MATHS (300 Marks)

  1. 1. Algebra
  1. a). Concept of a set.
  2. b). Operations on set.
  3. c). Venn diagrams.
  4. d). De Morgan laws.
  5. e). Cartesian product.
  6. f). Relation.
  7. g). Equivalence relation.
  8. h). Representation of real numbers on line.
  9. i). Complex numbers.
    1. i. Basic properties.
    2. ii. Modulus.
    3. iii. Argument.
    4. iv. Cube roots of unity.
  10. j). Binary system of numbers.
    1. i. Conversion of a number in decimal system to binary system.
    2. ii. Conversion of a number in binary system to decimal system.
  11. k). Arithmetic, geometric & harmonic progressions.
  12. l). Quadratic equations with real coefficients.
  13. m). Solution of linear in-equations of two variables by graphs.
  14. n). Permutation & combination.
  15. o). Binomial theorem & its applications.
  16. p). Logarithms & their applications.
  1. 2. Matrices and determinants
  1. a). Types of matrices.
  2. b). Operations on matrices.
  3. c). Determinant of a matrix.
  4. d). Basic properties of determinants.
  5. e). Adjoint & inverse of a square matrix.
  6. f). Applications
    1. i. Solution of a system of linear equations in two or three unknowns by cramer’s rule.
    2. ii. Solution of a system of linear equations in two or three unknowns by matrix method.
    1. 3. Trigonometry
    1. a). Angles & their measures in degrees.
    2. b). Angles & their measures in radians.
    3. c). Trigonometrical ratios.
    4. d). Trigonometric identities.
    5. e). Sum & difference formulae.
    6. f). Multiple & sub-multiple angles.
    7. g). Inverse trigonometric functions.
    8. h). Applications
      1. i. Height & distance.
      2. ii. Properties of triangles.
      1. 4. Analytical geometry of two & three dimensions
      1. a). Rectangular Cartesian coordinates system.
      2. b). Distance formula.
      3. c). Equation of a line in various forms.
      4. d). Angle between two lines.
      5. e). Distance of a point from a line.
      6. f). Equation of a circle
        1. i. In standard form.
        2. ii. In general form.
      7. g). Standard forms of parabola.
      8. h). Standard forms of ellipse.
      9. i). Standard forms of hyperbola.
      10. j). Eccentricity & axis of a conic.
      11. k). Point in a three dimensional space.
      12. l). Distance between two points (in two & three dimensional space).
      13. m). Direction cosines.
      14. n). Direction ratios.
      15. o). Equation of two points.
      16. p). Equation of a plane in various forms.
      17. q). Equation of a line in various forms.
      18. r). Angle between two planes.
      19. s). Angle between two lines.
      20. t). Equation of a sphere.
        1. 5. Differential calculus
        1. a). Concept of real valued function
          1. i. Domain of a function
          2. ii. Range of a function
          3. iii. Graph of a function
        2. b). Composite functions
          1. i. One to one functions.
          2. ii. Onto functions.
          3. iii. Inverse functions.
        3. c). Notion of limit.
        4. d). Standard limits – examples.
        5. e). Continuity of functions
          1. i. Examples.
          2. ii. Algebraic operations on continuous functions.
        6. f). Derivative of a function at a point.
        7. g). Geometrical interpretation of a derivative & its applications.
        8. h). Physical interpretation of a derivative & its applications.
        9. i). Derivatives of sum, product & quotient of functions.
        10. j). Derivative of a function w.r.t another function.
        11. k). Derivative of a composite function.
        12. l). Second order derivatives.
        13. m). Increasing & decreasing functions.
        14. n). Applications of derivatives in problems of
          1. i. Maxima.
          2. ii. Minima.
          1. 6. Integral calculus & differential equations
          1. a). Integration of inverse of differentiation.
          2. b). Integration by substitution.
          3. c). Integration by parts.
          4. d). Standard integrals involving
            1. i. Algebraic expressions.
            2. ii. Trigonometric functions.
            3. iii. Exponential functions.
            4. iv. Hyperbolic functions.
          5. e). Evaluation of definite integrals - applications.
          6. f). Determination of areas of plane regions bounded by curves – applications.
          7. g). Definition of order of a differential equation.
          8. h). Formation of differential equation by examples.
          9. i). General solution of a differential equation.
          10. j). Particular solution of a differential equation.
          11. k). Solution of first order differential equations of various types – examples.
          12. l). Solution of first degree differential equations of various types – examples.
          13. m). Applications in problems of growth.
          14. n). Applications in problems of decay.
            1. 7. Vector algebra
            1. a). Vectors in two dimensions.
            2. b). Vectors in three dimensions.
            3. c). Magnitude of a vector.
            4. d). Direction of a vector.
            5. e). Unit vectors.
            6. f). Null vectors.
            7. g). Addition of vectors.
            8. h). Scalar multiplication of vectors.
            9. i). Scalar product of dot product of two vectors.
            10. j). Vector product or cross product of two vectors.
            11. k). Applications
            1. i. In work done by a force.
            2. ii. In moment of a force.
            3. iii. In geometrical problems.
            1. 8. Statistics & probability
            1. a). Statistics
              1. i. Classification of data – examples.
              2. ii. Frequency distribution – examples.
              3. iii. Cumulative frequency distribution – examples.
              4. iv. Graphical representation of histogram – examples.
              5. v. Graphical representation of pie-chart – examples.
              6. vi. Graphical representation of frequency polygon – examples.
              7. vii. Measures of central tendency (Mean, Mode & Median).
              8. viii. Variance of standard deviation
              9. ix. Determination of standard deviation.
              10. x. Comparison of standard deviation
              11. xi. Correlation & regression.
            2. b). Probability
              1. i. Random experiment.
              2. ii. Outcomes & associated sample space.
              3. iii. Mutually exclusive events.
              4. iv. Exhaustive events.
              5. v. Impossible events.
              6. vi. Certain events.
              7. vii. Union of sets.
              8. viii. Intersection of events.
              9. ix. Complementary events.
              10. x. Elementary events.
              11. xi. Composite events.
              12. xii. Classical definition of probability – examples.
              13. xiii. Statistical definition of probability – examples.
              14. xiv. Elementary theorems on probability (with simple problems on same).
              15. xv. Conditional probability.
              16. xvi. Baye’s theorem (with simple problems).
              17. xvii. Random variable as a function on sample space.
              18. xviii. Binomial distribution.
              19. xix. Examples of random experiments giving rise to binomial distribution.
              1. GENERAL ABILITY TEST (600 Marks)

              1. PART – A: ENGLISH (200 Marks)

              The question paper on English will be designed to test the candidate’s understanding of English & workman like use of words. To test candidate’s proficiency in English, the syllabus covers various aspects like:-

              1. 1. Grammar & usage.
              2. 2. Vocabulary.
              3. 3. Reading comprehension.
              4. 4. Reading cohesion in extended text.

              Questions are asked usually on following topics :-

              1. 1. Error spotting.
              2. 2. Sentence correction.
              3. 3. Fill in the blanks (grammar & vocabulary based).
              4. 4. Reading Comprehension.
              5. 5. Antonyms & Synonyms.
              1. PART – B: GENERAL KNOWLEDGE (400 Marks)

              1. PHYSICS (25% weightage) (~100 marks)

              1. Physical properties of matter, States of matter, Mass, Weight, Volume, Density, Specific gravity, Principle of Archimedes, Pressure barometer.

              2. Motion of objects, Velocity, Acceleration, Newton’s laws of motion, Force, Momentum, Parallelogram of forces, Stability & equilibrium of bodies, Gravitation, Elementary idea of work, Elementary idea of power.

              3. Elementary idea of energy, Effects of heat, Measurement of temperature, Measurement of heat, Change of state, Latent heat, Modes of transference of heat.

              4. Sound waves, Properties of sound waves, Simple musical instruments.

              5. Rectilinear propagation of light, Reflection, Refraction, Spherical mirrors, Spherical lenses, Human eye.

              6. Natural magnets, Artificial magnets, Properties of a magnet, Earth as a magnet.

              7. Static & current electricity, Conductors, Non – conductors, Ohm’s law, Simple electrical circuits, Heating effects of current, Lighting effects of current, Magnetic effects of current, Measurement of electrical power, Primary & secondary cells, Use of X-rays.

              8. General principles in the working of Simple pendulum, Simple pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure cooker, Thermos flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s compass, Lightening conductors, Safety fuses.

              1. SOCIAL STUDIES (20% weightage) (~80 marks)

              1. History:-Broad survey of Indian history with emphasis on culture & civilisation, Freedom movement in India.

              2. Elementary study of Indian constitution and administration, Elementary knowledge of five year plans in India, Panchayati Raj, Co-operatives & community development, Bhoodan, Sarvodaya, National integration & welfare state, Basic teachings of Mahatma Gandhi.

              3. Forces shaping modern world, Renaissance, Exploration & discovery, War of American Independence, French revolution, Russian revolution, Impact of science & technology on society.

              4. Forces shaping modern world, Renaissance, Exploration & discovery, War of American Independence, French revolution, Russian revolution, Impact of science & technology on society.

              5. Concept of one world, United Nations (UN), Democracy, Socialism, Communism, Role of India in present world.

              1. GEOGRAPHY (20% weightage) (~80 marks)

              1. The earth, its shape & size, Latitudes & longitudes, Concept of time, International date line, Movements of earth & their effects, Origin of earth, Rocks & their classification, Weathering – mechanical & chemical.

              2. Earthquakes, Volcanoes, Ocean currents, Tides, Atmosphere & its composition, Temperature & atmospheric pressure, Planetary winds.

              3. Cyclones, Anti-cyclones, Humidity, Condensation & precipitation, Types of climate, Major natural regions of the world.

              4. Regional geography of India, Climate, Natural vegetation, Mineral & power resources in India, Location & distribution of agricultural activities, Location & distribution of industrial activities, Important sea ports in India, Main Indian land, air & sea routes, Main items of imports & exports of India.

              1. CHEMISTRY (15% weightage) (~60 marks)

              1. Physical & chemical changes, Elements, Mixtures, Compounds, Symbols, formulae & simple chemical equations, Law of chemical combination (excluding problems), Properties of air, Properties of water.

              2. Preparation & properties of hydrogen, Preparation & properties of nitrogen, Preparation & properties of oxygen, Preparation & properties of cabondioxide, Oxidation, Reduction, Acids, bases & salts.

              3. Carbon – different forms, Fertilizers – natural & artificial, Material used in preparation of substances like soap, glass, ink, paper, cement, paints, safety matches & gun powder, Elementary idea of structure of atom, Elementary idea of atomic equivalent, Elementary idea of molecular weights, Elementary idea of valency.

              1. GEN. SCIENCE (10% weightage) (~40 marks)
              1. 1. Difference between living & non-living.
              2. 2. Basis of life.
                1. a). Cells
                2. b). Protoplasm.
                3. c). Tissues
              3. 3. Growth & reproduction in plants.
              4. 4. Growth & reproduction in animals.
              5. 5. Elementary knowledge of human body & its organs.
              6. 6. Common epidemics
                1. a). Types / what are common epidemics.
                2. b). Causes of common epidemics.
                3. c). Prevention of common epidemics.
              7. 7. Food – source of energy for man
                1. a). Constituents of food.
                2. b). Balanced diet.
              8. 8. Solar system
                1. a). Meteors.
                2. b). Comets.
                3. c). Eclipses.
              9. 9. Achievements of eminent scientists.
              1. CURRENT EVENTS (10% weightage) (~40 marks)
              1. 1. Knowledge of important events that have happened in India in recent years.
              2. 2. Current important world events.
              3. 3. Prominent personalities (including those connected with cultural activities & sports)
                1. a). National prominent personalities.
                2. b). International prominent personalities.