3appx

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.

Matrices and Determinants: 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. Identitiy 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 :

Integral Calculus : 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.

Each candidate will be interviewed by a Board 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.

1. Candidates must use only the form supplied with the information Brochure purchased from any of the designated Head Post Offices/Post Offices listed in Appendix III. Form should be purchased from designated post offices only and not from any other agency. Candidates must use the form supplied with the Information Brochure only and they should in no case use photocopy/reproduction/unauthorisedly printed copy of the Form. The form will NOT be supplied by the Commission’s office.

2. The application form must be filled in by the candidates in their own hand. Since this form will be processed on computerised machines, candidates should exercise due care in handling and filling up the application form. They should use HB pencil only to darken the circles. For writing in the boxes, they should use blue or black pen.

Since the entries made by the candidates by darkening the circles will be taken into account while processing the applications on computerised machines, they should make these entries very carefully and accurately. Entries in the boxes are meant for confirmatory purposes and these should also, therefore, be made correctly. There should be no variation between the entries made by the candidates by darkening the circles and those written in the accompanying boxes.

In case of any variation between the entries made by the candidates in the boxes and the accompanying circles, the entries in the boxes will be treated as authentic and final.

3. Candidates should ensure that the signatures appended by them in all the places viz. in their application form, Attendance List etc. and in all the correspondence with the Commission, should be identical and there should be no variation of any kind. If any variation is found in the signatures appended by him at different places, his candidature will be liable to be cancelled by the Commission.

4. No change in the entries made in original application form will be allowed under any circumstances.

5. The candidates are advised in their own interest to ensure that the applications reach the Commission’s Office on or before the closing date. Applications received in the Commission’s Office after the closing date will not be considered.

6. While filling in his application form, the candidate should carefully decide about his choice for the centre for the examination. More than one application from a candidate giving different centres will not be accepted in any case. Even if a candidate sends more than one completed application, the Commission will accept only one application at their discretion and the Commission’s decision in the matter shall be final.

7. On the Acknowledgment Card, the candidates should write their application form No. (as printed below the bar code on the form) and the name of examination viz. "Special Class Railway Apprentices' Examination, 2007". They should also write clearly and legibly their mailing address on the Acknowledgment Card. A postage stamp of Rs. 6/- should be affixed on the card. The Acknowledgment Card should not be stapled or pinned or tagged or pasted with the Application Form.

Eligibility Conditions (in brief)

(i) Age limits :

17-21 years as on 1.8.2007. (Upper age limit relaxable for SCs/STs, OBCs and certain other categories as specified in Para 3(II) of Notice).

(ii) Educational Qualifications :

Please refer para 3(III) of Notice.

(iii) Fee :

Rs. 50/- (Rupees Fifty only)

(No fee for SCs/STs only). (Ref. Para 4 of Notice).

Darken the circle against "SCRA", in the boxes pertaining to Name of examination, write SCRA starting from the first box on the left. Also write 2007 in the boxes meant for year of examination. Candidates are advised to ensure that the name of examination viz. SCRA is correctly written by them in the box. Any error in this regard may result in rejection of their application form.

If you have paid the requisite fee of Rs. 50/- (Rupees Fifty only), darken circle 1 and write 1 in the box; or

If you have not paid the fee and are claiming fee remission as SC or ST, darken circle 2 and write 2 in the box.

N.B. : Fee is payable only in the form of single Central Recruitment Fee Stamp, as per instructions against Column 12.

If you are not a physically handicapped person, darken circle 1 for No and write 1 in the box; or

If you are a physically handicapped person, darken circle 2 for yes and write 2 in the box.

If you are Orthopedically handicapped, darken circle 1 and write 1 in the box; or

If you belong to General Category (Others), darken circle 4 and write 4 in the box.

Note 1 : Candidates belonging to OBCs but comming in the Creamy Layer and thus not being entitled to OBC reservation should indicate their community as "General Category Code No. 4".

Note 2 : Candidates belonging to neither SC, ST, nor OBC communities should write Code No. 4 (General Category) against the Column for Community and not leave it blank.

Note 3 : No change in the community status indicated by a candidate in his/her application form for the Examination will ordinarily be allowed by the Commission at a subsequent stage.

For filling up this column, first write in the boxes your full name (in English) in capital letters exactly as recorded in your Matriculation/High School/Secondary or equivalent examination certificate. Write a single letter in a box. Leave a box blank between any two parts of the name. Then darken the corresponding circle below each letter. Do not darken a circle below a blank box. Do not overshoot the boxes. Abbreviate name only if necessary. Do not use any prefix such as shri, Km., Dr. etc. with your name.

Darken the appropriate circles for the day, month and year of your birth as recorded in your Matriculation/High School/Secondary or equivalent examination certificate. Then write in the boxes using numerals 01 to 31 for day; numerals 01 to 12 for month and the last two digits for the year of birth.

Write your father’s name (in English) in capital letters. Write a single letter in each box. Leave a box blank between any two parts of the name. Do not use any prefix such as Shri, Dr. etc.

Write your complete mailing address including your name in English capital letters or Hindi within the box provided for the purpose. Also write the PIN Code therein. Write with blue or black ball pen only. Do not write outside the box. Please note that this address will be photocopied as such in all letters to be sent to you and therefore, it should be very clearly and legibly written.

If you make any mistake in writing the address, cover the whole box with an exact sized white paper slip and rewrite your address on that.

Paste firmly in the space provided your recent photograph of 4 cm. x 5 cm. size preferably in black & white. Do not staple the photograph. Photograph should neither be signed by you nor it should be got attested.

Fee to be paid for the Special Class Railway. Apprentices' Examination is Rs. 50/- (Rupees Fifty only ). SC/ST candidates are not required to pay any fee. No fee exemption is however, available to OBC candidates and they are required to pay the prescribed full fee.

Fee is payable only through Central Recruitment Fee Stamp (Not postage stamps). No other mode of payment is acceptable. Obtain only one single CRF Stamp of Rs. 50/- denomination from the post office and paste it firmly within the box. After pasting the CRF Stamp on the form, get it cancelled from the post office of purchase in the space provided. Do not staple the CRF Stamp.