The questions are designed to test your understanding and command of the English language.

The questions are designed to test your general awareness of the environment around you and its application to society. The level of answers to questions should be as expected of students of standard XII or equivalent.

**Man and His Environment**
Evolution of life, plants and animals, heredity and environment-Genetics, cells, chromosomes, genes. Knowledge of the human body, nutrition, balanced diet, substitute foods, public health and sanitation including control of epidemics and common diseases. Environmental pollution and its control. Food adulteration, proper storage and preservation of food grains and finished products, population explosion, population control. Production of food and raw materials. Breeding of animals and plants, artificial insemination, manures and fertilizers, crop protection measures, high yielding varieties and green revolution, main cereal and cash crops of India.

Solar system and the earth. Seasons, Climate, Weather, Soil - its formation, erosion. Forests and their uses. Natural calamities cyclones, floods, earthquakes, volcanic eruptions. Mountains and rivers and their role in irrigation in India. Distribution of natural resources and industries in India. Exploration of underground minerals including Oil. Conservation of natural resources with particular reference to the flora and fauna of India.

History, Politics and Society in India Vedic, Mahavir, Budhdha, Mauryan, Sunga, Andhra, Kushan. Gupta ages (Mauryan Pillars, Stupa Caves, Sanchi, Mathura and Gandharva Schools, Temple architecture, Ajanta and Ellora). The rise of new social forces with the coming of Islam and establishment of broader contacts. Transition from feudalism to capitalism. Opening of European contacts. Establishment of British rule in India. Rise of nationalism and national struggle for freedom culminating in Independence.

** Constitution of India and its Characteristic**
**Features**
Democracy, Secularism, Socialism, equality of opportunity and Parliamentary form of Government. Major political ideologies -Democracy, Socialism, Communism and Gandhian idea of non-violence. Indian political parties, pressure groups, public opinion and the Press, electoral system.

India's foreign policy and non - alignment, Arms race, balance of power. World organisation - political, social, economic and cultural. Important events (including sports and cultural activities) in India and abroad during the past two years.

**Broad Features of Indian social system**
The caste system, hierarchy, recent changes and trends. Minority social institution - marriage, family, religion and acculturation. Division of labour, co-operation, conflict and competition, Social control - reward and punishment, art, law, customs, propaganda, public opinion, agencies of social control - family, religion, State educational institutions; factors of social change - economic, technological, demographic, cultural; the concept of revolution.

**Social Disorganisation in India**
Casteism, communalism, corruption in public life, youth unrest, beggary, drugs, delinquency and crime, poverty and unemployment. Social planning and welfare in India, community development and labour welfare; welfare of Scheduled Castes and Backward Classes.

**Money**
Taxation, price, demographic trends, national income, economic growth. Private and Public Sectors; economic and non-economic factors in planning, balanced versus imbalanced growth, agricultural versus industrial development; inflation and price stabilization, problem of resource mobilisation. India's Five Year Plans.

The questions are designed to assess your basic intelligence and mechanical aptitude.

**Algebra**
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.

**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 Cofactors. 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 < to 3 are to be considered). Idea of a Group, Order of a Group, Abelian Group. Identitiy and inverse elements

**Trigonometry**
Addition and subtraction formulae, multiple and sub-multiple angles. Product and factoring formulae. Inverse trigonometric functions -Domains, Ranges and Graphs. DeMoivre's theorem, expansion of Sin nO and Cos nO in a series of multiples of Sines and Cosines. Solution of simple trigonometric equations. Applications: Heights and Distance.

**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.

**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.

**Integral Calculus and Differential equations**
Integral Calculus: Integration as inverse of differential, 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 coefficients.

** 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. 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.

**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**
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.