Online Entrance

Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams; Complement of a set; Operations on Sets (Union, Intersection and Difference of Set); Applications of sets: Ordered Pairs, Cartesian Product of Two sets; Relations: Domain, Co-domain and Range: Functions: into, on to, one - one in to, one-one on to Functions; Constant Function; Identity Function; composition of Functions; Invertible Functions; Binary Operations.

Complex Numbers in the form ; Real and Imaginary Parts of a complex Number; Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane; Modulus and Argument of a Complex Number; Algebra of Complex Numbers; Triangle Inequality; Polar Representation of a Complex Number; Square Root of a Complex Number; Cube Roots of Unity.

Solution of a Quadratic Equation in the Complex Number System by (i) Factorization (ii) Using Formula; Relation between Roots and Coefficients; Nature of Roots; Formation of Quadratic Equations with given Roots; Symmetric Functions of Roots; Equations Reducible to Quadratic Forms.

Concept of a Matrix; Types of Matrices; Equality of Matrices (only real entries may be considered): Operations of Addition, Scalar Multiplication and Multiplication of Matrices; Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only; Determinant of a Square Matrix; Minors and Cofactors; singular and non-singular Matrices; Applications of Determinants in (i) finding the Area of a Triangle (ii) solving a system of Linear Equations (Cramer’s Rule); Transpose, Adjoint and Inverse of a Matrix; Consistency and Inconsistency of a system of Linear Equations; Solving System of Linear Equations in Two or Three variables using Inverse of a Matrix (only up to 3X3 Determinants and Matrices should be considered).

Definition; order and degree; general and particular solutions of a differential equation; formation of differential equations whose general solution is given; solution of differential equations by method of Separation of variables; Homogeneous differential equations of first order and their solutions; Solution of linear differential equations of the type    where P (x), Q (x) are functions of x; Solutions of Second order differential equations

Physics – Scope and excitement; Physics in relation to science, society and technology – inventions, names of scientists and their fields, nobel prize winners and topics, current developments in physical sciences and related technology. Units for measurement – systems of units, S .I units, conversion from other systems to S.I units. Fundamental and derived units. Measurement of length, mass and time, least count in measuring instruments (eg. vernier calipers, screw gauge etc), Dimensional analysis and applications, order of magnitude, accuracy and errors in measurement, random and instrumental errors, significant figures and rounding off principles.

Objects in motion in one dimension – Motion in a straight line, uniform motion – its graphical representation and formulae; speed and velocity - instantaneous velocity; ideas of relative velocity with expressions and graphical representations; Uniformly accelerated motion, position – time graph, velocity – time graph and formulae. Elementary ideas of calculus – differentiation and integration – applications to motion.

Vectors and scalars, vectors in two and three dimensions, unit vector, addition and multiplication, resolution of vector in a plane, rectangular components, scalar and vector products. Motion in two dimensions – projectile motion, ideas of uniform circular motion, linear and angular velocity, relation between centripetal acceleration and angular speed.

Frictional electricity; Properties of electric charges - conservation, additivity and quantisation. Coulomb’s law – Forces between two point electric charges, Forces between multiple electric charges; Superposition principle and continuous charge distribution. Electric field and its physical significance, electric field due to a point charge, electric field lines; Electric dipole, electric field due to a dipole and behavior and dipole in a uniform electric field. Electric potential-physical meaning, potential difference, electric potential due to a point charge, a dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of point charges, electric dipoles in an electrostatic field. Electric flux, statement of Gauss’ theorem-its application to find field due to an infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Conductors and insulators-presence of free charges and bound charges; Dielectrics and electric polarization, general concept of a capacitor and capacitance, combination of capacitors in series and in parallel, energy stored in a capacitor, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Van de Graff generator.

Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics, limitations of Ohm’s law, electrical resistivity and conductivity, classification of materials in terms of conductivity; Superconductivity (elementary idea); Carbon resistors, colour code for carbon resistors; combination of resistances - series and parallel. Temperature dependence of resistance. Internal resistance of a cell, Potential difference and emf of a cell, combination of cells in series and in parallel. Kirchoff’s laws-illustration by simple applications, Wheatstone bridge and its applications, Meter bridge. Potentiometer - principle and applications to measure potential difference, comparison of emf of two cells and determination of internal resistance of a cell. Electric power, thermal effects of current and Joule’s law; Chemical effects of current, Faraday’s laws of electrolysis, Electro-chemical cells, Primary and secondary cells, solid state cells. Thermoelectricity-origin, elementary ideas of Seebeck effect, Peltier effect and Thomson effect. Thermocouple, Thermo emf, neutral and inversion temperatures, Measurement of temperature using a thermo- couple.

Laws of chemical combination: Law of conservation of mass. Law of definite proportion, Law of multiple proportions. Gay-Lussac’s law of combining volumes. Dalton’s atomic theory. Mole concept. Atomic, molecular and molar masses. Chemical equations. Balancing and calculation based on chemical equations.

Atomic structure: Fundamental particles. Rutherford model of atom. Nature of electromagnetic radiation. Emission spectrum of hydrogen atom. Bohr model of hydrogen atom. Drawbacks of Bohr model. Dual nature of matter and radiation. de Broglie relation. Uncertainty principle. Wave function (mention only). Atomic orbitals and their shapes (s, p and d orbitals only). Quantum numbers. Electronic configurations of elements. Pauli’s exclusion principle. Hund’s rule. Aufbau principle.

Kossel and Lewis approach of bonding. Ionic bond. Lattice energy. Born-Haber cycle. Covalent bond. Lewis structure of covalent bond. Concept of orbital overlap. VSEPR theory and geometry of molecules. Polarity of covalent bond. Valence bond theory and hybridization (sp, sp2, sp3, dsp2, d2sp3 and sp3d2). Resonance. Molecular orbital method. Bond order. Molecular orbital diagrams of homodiatomic molecules. Bond strength and magnetic behaviour. Hydrogen bond. Coordinate bond. Metallic bond.

Gaseous state: Boyle’s law. Charles’ law. Avogadro’s hypothesis. Graham’s law of diffusion. Absolute scale of temperature. Ideal gas equation. Gas constant and its values. Dalton’s law of partial pressure. Aqueous tension. Kinetic theory of gases. Deviation of real gases from ideal behaviour. van der Waals equation. Liquefaction of gases. Joule-Thomson effect. Critical temperature.

Liquid state: Properties of liquids. Vapour pressure and boiling point. Surface tension. Viscosity.

Solid state: Types of solids (ionic, covalent and molecular). Space lattice and unit cells. Cubic crystal systems. X-ray studies of crystals. The Bragg equation. Close packing. Different voids (tetrahedral and octahedral only). Structures of simple ionic compounds of AB and AB2 types. Density calculations. Point defects (Frenkel and Schottky). Electrical properties of solids. Conductors, semiconductors and insulators. Piezoelectric and pyroelectric crystals. Magnetic properties of solids. Diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic substances.

System and surrounding: Types of systems. Types of processes. Intensive and extensive properties. State functions and path functions. Reversible and irreversible processes. Zeroth law.

First law of thermodynamics: Internal energy and enthalpy. Application of first law of thermodynamics. Enthalpy changes during phase transition. Enthalpy changes in chemical reactions. Standard enthalpy of formation. Hess’s law of constant heat summation and numerical problems.

Second law of thermodynamics: Entropy and Gibbs free energy. Free energy change and chemical equilibrium. Criteria for spontaneity.

Rate of reaction. Average and instantaneous rates. Rate expressions. Rate constant. Rate law. Order and molecularity. Integrated rate law expressions for zero and first order reactions and their derivations. Units of rate constant. Half life period. Temperature dependence of rate constant. Arrhenius equation. Activation energy and related numerical problems. Elementary and complex reactions with examples.

Biology and its branches: relationship with other sciences; scientific methods in biology; historical break through (ancient, medieval and modern); scope in biology and career options; role of Biology in dispelling myths and misbelieves; Characters of living organisms (elementary ideas of organization, metabolism, energy transfer devices of life, homeostasis, growth and reproduction, adaptation, survival and death).

Cell as a basic unit of life; Cell theory; Cell as a self-contained unit, unicellularity and multicellularity, prokaryotic and eukaryotic systems. Tools and techniques: Different types of optical microscope, electron microscope and cell fractionation (centrifugation, chromatography and electrophoresis).

Ultra Structure: Prokaryotic and eukaryotic cell, cell wall, cell membrane (Fluid Mosaic Model), unit membrane concept, membrane transport, cellular movements (endocytosis and exocytosis); Description of cell organelles and their functions (nucleus, mitochondria, plastids, endoplasmic reticulum, golgi bodies, lysosomes, cytoskeletal structures, cilia and flagella, centriole, ribosomes).

Macromolecules of cell: Inorganic and organic materials (water, salt, mineral ions, carbohydrates, lipids, amino acids, proteins, nucleotides, nucleic acids (RNA and DNA), enzymes (properties, chemical nature and mechanism of action), vitamins, hormones and steroids.

Cell cycle: Cell division, description of amitosis, mitosis and meiosis – their significance, differences in animal and plant cell divisions, karyotype analysis.

Modes of reproduction in flowering plants Vegetative propagation (natural and artificial), micro-propagation, significance. Sexual reproduction: Development of male and female gametophytes, pollination types and factors, double fertilization, incompatibility; embryo development, seed and fruit development, parthenogenesis and parthenocarpy. Plant Growth Characteristic features, measurement of growth, growth curve, growth rate, growth regulators (phytohormones): auxins, gibberellins, cytokines, ethylene, abscisic acid (ABA) and their role. Seed germination: types, mechanism and factors affecting germination, role of growth regulators in seeddormancy. Senescence, abscission, stress factors (salt and water) and growth. Plant movements: phototropism, geotropism, hydrotropism, turgor growth movements (tropic, nastic and nutation), Process of flowering, photoperiodism and vernalisation.

1. Salient features of different Phyla with examples. 1.1 General features of animals 1.1.1 Grades of organization and body plan 1.1.2 body symmetry 1.1.3 germ layers (diploblastic & triploblastic organization) 1.1.4 segmentation 1.1.5 coelom 1.1.6 Heterotrophic mode of Nutrition 1.1.7 Movement 1.1.8 Reproduction and Development
2.Kingdom Protista (Protozoan Protists only) eg: Amoeba, Paramecium, Trypanosoma, Entamoeba, Plasmodium
3. Phylum Porifera eg: Sycon, Leucosolenia, Spongilla
4. Phylum Cnidaria eg: Hydra, Obelia colony, Physalia, Aurelia, Sea Anemone, Corals
5. Phylum Playhelminthes eg.: Taenia, Fasciola, Planaria
6. Phylum Nemathelminthes eg: Ascaris, Rhabditis, Wuchereria, Ancylostoma
7. Phylum Annelida eg: Nereis, Aphrodite, Pheretima, Hirudinaria, Chaetopterus, Bonellia
8. Phylum Arthropoda eg: Araneus (Spider), Limulus (King Crab), Bruthus (Scorpion), Eupgurus (Hermit Crab), Penaeus (Marine prawn), Palaemon (fresh water prawn), Lepisma, Apis, Musca (House fly), Mosquito, Leptocorisa (paddy pest), Barnacles, Silk worm, Oryctes
9. Phylum Mollusca eg: Pila, Mussel (fresh water & marine), Pinctada, Loligo, Octopus, Teredo
10 Phylum Echinodermata eg: Asterias, Echinus, Antedon, Sea cucumber, Ophiura.

PHYLUM CHORDATA: Subphylum [a]-Hemichordata eg: Balanoglossus Subphylum [b]- Urochordata eg: Ascidia.. Subphylum [c] - Cephalochordata eg: Amphioxus Subphylum [d]-Vertebrata–Classification up to classes
Super class I. Agnatha. Class – Cyclostomata eg: Petromyzon and Myxine.

Super class II. Gnathostomata Class a - Chondrichthyes (Cartilaginous fishes) eg.: Scoliodon, Trygon, Torpedo (Narcine), Pristis. Class b. Osteichthyes (Bony fishes) eg.: Catla, Anabas, Channa, Exocoetus, Remora, Hippocampus, Tuna, Cybium, Pomfret, Etroplus, Tilapia, Sardine, Mackeral. Class c. Amphibia eg: Bufo, Rana, Hyla, Rhacophorus, Salamander, Amblystoma, lchthyophis Class d. Reptilia eg: Chelone, Testudo, Sphenodon, Hemidactylus, Chameleon, Calotes, Draco, Phrynosoma, Varanus, Python, Naja, Krait, Viper, Crocodile, Alligator, Gavialis, Crotalus, Enhydrina, Dryophis, Typhlops. Class e. Aves eg: Ardea (Grey Heron), Corvus, Paro, Gallus, Columba, Psittacula, Bubo, Milvus, Struthio (Ostrich), Kiwi, Class f. Mammalia eg: Platypus, Kangaroo, Mole, Bat, Whale, Loris, Macaques, Macaca radiata, Macaca silenus (Lion-tailed monkey) Common Langur, Gorilla, Chimpanzee, Orangutan, Panthera, Elephas.

The syllabus for the months of September and October will be published on august.