# Jammu Kashmir BPEE CET Mathematics Syllabus

**Jammu Kashmir BPEE Common Entrance Test Mathematics Syllabus** – Page 2

**Unit I : Algebra**

**1) Sets, Relations and Functions : 14 Marks**

Sets and their representation, finite and infinite sets, subsets, empty set, and universal set, complement of a set, union and intersection of sets and their algebraic properties including De-Morgans Laws. Difference of sets and symmetric difference of sets. Cartesian product of sets, Relations, Equivalence relations. Function (Mapping). Domain and range of function. Into, onto, one-one and many one functions. Composition of functions.

**2)** Complex number in the form a+ib, representation of complex numbers by points in a plane. Argand diagram, algebra of complex numbers. Real and imaginary parts of complex numbers. Modulus and argument (amplitude) of a complex number, complex conjugate. Polar representation of complex numbers Square root of a complex number, cube roots of unity. Triangle inequality.

**3)** Theory of Quadratic Equations Solution of quadratic equation in complex number system, ax 2 + bx + c = 0; a, b, c, R. Relation between roots and coefficients, nature of roots of a quadratic equation. Formation of quadratic equation with given roots.

**4) Sequences and Progressions :**

Arithmetic progression and geometric progression, nth term, sum of n terms of an A.P, Arithmetic mean, insertion of Arithmetic means between any two given numbers, nth term and sum to n terms and infinite number of terms of a G.P. Insertion of G.M. between any two given numbers.Recurring decimal numbers and G.P.

**5) **Binomial Theorem: Expansion of binomial with positive integral index, general and particular terms. Finding middle terms and term independent of x, Expansion of binomial with any index.

**6) Permutation and Combination :**

Fundamental principals of counting. The factorial notation. Permutation as an arrangement, meaning of P(n,r), meaning of C(n,r). Application of permutation and combination.

**7) Exponential and Logarithmic Series :**

Concept of e as the sum of infinite series, proof of 2<e<3 exponential function ex as the infinite series 1+x/1!+—- and its graph logarithmic function log x and its graph. The infinite series for loge(1+X) loge(1-X)

**Unit II : Two Dimensional Geometry – 07 Marks**

**1) Point :** Distance formula, area of a triangle. Condition of collinearity of three points and section formula. Centroid and in center of triangle. Locus and its equation. Slope of line. Intercept of a line on coordinate axes.

**2) Straight line :** various forms of equations of a line, intersection of lines. Angle between two lines. Lines parallel and perpendicular to a given line. Condition for concurrency of three lines. Distance of a point from a line and distance between two parallel lines. Coordinates of orthocentre and circumcentre of a triangle.

**3) Pair of straight lines :** Homogeneous equation of second degree in x and y represents a pair of straight lines passing through origin. Angle between pair of lines through origin and condition of parallelism and perpendicularity. Joint equation of angle bisectors. Condition for general second degree equation to represent a pair of lines.

**4) Circle :** Standard equation of a circle, general form of the equation of a circle, its center and radius. Equation of circle whose end points of diameter are given. Point of intersection of a line and a circle with center at origin and condition for a line to be tangent to a circle. Length of tangent, equation of tangent to a circle at a given point Equation of family of circles through the intersection of two circles.

**5) Conic section :** Equations of parabola, ellipse and hyperbola in standard forms. Condition for a line y = mx +c to be tangent to parabola, ellipse and hyperbola.

**Unit III : Trigonometry – 09 Marks**

1) Circular functions and their properties

2) Application of circular functions of difference and sum of two angles. Application of sum and product of sines and of cosines of angles.

3) Application of sine and cosine rule.

4) Trigonometric equations.

5) Inverse trigonometric functions – Principle values, properties of inverse trigonometric functions within the principle values.

**Unit IV : Determinants and Matrices – 06 Marks**

1) Determinants: their expansion, minors and cofactor, properties of determinants.

2) Application of determinants in solution of equations up to three variables (Crammer rule), Area of triangle.

3) Matrices, definition with examples, types of matrices, equality of matrices, addition and scalar multiplication of matrices and their properties.

4) Transpose of a matrix, symmetric and skew symmetric matrices, matrix multiplication.

5) Adjoint and inverse of matrices. Solution of simultaneous linear equations up to three variables by matrix inversion method.

**Note :** In the treatment up to 3×3 determinants and matrices be considered.

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BPEE CET Common Entrance Test Mathematics Syllabus

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