Topic

Algebra

Matrices & Determinants

Trigonometry

Analytical Geometry Of Two and Three Dimensions

Differential Calculus

Integral Calculus and Differential Equations

Vector Algebra

Statistics and Probability

English

General Knowledge : 

History, Freedom & Movement, Geography

Current Events

Science (Physics, Chemistry, Biology)

Concept of set, operations on sets, Venn diagrams.

De Morgan laws, Cartesian product, relation, equivalence relation.

If one of the roots of the equation 2x² + ax +b = 0 is 2, then what is (a – b) equal to?

If p+q = 10 and pq = 5, What will be the numerical value of (p/q + q/p)

 If 6x-5y = 13 , 7x + 2y = 23 , then 11x + 18 y =?

Representation of real numbers on a line.

Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers.

Conversion of a number in decimal system to binary system and vice versa. Arithmetic, Geometric and Harmonic progressions.

Quadratic equations with real coefficients. Solution of linear inequations of two  variables by graphs.

Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants.

Adjoint and inverse of a square matrix, Applications-Solution of a system of linear
equations in two or three unknowns by Cramer’s rule and by Matrix Method.

Angles and their measures in degrees and in radians. Trigonometrical ratios.

Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.

Inverse trigonometric
functions. Applications-Height and distance, properties of triangles.

Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms.

Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form.

Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic Point in a three-dimensional space, distance between two points.

Direction Cosines and direction ratios. Equation two points Direction Cosines and direction ratios,

Direction Cosines and direction ratios

Concept of a real valued function–domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit,

Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions. Derivative of function at a point,

geometrical and physical interpretation of a derivative—applications. Derivatives of sum, product and quotient of functions, derivative of a function

 with respect to another function, derivative of a composite function. Second order derivatives.

Increasing and decreasing functions. Application of derivatives in problems of maxima and minima

What is the solution of differential equation y= ln x – ln y ?


What is the solution of the differential equation

What is the slope of the tangent to the curve  at x = 2t³ + 5t – 5, y = 4t² – 4t – 3 at t = 6 ?

How many tangents are parallel to x axis for the curve y = x² – 4x + 3 ?

Integration as inverse of differentiation, integration by substitution and by parts,

standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.

Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications.

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 equations of various types—examples.

Application in problems of growth and decay.

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors,

addition of vectors, scalar multiplication of a vector, scalar product or dot product of
two vectors.

Vector product or cross product of  two vectors. Applications—work done by a force and moment of a force and in geometrical problems.

 If a, b and c are unit vectors, then |a – b|² + |b – c|² + |c – a|² does not exceed?

Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along b and c respectively are given by _________.?

Statistics : Classification of data, Frequency  distribution, cumulative frequency distribution examples.

Graphical representation—Histogram, Pie Chart, frequency polygon—
examples. Measures 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.

 Select the word that is most similar in meaning to the underlined word.
The slump in business made Mr. Sharma Bankrupt. a) Rise
b) Disease
c)  Fall
d) Theft

Physical Properties and States of Matter,

Mass, Weight, Volume, Density, and Specific Gravity,

Principle of Archimedes, Pressure Barometer.

Which one among the following waves carries the maximum energy per photon?
(a) X-rays
(b) Radio waves
(c) Light waves
(d) Microwaves

Which one of the following is the value of 1 kWh of energy converted into joules?
(a) 1.8 x 106 J
(b) 3.6 x 106 J
(c) 6.0 x 106 J
(d) 7.2 x 106 J

Which one of the following is an example of the force of gravity of the earth acting on a vibrating pendulum bob?
(a) Applied force
(b) Frictional force
(c) Restoring force
(d) Virtual force

Two convex lenses with power 2 dioptre are kept in contact with each other. The focal length of the combined lens system is
(a) 0.10 m
(b) 2 m
(c) 4 m
(d) 0.25 m

A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13.6 x 103 kg/m3. If X is the weight of the water and Y is the weight of the mercury, then
(a) X = Y
(b) X = 13.6 Y
(c) Y = 13.6 X
(d) None of the above

How long does light take to reach the Earth from the Sun?
(a) About 4 minutes
(b) About 8 minutes
(c) About 24 minutes
(d) About 24 hours

Barometer. Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion,

Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies,

Gravitation, elementary ideas of work, Power and Energy. Effects of Heat, Measurement of Temperature and Heat,

change of State and Latent Heat, Modes of
transference of Heat.

Sound waves and their properties, Simple
musical instruments.

Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses, Human Eye.

Natural and Artificial Magnets,

Properties of a Magnet, Earth as a Magnet.

Static and Current Electricity, conductors and Nonconductors, Ohm’s Law,

Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current,

Measurement of
Electrical Power, Primary and Secondary Cells, Use of X-Rays.

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.

Physical and Chemical changes. Elements, Mixtures and Compounds, Symbols,

Formulae and Simple Chemical Equations, Law of Chemical Combination

(excluding problems).
Properties of Air and Water.

The ionization energy of hydrogen atom in the ground state is
(a) 13·6 MeV
(b) 13·6 eV
(c) 13·6 Joule
(d) Zero

Which compound, when dissolved in water, conducts electricity and forms a basic solution?
(a) HCl
(b) CH3COOH
(c) CH30H
(d) NaOH

The proposition ‘equal volumes of different gases contain equal numbers of molecules at the same temperature and pressure’ is known as
(a) Avogadro’s hypothesis
(b) Gay-Lussac’s hypothesis
(c) Planck’s hypothesis
(d) Kirchhoff’s theory

Zinc is used to protect Iron from corrosion because zinc is
(a) more electropositive than iron
(b) cheaper than iron
(c) a bluish-white metal
(d) a good conductor of heat and electricity

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide,

Oxidation and Reduction. Acids, bases and salts. Carbon—different forms.

Fertilizer —Natural and
Artificial. Material used in the preparation of substances like Soap,
Glass, Ink, Paper, Cement,

Paints, Safety Matches and Gun- Powder. Elementary ideas about the structure of Atom,

Atomic Equivalent and Molecular Weights, Valency.

Difference between the living and non-living.

Basis of Life—Cells, Protoplasms and Tissues.

Growth and Reproduction in Plants an Animals.

Golden rice is a genetically modified crop plant where the incorporated gene is meant for the biosynthesis of
(a) Omega-3 fatty acids
(b) Vitamin A
(c) Vitamin B
(d) Vitamin C

Melanin is the natural pigment that gives colour to human skin, hair and the iris. It provides protection against
(a) Ultraviolet radiation
(b) Infrared radiation
(c) X-ray radiation
(d) Short wave radio radiation

Tendons through which muscles are connected to bones are tightly compacted bundles of which one of the following long fibrous protein?
(a) Fibrin
(b) Collagen
(c) Elastin(d) Cellulose

Elementary knowledge of Human Body and its important organs.

Common Epidemics, their causes and prevention.

Food—Source of Energy for man. Constituents of food, Balanced Diet.

The Solar System—Meteors and Comets, Eclipses.
Achievements of Eminent Scientists.

Who among the following is the author of the book The Indian Struggle, 1920 – 1934?
(a) Maulana Abul Kalam
(b) Jayprakash Narayan
(c) Subhash Chandra Bose
(d) Manabendra Nath Roy

Which one of the following associations was founded in London by Dadabhai Naoroji in 1866?
(a) The Bengal British India Society
(b) The East India Association
(c) The British Indian Association
(d) The Madras Native Association

Which one of the following travelogues has given an insight on the reign of Muhammad Bin Tughlaq?
(a) Ibn Battuta’s Rihla
(b) Francois Bernier’s Travels in the Mogul Empire
(c) Niccolao Manucci’s Storia do Mogor
(d) Tavernier’s Travels in India

Freedom Movement in India.

Elementary study of Indian Constitution and Administration. Elementary knowledge of Five Year Plans of India.

Panchayati Raj, Co-operatives and Community Development.

Bhoodan, Sarvodaya, National Integration and
Welfare State, Basic Teachings of Mahatma Gandhi.

Forces shaping the modern world; Renaissance, Exploration and Discovery;

War of American Independence. French Revolution,
Industrial Revolution and Russian Revolution.

Impact of Science
and Technology on Society.

Concept of one World, United Nations,
Panchsheel, Democracy,

Socialism and Communism. Role of India
in the present world.

The Earth, its shape and size. Lattitudes and Longitudes, Concept of time.

International Date Line. Movements of Earth and their effects.

The Coriolis effect is the result of
(a) Pressure gradient
(b) Earth’s axis of inclination
(c) Earth’s rotation
(d) Earth’s revolution

Which one of the following is not an igneous rock?
(a) Gabbro
(b) Granite
(c) Dolomite
(d) Basalt

Which one of the following States in India has the largest area under forest cover?
(a) Maharashtra
(b) Chhattisgarh
(c) Madhya Pradesh
(d) Andhra Pradesh

Sunrise in eastern Arunachal Pradesh would be about how many hours before the sunrise in western Gujarat?
(a) One hour
(b) Two hours
(c) Three hours
(d) Four hours

Where is Mekong Delta located?
(a) Thailand
(b) Cambodia
(c) Myanmar
(d) Vietnam

Origin of Earth. Rocks and their classification; Weathering—Mechanical and Chemical, Earthquakes and Volcanoes.

Ocean Currents and Tides Atmosphere and its composition

Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anti-cyclones;

Humidity; Condensation and Precipitation

Types of Climate, Major Natural regions of the World. Regional Geography of India Climate, Natural vegetation.

Mineral and Power resources; location and distribution of agricultural and Industrial activities

Important Sea ports and main sea, land and air routes of India.

Main items of Imports and Exports of India.

Knowledge of Important events that have happened in India in the recent years.

Current important world events. Prominent personalities—both Indian and International

including those connected with cultural activities and sports.