.
- Expansion.
- Properties of determinants.
- Simple problems using properties of determinants

Cramer’s Rule

(ii) Matrices

Martin’s Rule

**Boolean Algebra**

Boolean algebra as an algebraic structure, principle of duality, Boolean function. Switching circuits, application of Boolean algebra to switching circuits.

**Conics**

As a section of a cone.

Definition of Foci, Directrix, Latus Rectum.

(i) Parabola

(ii) Ellipse

(iii) Hyperbola

**Inverse Trigonometric Function****Calculus**

(i) Differential Calculus

(ii) Integral Calculus

**Correlation and Regression****Probability****Complex Numbers****Differential Equations**

- Definition and meaning of correlation and regression coefficient.
- Coefficient of Correlation by Karl Pearson.
- Rank correlation by Spearman’s (Correction included).
- Lines of regression of x on y and y on x.

- Random experiments and their outcomes.
- Events: sure events, impossible events, mutually exclusive events, independent events and dependent events.
- Definition of probability of an event.
- Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem).

- Argument and conjugate of complex numbers.
- Sum, difference, product and quotient of two complex numbers additive and multiplicative inverse of a complex number.
- Simple locus question on complex number;
- Triangle inequality.
- Square root of a complex number.
- Demoivre’s theorem and its simple applications.
- Cube roots of unity: 1,ω,ω
^{2}; application problems.

- Differential equations, order and degree.
- Solution of differential equations.
- Variable separable.
- Homogeneous equations and equations reducible to homogeneous form.
- Linear form

SECTION B

**Vectors****Co-ordinate Geometry in 3-Dimensions**

- Scalar (dot) product of vectors.
- Cross product – its properties – area of a triangle, collinear vectors.
- Scalar triple product – volume of a parallelopiped, co-planarity.

**(i) Lines**

- Cartesian and vector equations of a line through one and two points.
- Coplanar and skew lines.
- Conditions for intersection of two lines.
- Shortest distance between two lines.

**(ii) Planes**

- Cartesian and vector equation of a plane.
- Direction ratios of the normal to the plane.
- One point form.
- Normal form.
- Intercept form.
- Distance of a point from a plane.
- Angle between two planes, a line and a plane.
- Equation of a plane through the intersection of two planes

**Probability**

Baye’s theorem; theoretical probability distribution, probability distribution function; binomial distribution – its mean and variance.

SECTION C

**Discount**

True discount; banker’s discount; discounted value; present value; cash discount, bill of exchange.

** 4. ****Annuities**

Meaning, formulae for present value and amount; deferred annuity, applied problems on loans, sinking funds, scholarships.

**Linear Programming**

Introduction, definition of related terminology such as constraints, objective function, optimization, isoprofit, isocost lines; advantages of linear programming; limitations of linear programming; application areas of linear programming; different types of linear programming (L.P.), problems, mathematical formulation of L.P problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimum feasible solution.

**Application of derivatives in Commerce and Economics**

Cost function, average cost, marginal cost, revenue function and break even point.

**Index numbers and moving averages**

- Price index or price relative.
- Simple aggregate method.
- Weighted aggregate method.
- Simple average of price relatives.
- Weighted average of price relatives (cost of living index, consumer price index).

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