**Special Class Railway Apprentices Examination – SCRA 2016 Mathematics Syllabus**

**UPSC Special Class Railway Apprentices ( SCRA ) Exam 2016 Notification will be announced soon.**

Paper I | English |

General Knowledge | |

Psychological Test | |

Paper II | Physics |

Chemistry | |

Paper III | Mathematics |

**Paper – III**

**Mathematics**

**1. Algebra :**

Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal set and Power set, Venn diagrams and simple applications. Cartesian product of two sets, relation and mapping – examples, Binary operation on a set – examples.

Representation of real numbers on a line. Complex numbers : Modulus, Argument, Algebraic operations on complex numbers. Cube roots of unity. Binary system of numbers, Conversion of a decimal number to a binary number and vice-versa. Arithmetic, Geometric and Harmonic progressions. Summation of series involving A.P., G.P., and H.P.. Quadratic equations with real co-efficients. **Quadratic expressions :** extreme values. Permutation and Combination, Binomial theorem and its applications.

Types of matrices, equality, matrix addition and scalar multiplication – properties. Matrix multiplication – non-commutative and distributive property over addition. Transpose of a matrix, Determinant of a matrix. Minors and Co-factors. Properties of determinants. Singular and non-singular matrices. Adjoint and Inverse of a square-matrix, Solution of a system of linear equations in two and three variables-elimination method, Cramers rule and Matrix inversion method ( Matrices with m rows and n columns where m, n less than equal to 3 are to be considered ).

Idea of a Group, Order of a Group, Abelian group. Identity and inverse elements-Illustration by simple examples.

**2. Trigonometry :**

Addition and subtraction formulae, multiple and sub-multiple angles. Products and factoring formulae. Inverse trigonometric functions – Domains, Ranges and Graphs. DeMoivre’s theorem, expansion of Sin n0 and Cos n0 in a series of multiples of Sines and Cosines. Solution of simple trigonometric equations. **Applications :** Heights and Distance.

**3. Analytic Geometry ( two dimensions ) :**

Rectangular Cartesian. Coordinate system, distance between two points, equation of a straight line in various forms, angle between two lines, distance of a point from a line. Transformation of axes. Pair of straight lines, general equation of second degree in x and y – condition to represent a pair of straight lines, point of intersection, angle between two lines. Equation of a circle in standard and in general form, equations of tangent and normal at a point, orthogonality of two cricles. Standard equations of parabola, ellipse and hyperbola – parametric equations, equations of tangent and normal at a point in both cartesian and parametric forms.

**4. Differential Calculus :**

Concept of a real valued function – domain, range and graph. Composite functions, one to one, onto and inverse functions, algebra of real functions, examples of polynomial, rational, trigonometric, exponential and logarithmic functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative – applications. Derivative of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function, chain rule. Second order derivatives. Rolle’s theorem (statement only), increasing and decreasing functions. Application of derivatives in problems of maxima, minima, greatest and least values of a function.

**5. Integral Calculus and Differential equations :**

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expression, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals-determination of areas of plane regions bounded by curves – applications.

**Differential equations :** Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equation of various types – examples. Solution of second order homogeneous differential equation with constant co-efficients.

**6. Vectors and its applications :**

Magnitude and direction of a vector, equal vectors, unit vector, zero vector, vectors in two and three dimensions, position vector. Multiplication of a vector by a scalar, sum and difference of two vectors, Parallelogram law and triangle law of addition. Multiplication of vectors – scalar product or dot product of two vectors, perpendicularity, commutative and distributive properties. Vector product or cross product of two vectors – its properties, unit vector perpendicular to two given vectors. Scalar and vector triple products. Equations of a line, plane and sphere in vector form – simple problems. Area of a triangle, parallelogram and problems of plane geometry and trigonometry using vector methods. Work done by a force and moment of a force.

**7. Statistics and probability :**

**Statistics :**

Frequency distribution, cumulative frequency distribution – examples. Graphical representation – Histogram, frequency polygon – examples. Measure of central tendency – mean, median and mode. Variance and standard deviation – determination and comparison. Correlation and regression.

**Probability :**

Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events.

** Definition of Probability :**

classical and statistical – examples. Elementary theorems on probability – simple problems. Conditional probability, Bayes’ theorem – simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

**8. UPSC Personality Test :**

Each candidate will be interviewed by a UPSC Boards for Interview who will have before them a record of his career both academic and extramural. They will be asked questions on matters of general interest. Special attention will be paid to assessing their potential qualities of leadership, initiative and intellectual curiosity, tact and other social qualities, mental and physical energy, power of practical application and integrity of character.

please send my scra 2012 admit card.

Hi

Pls visit the UPSC official website for E-admit card : http://upsc.nic.in/onlineadmitcard/main.aspx

Regards.

when will i get my admit card sir?

Hi

Pls visit the UPSC official website : http://upsc.gov.in/exams/misc/scraecard.htm#PageTop

Regards.

sir i do not get my admit card by post, so in this case can i sit in the exam with e-admit card.

Hi

Yes you can take that e-admit card print out copy with you to sit for the SCRA Exam.

In case the photograph is not printed / available on the e-Admit Card ( Admission Certificate ), candidates are advised to carry three (3) photographs ( one identical photograph for each session ) alongwith proof of identity such as Identity Card or Voter Identity Card or Passport or Driving License and printout of e-Admit Card ( Admission Certificate ) at the venue of the Examination.

Regards.

when will the application form of SCRA exam declared

when will the application forms of scra come out?

Hi

The notification for SCRA Exam 2013 has not yet been announced. Please wait and keep watching : http://www.upscexam.com/notification/upsc/Union-Public-Service-Commission-UPSC-Examination-Time-Table.html

sir this is my detal please sand me my admit coard

can i know the detail of scra

what is the timing of all 3 papers of SCRA exam.wich will be conduct on 29 01 2012

When we receive our admit card?

May i want to know the marks evaluation pattern of SCRA.

What was cut off marks of SCRA and is there sectional cut off for every section of exam.

plz reply on my mail .

thanx.

when i’ll recieve my admit card and whts the sectional cut off for every section of exam

thanks