About Arunachal Pradesh Public Service Commission: Immediately after the reconstitution of Arunachal Pradesh as a State, a need was felt for the State to have its own Public Service Commission to recruit and manage the Public Service of the State. Thus, the Arunachal Pradesh Public Service Commission was established on 4 April 1988 under Article 315 of the Indian Constitution, with Shri TS Deori as its first Chairman and Shri M.R Das, IAS(Retd) & Shri Y. Tikhak as its first two Members. The Commission today consists of a Chairman, and four members and is served by a Secretariat. Arunachal Pradesh Public Service Commission Regulations No OM-15/88 dated 29 March 1988, as amended from time to time, govern the functioning of the Commission.
The Commission, till recently, was functioning from a temporary office building, allotted by the State Government, earlier meant for the Administrative Training Centre. A new building for holding Recruitment Examinations, with a capacity of 920 seats, was added in 2018. A Guest House came up in 2019. The Commission’s permanent Campus has been approved and is to come up, post-demolition of the existing office building. The Commission has shifted its offices to the Guest House Building and functions from there in the interim.
Detailed Syllabus:
Arunachal Pradesh Public Service Commission has released the syllabus for the posts of Trained Graduate Teacher (Mathematics). Candidates who got shortlisted in the Written test are only eligible to appear in the interview.
Paper I Syllabus:
Unit I:-
- Linear equation in two variables: Pairs of linear equations in two variables, condition for consistency and inconsistency, solution of pair of linear equations in two variables, algebraic method of solving a pair of linear equations, substitution method, elimination method, cross multiplication method.
- Principle of Mathematical Induction.:- Process of proof by induction, the principle of mathematical induction and its simple application.
- Complex number and quadratic equation:- Need for complex numbers especially V-t to motivate by the inability to solve quadratic equation x’+ I = 0, Brief description of Properties of complex numbers. Argand plane and polar representation of a complex number, solution of quadratic equation in the complex number system.
- Linear In equation: – Linear inequation, solution of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of a system of linear inequalities in two variables. Solution of a system of linear inequalities in two variables graphical.
- Permutations and Combinations: – Fundamental Principle of counting, factorial n (nl). Permutations and combinations and their simple applications.
- Binomial Theorem: – Statements and proof of the binomial theorem for positive integral indices. General and Middle terms in binomial expansion, simple application.
- Sequence and Series:- Sequence and series, Arithmetic progression (A.P), Arithmetic Mean (A.M). Geometric Progression (G.P), Geometric Mean (G.M), a sum of n terms of A.P and G.P, General terms of A.P & G.P, the relation between A.M to G.M, the sum of n terms of the special series Xn (sum of first n natural numbers), Xn2 (sum of the square of first n natural numbers) and Xn3 (sum of cubes of first n natural numbers)
UNIT -II: AREAS AND VOLUME
Area of a triangle using Heron’s formula and its application in finding the area of a quadrilateral, surface area and volume of cubes, cuboids, cones, cylinder, spheres and hemispheres.
UNIT -III: STATISTICS
Introduction of statistics, collection of data, presentation of data in tabular form, Mean, median, mode of ungrouped and grouped data, mean deviation and standard deviation of ungrouped and grouped data, variance.
Paper-II:
Unit I:- Matrices and Determinants:-
Concept, notion order, equality, types of matrices, transpose of a matrix, symmetric and skews metric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication, Concept of elementary row and column transformation,. Invertible matrices. Determinant of a square matrix (up to 3×3 order), properties of determinant, Minors and co- factors and application of determinants in finding the area ofa triangle, Adjoint and inverse of a matrix, solving a system of linear equations in two or three variable ( having unique solution ) using the inverse of a matrix.
UNIT-II: PROBABILITY
Multiplication theorem on probability, conditional probability independent events, total probability, Baye’s theorem, Random variables and probability distribution, mean and variance of the random variable, Bernoulli’s trials and Binomial distribution.
UNIT-III: VECTOR
Vector and scalars, Direction cosines and direction ratios of a vector, types of vector, the addition of vectors, multiplication of a vector by a scalar, section formula, scalar(dot) product and vector (cross) Product of two vectors, projection of a vector on another vector, scalar and vector product of three vectors
UNIT _ VI: CALCULUS
DIFFERENTIAL CALCULUS
Continuity and differentiability, derivative ol composite function, chain rule, a derivative of an inverse trigonometric function, the derivative of an implicit function, Concept of exponential and logarithmic function and their derivatives. Logarithmic differentiation, a derivative of a function expressed in parametric forms. Second-order derivative. Application of derivatives rate of change of quantities, increasing and decreasing functions, tangents and normals, maxima and minima, approximation.
INTEGRAL CALCULUS:-
Integration as the inverse process of differentiation, integration ol a variety of functions by substation, by a partial fraction and by parts, Definite integrals, Some Properties of definite integrals, Application of integrals in finding the area under simple curves, especially lines/circles/parabolas /ellipses (in standard form only ) and area between the two above said curves.
DIFFERENTIAL EQUATIONS:-
Definition, order, and degree, general and particular solution of a differential equation, Formation of differential equation whose general solution is given, Solution of differential equation by the method of separation of variables, homogenous differential equation of first order and first degree, Solution of linear differential equations of the form dy/dx + py: q where p and q are functions of x or constants ( or dx/dy + Py: Q where P, Q are functions of y or constants)
ANALYTICAL GEOMETRY
Coordinate Geometry, the Cartesian plane, coordinates of a point in the Cartesian plane, the distance between two points, sections formula, area of a triangle, straight line, slope of a line, various forms of the equation of a line, general equation of a line distance of a point form a line, Conic section, eclipse, parabola, hyperbola, circle, pair of straight lines. Homogenous equation of 2nd degree, the angle between a pair of straight lines, Condition for the general equation of 2nd degree to represent a pair of straight lines, vector and Cartesian form of the equation of straight lines in space. Shortest distance between two lines in space and equation of shortest distance, Vector and Cartesian equation of a plane, General equation of a sphere, intersection of plane and sphere, and equation of a tangent plane.
TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle, the relationship between the trigonometric ratios, trigonometric identities, trigonometric ratios of complementary angles, height and distances. Positive and negative angles, measuring angles in radians and degrees and their conversion from one measure to another measure. Identities related to sin2x, Cos 2x, tan2x, sin3x, Cos3x and tan3x. The general solution of the trigonometric equation of the type of sinx = sincr, cosx= coscr and tanx==tano. The simple application of sine and cosine formula, Inverse trigonometric function: definition, domain, range and principle value branch. Elementary properties of an inverse trigonometric function, De-moivre’s theorem for rational indices, expansion of sinnx and cosnx in the power of x, the exponential expression for circular function and its arguments, Gregory’s Series, hyperbolic function.
Important Links
| Detailed Syllabus | Click Here |
| APPSC Official Website | Click Here |
| Go to Sarkari Result | Click Here |