To prepare for the exam
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Subject: Mathematics
1- Algebra
Theory of equations, A.P., G.P. and H.P., sum of squares and cubes of natural numbers,
permutation and combination, binomial theorem, exponential and logarithmic series.
Algebra of sets, relation and function, types of relations, equivalence relation, types of
functions, composition of functions, inverse of a function, binary operations on a set, group,
subgroup, normal subgroup, quotient group, cyclic group, order of an element in a group,
permutation group, even and odd permutations, Lagrange's theorem and its
consequences, group homomorphism. Determinants, types of matrices, algebraic
operations on matrices, symmetric and skew symmetric matrices, Hermitian and skew
Hermitian matrices, inverse of a matrix, rank of a matrix, application of matrix in solving
system of linear equations, eigen values, eigen vectors of a matrix, Cayley-Hamilton's
theorem and its applications.
2- Real Analysis
Sequence of real numbers, bounded and monotonic sequences, convergent sequences,
convergence of series of positive terms, comparison test, Cauchy's nth root test, ratio test,
Raabe's test, logarithmic test, De Morgan and Bertrand test. alternating series and Leibnitz
test.
3- Vector Analysis
Operations with vectors, scalar and vector product of two and three vectors and its
applications, vector differentiation, gradient, divergence and curl,
4-Complex Analysis
Complex numbers, functions of a complex variable, De-Moivre's theorem and its
applications, nth roots of unity, exponential, direct and inverse trigonometric, hyperbolic and
logarithmic functions of a complex Variable. Continuity and differentiability of complex
functions, Cauchy-Riemann equation, analytic functions, harmonic functions.
5. Calculus
Limit of a function, continuity and differentiability, Rolle's theorem, Langrange's mean
value theorem, L'Hospital rule, successive differentiation, tangent and normal, maxima
and minima, Increasing and decreasing functions. Limit, continuity and differentiability of
function of two variables, partial differentiation. Methods of integration, definite integrals,
application of integration to find area bounded by curves, length of a curve, surface area
and volumes of solids of revolution.
Solutions of differential equations of first order and of first degree.
6- Geometry
General equation of second degree and its classification as pair of straight lines, circle,
parabola, ellipse and hyperbola, Asymptotes of hyperbola, Transferring of origin and
rotation of axis.
Direction cosines and direction ratio's of a line, Cartesian and Vector equation of a plane,
Cartesian and vector equation of a line, coplanar and skew lines, shortest distance
between two lines, angle between two planes, two lines, a line and a plane, distance of a
point from a plane, sphere, cone and cylinder.
7- Statistics and Probability
Frequency distribution, Graphical representation of statistical data, Measures of central
tendency - Mean, median and mode of grouped and ungrouped data. Theorems on
addition and Multiplication of probability
How to prepare gk part for lt grade? N what will be it's weightage in the exam?
SYLLABUS GENERAL STUDIES (1) History of India and Indian National movement:- In History of India emphasis should be on broad understanding of social, economic and politic aspects of Indian history. In the Indian National movement, the candidates are expected to have synoptic view of the freedom movement, growth of nationalist and attainment of Independence. (2) Indian and World Geography- Physical, Social, Economic Geography of India and the World :- Questions on the Geography of India will relate to Physical, Social & Economic Geography of India. In World Geography only general understanding of the subject will be expected. (3) Indian Polity and Governance, Constitution, Political system, Panchayati Raj & Public Policy, rights-issues etc :- Indian polity and Governance questions will test knowledge of country's Constitution, political- system including Panchayati Raj and Community Development. (4) Indian Economy and Social Development :- The candidates will be tested withrespect to problems and relationship between population, Environment, Urbanisation., broad features of economic policy in India and Indian Culture. (5) Current Events of National and International Importance:- This will also include questions on Games & Sports. (6) Indian Agriculture :- The candidates will be expected to have general Understanding of agriculture in India, agricultural produce and its marketing. (7) General Science :- Questions On General Science will cover general appreciation and Understanding of science including matters of everyday observation and special study of any scientific discipline. This will also include questions on role of science and technology in the development of India. (8) Elementary Mathematics up to class 10th level :-Arithmetic, Algebra and Geometry. Note:-The candidates are expected to have general awareness about the above topics with special reference to UP.
Plan of Examination & Syllabus Plan of Examination There will be one question paper of multiple choice objective type and each question will carry 01 Marks. The aforesaid Question paper will be divided into two parts: Part first (1) – General Studies – 30 Questions (Objective Type) Part second (2) – Main Subject – 120 Questions (Objective Type) Total Number of Questions – 150 Time Period – 2.00 hrs. (120 Minutes) Maximum Marks – 150 NOTE: For the post of Assistant Teacher, Social Science (Men/Women Branch), there shall be 04 sections in the main subject viz. Geography, History, Economics and Civics comprising of 60 questions in each section. The candidates shall choose any 02 sections out of the aforesaid 04 sections and answer them.
Can candidate with B.tech Mechanical+ B.ed eligible to appear?