Scheme for P.S.T for recruitment to the post of Lecturer in Govt. Polytechnics in W.B.G.S. under the Technical
Education & Training Deptt., Govt. of W.B.
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| 1. Duration: 1 hour 30 minutes 1. 2. Type of test: MCQ 3. Full Marks: 100 4. No. of questions: 100 multiple choice questions with 1 mark against each question. There shall be negative marks as per norms @ 1/3 for each wrong answer. |
Syllabus for preliminary examination for recruitment to the posts of Lecturer in Mathematics
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1. Algebra : Complex Number : Demoiver’s theorem, its applications. Exponential, Sine, Cosine, Logarithm of a Complex Number. Theory of Equations : Relation between roots and co-efficients, symmetric function of roots, transformation of equation, multiple root. Determinant and matrix : Properties and applications. Inequality : AM >= GM >= HM and its applications. |
| 2.Set Theory : Basic concepts, mapping, group, ring, field. |
| 3. Boolean Algebra : Basic concepts. Boolean variables and functions and their truth tables. NOT. OR and AND gates. Binary systems. |
| 4. Vector : Vector addition, Scalar and vector product. Application of vector algebra in geometrical and trigonometrical problems. |
| 5. Calculus : Differential Calculus - Sequence, series, Limit, continuity, differentiability, Successive derivatives. Rolle’s theorem. Mean value theorem. Integral Calculus - Indefinite integral, definite integral and its properties, definite integral as limit of sum. Beta and Gama functions. |
| 6.Application of Calculus : Tangent & normal, curvature, pedal equation, curve-tracing, area, rectification. |
| 7. Differential Eguation: Linear equation, Clairaut’s equation, Complementary function, particular integral of higher order. Linear equations witl" constant Co-efficient. |
| 8. Geometry : Translation and rotation of axes. Reduction into Canonical form. Pair of straight lines. Circle, Parabola, ellipse, hyperbola — simple properties. Equation of straight lines in space, equation of plane. |
| 9. Numerical Analysis : Errors in numerical computation — gross error, round off, truncation error, significant figure, absolute, relative, percentage error. Operators - ∆ ∇∈ Difference table, Newton’s forward and backward interpolation formula. |
| 10. Probability : Basic concepts, addition and multiplication rule of probabilities. Conditional probability, Bay’s theorem. |
| 11. Dynamics : Motion in a straight line under variable acceleration, motion under inverse square law, motion in resisting medium. Impact of elastic bodies, loss of KE in direct and oblique impact. |
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