## Syllabus for the Second Round Competition (National Level)

### 1. Arithmetic:

i) Time and work

ii) Profit and loss

iii) Simple and compound Interest.

iv) Population growth and depreciation.

v) VAT, discount, commission and tax.

### 2. Mensuration:

i) Area and perimeter of rectangle, square, trapezium, triangles etc.

ii) Area of 4 walls, 4 walls and ceiling, 4 walls, ceiling and floor and area of path.

iii) Cost of carpeting, cementing and coloring etc.

iv) Lateral surface area, total surface area and volume of triangular prism, pyramids, cube and cuboid.

v) Curved surface area, Total surface area and volume of of cylinder, spheres, hemisphere, cones and combined solids.

### 3. Matrices, determinants and system of linear equations.

i) Definition and types of matrices, operation on matrices.

ii) Transpose of a matrices, Inverse of a matrices and rank with some properties.

iii) Dependent and independent lines, consistency and inconsistency of the lines.

iv) Solution of the system of linear equations.

### 4. Algebra

i) Laws and indices and simplification.

ii) Polynomial equation and Quadratic equation.

iii) Inequalities.

iv) Diophantine product and cross product of vectors.

### 5. Sequence and series.

i) Arithmetic sequence, geometric sequence and harmonic sequence.

ii) Sum to infinity terms and sum to n terms of the series.

iii) Arithmetic geometric series.

### 6. Complex number

Definition, operation on complex numbers, conjugate, Absolute value, square roots, cube roots and its application, Polar form and Use of De-Moivre’s theorem.

### 7. Vectors.

i) Vector geometry.

ii) Scalar Operation on complex numbers.

iii) Conjugate and absolute value of a complex numbers.

iv) Square root, cube roots and their properties.

v) Polar form and DE-Moivre’s theorem and its application.

### 8. Permutation and combination.

i) Basic principle of counting.

ii) Total no of permutations of n distinct objects taken r at a time.

iii) Circular permutation.

iv) Permutations if the objects are repeated.

v) Permutations if the objects can be repeated.

vi) Combination of the n distinct objects taken r at a time.

vii) Combinations if the objects are repeated.

viii) Mixture problem of Permutation and combination.

### 9. Probability.

i) Trials, Events, Mutually exclusive events, Dependent and independent events.

ii) Addition and Multiplication theorem of probability and their applications.

### 10. Set ,Function and Relation.

Definition, Method of describing sets, subsets, Operation on sets and cardinality of sets. Definition, types of function, Inverse of a function, composite function, transcendental function, Domain and Range. Symmetricity, odd and even function, graph of quadratic, cubic, trigonometrical function, exponential function, logarithm function etc.

### 11. Co-Ordinate Geometry.

i) Distance formula, Section formula, mid-point formula, Centroid of a triangle, orthocenter, circumcenter, slopes and intercepts.

ii) Equation of straight lines in different condition.

iii) Area of triangles and quadrilateral.

iv) Pair of straight lines, homogenous equation of second degree, second degree equation, equation of circle, equation of tangents and normal.

### 12. Geometry.

i) Measurement of angle.

ii) Trigonometrical ratios, properties and values.

iii) Inverse circular function.

iv) Properties of triangle.

v) Compound angles, multiple angles, sub multiple angles and their properties.

vi) Conditional identities, general solution of trigonometrical equation.

vii) Height and distance.

#### Number of Questions: 6

Time: 3 Hrs

Note: Questions are based on Logic.