nest.lpu.in Syllabus LPUNEST 2014 National Eligibility and Scholarship Test : Lovely Professional University

Name of the Organisation : Lovely Professional University (nest.lpu.in)
Type of Announcement : Syllabus
Designation : LPUNEST LPU-NEST 2014 National Eligibility and Scholarship Test

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Syllabus for LPUNEST 2014 :
Syllabus for NEST-Junior (Stream Code: A)
ENGLISH (Subject Code: 01) Gender, Noun, Antonyms, Synonyms, One word Substitution, Active & Passive voice, Auxiliary verbs, Completing Statements, Spelling Bee, Singular/Plural, Idiomatic expressions, Conjunctions, Figurative expressions, Verbs types, Collective Phrases.

MATHEMATICS (Subject Code: 02)
Unit 1: Number Systems: Real Numbers: Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results – irrationality of v2, v3, v5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

Unit 2: Algebra:
Polynomials: Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.
Pair of linear equations in two variables: Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically- by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.
Quadratic Equations: Standard form of a quadratic equation ax2 + bx + c = 0, (a? 0). Solution of the quadratic equations (only real roots) by factorization, by completing the quare and by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated.
Arithmetic Progressions: Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms and their application in solving daily life problems.

Unit 3: Geometry:
Triangles: Definitions, examples, counter examples of similar triangles.
1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right traingle.
Circles: Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to circle are equal.
Constructions:
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

Unit 4: Trigonometry & Co-Ordinate Geometry:
Introduction to Trigonometry: Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o & 90o. Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios.
Trigonometric Identities: Proof and applications of the identity sin2 A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.
Heights and Distances: Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30o, 45o and 60o.
Co-ordinate Geometry: Lines (In two-dimensions): graphs of linear equations. Geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.

Unit 5: Statistics and Probability:
Statistics: Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
Probability: Classical definition of probability. Simple problems on single events, not using set notation.

Unit 6: Mensuration:
Areas Related to Circles: Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
Surface areas and Volumes: (i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone. (ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids are taken.)

SCIENCE (Subject code: 03)
Unit 1: Chemical Substances I – Nature and Behaviour:
Chemical reactions: Chemical Equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, doubles displacement, precipitation, neutralization, oxidation and reduction.
Acids, bases and salts: Their definitions in terms of furnishing of H+ and OH- ions, General properties, examples and uses, concept of pH scale(Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of sodium hydroxide, Bleaching powder, Baking soda, washing soda and Plaster of Paris. Metals and non metals: Properties of metals and non-metals, reactivity series, formation and properties of ionic compounds, basic metallurgical processes, corrosion and its prevention.

Unit 2: Chemical Substances II:
Carbon compounds: Covalent bonding in carbon compounds. Versatile nature of carbon. Homologous series Nomenclature of carbon compounds containing functional groups (halogens, alcohol, ketones, aldehydes, alkanes and alkynes), difference between saturated hydrocarbons and unsaturated hydrocarbons. Chemical properties of carbon compounds (combustion, oxidation, addition and substitution reaction). Ethanol and Ethanoic acid (only properties and uses), soaps and detergents. Periodic classification of elements: Need for classification, modern Periodic table, gradation in properties, valency, atomic number, metallic and non-metallic properties.

Unit 3: World of Living:
Life Processes: “living being”. Basic concept of nutrition, respiration, transport and excretion in plants and animals. Control and Co-ordination in Animals and Plants: Tropic movements in plants; Introduction to plant hormones; control and co-ordination in animals: nervous system; voluntary, involuntary and reflex action, chemical co-ordination: animal hormones.
Reproduction: Reproduction in animal and plants (asexual and sexual) reproductive health-need for and methods of family planning. Safe sex vs. HIV/AIDS. Child bearing and women’s health. Heredity and evolution: Heredity; Mendel’s contribution- Laws for inheritance of traits: Sex determination: brief introduction; Basic concepts of evolution.

Unit 4: Effects of Current: Electric current, potential difference and electric current. Ohm’s law; Resistance, Resistivity, Factors on which the resistance of a conductor depends. Series combination of resistors, parallel combination of resistors and its applications in daily life. Heating effect of Electric current and its applications in daily life. Electric Power, Inter relation between P, V, I and R. Magnetic effects of current: Magnetic field, field lines, field due to a current carrying conductor, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming’s left hand rule. Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule, Direct current. Alternating current: frequency of AC. Advantage of AC over DC. Domestic electric circuits.

Unit 5: Natural Resources:
Sources of energy: Different forms of energy, conventional and non-conventional sources of energy: fossil fuels, solar energy; biogas; wind, water and tidal energy; nuclear energy. Renewable versus non-renewable sources. Conservation of natural resources Management of natural resources. Conservation and judicious use of natural resources. Forest and wild life, coal and petroleum conservation. Examples of People’s participation for conservation of natural resources.
The Regional environment: Big dams: advantages and limitations; alternatives if any. Water harvesting. Sustainability of natural resources. Our environment: Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable, substances.

Unit 6: Natural Phenomena:
Reflection of light at curved surfaces, Images formed by spherical mirrors, centre of curvature, principal axis, principal focus, and focal length. Mirror Formula (Derivation not required), Magnification.
Refraction; laws of refraction, refractive index. Refraction of light by spherical lens, Image formed by spherical lenses, Lens formula (Derivation not required), Magnification. Power of a lens; Functioning of a lens in human eye, defects of vision and their corrections, applications of spherical mirrors and lenses. Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.