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THE #1 BEST SELLING  THE #1 BEST SELLING ARIHANT PUBLICATIONS (INDIA) LIMITED  THE #1 BEST SELLING Arihant Publications (India) Ltd. All Ri...

THE #1 BEST SELLING  THE #1 BEST SELLING ARIHANT PUBLICATIONS (INDIA) LIMITED  THE #1 BEST SELLING Arihant Publications (India) Ltd. All Rights Reserved © Publisher No part of this publication may be re-produced, stored in a retrieval system or distributed in any form or by any means, electronic, mechanical, photocopying, recording, scanning, web or otherwise without the written permission of the publisher. Arihant has obtained all the information in this book from the sources believed to be reliable and true. However, Arihant or its editors or authors or illustrators don’t take any responsibility for the absolute accuracy of any information published and the damages or loss suffered there upon. All disputes subject to Meerut (UP) jurisdiction only. Administrative & Production Offices Regd. Office ‘Ramchhaya’ 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002 Tele: 011- 47630600, 43518550; Fax: 011- 23280316 Head Office Kalindi, TP Nagar, Meerut (UP) - 250002 Tele: 0121-2401479, 2512970, 4004199; Fax: 0121-2401648 Sales & Support Offices Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Meerut, Nagpur & Pune ISBN : 978-93-13196-77-8 Published by Arihant Publications (India) Ltd. For further information about the books published by Arihant log on to www.arihantbooks.com or email to [email protected] /arihantpub /@arihantpub Arihant Publications /arihantpub  THE #1 BEST SELLING CONTENTS PHYSICS 1. Units, Measurements and Dimensions 3-14 2. Scalars and Vectors 15-23 3. Motion in 1, 2 & 3 Dimensions and Projectile Motion 24-44 4. Newton's Laws of Motion and Friction 45-62 5. Circular Motion 63-72 6. Work, Energy and Power 73-83 7. Centre of Mass, Momentum and Collision 84-94 8. Rotational Motion of Rigid Body 95-106 9. Gravitation 107-118 10. Simple Harmonic Motion 119-131 11. Fluid Mechanics 132-146 12. Elasticity 147-155 13. Waves Motion 156-164 14. Sound Wave 165-174 15. Heat, Temperature and Calorimetry 175-184 16. Physics for Gaseous State 185-194 17. Laws of Thermodynamics 195-205 18. Transmission 206-214 19. Ray Optics 215-233 20. Waves Optics 234-242 21. Electric Charge 243-251 22. Gauss's Law and Electric Potential Theory 252-262 23. Electric Capacitor 263-270 24. Current Electricity 271-288 25. Magnetic Field 289-300  THE #1 BEST SELLING 26. Magnetostatics 301-310 27. Electromagnetic Induction (EMI) 311-318 28. Alternating Current and EM Wave 319-330 29. Cathode Rays, Photoelectric Effect of Light and X-Rays 331-340 30. Atomic Structure 341-348 31. Nucleus 349-357 32. Semiconductor Devices and Logic Gates 358-375 33. Universe 376-380 CHEMISTRY 1. Some Basic Concepts of Chemistry 383-394 2. Atomic Structure 395-408 3. Nuclear Chemistry 409-416 4. Chemical Bonding 417-431 5. Periodic Properties 432-441 6. States of Matter 442-454 7. Chemical Thermodynamics 455-466 8. Chemical and lonic Equilibria 467-480 9. Chemical Kinetics 481-491 10. Solution 492-501 11. Adsorption and Colloidal System 502-510 12. Redox Reactions 511-517 13. Electro-chemistry 518-529 14. Hydrogen 530-537 15. s-Block Elements 538-549 16. Metallurgy 550-558 17. p-Block Elements - I (Group 13 & 14) 559-567 18. p-Block Elements - II 568-586 19. d - and f-Block Elements 587-597  THE #1 BEST SELLING 20. Coordination Compounds and Organometallics 598-607 21. General Organic Chemistry 608-625 22. Purification and Estimation of Organic Compounds 626-631 23. Hydrocarbons 632-650 24. Halogen Derivatives of Hydrocarbons 651-663 25. Alcohol, Phenol and Ether 664-678 26. Aldehyde and Ketones 679-695 27. Carboxylic Acid and Its Derivatives 696-706 28. Nitrogen Containing Compounds 707-720 29. Polymers, Biomolecules and Chemistry in Action 721-738 30. Qualitative Analysis 739-743 31. Stereochemistry 744-756 MATHEMATICS 1. Complex Number 759-769 2. Quadratic Equation 770-779 3. Sequences and Series 780-792 4. Exponential and Logarithmic Series 793-800 5. Permutations and Combinations 801-811 6. Binomial Theorem and Mathematical Induction 812-823 7. Matrices 824-832 8. Determinant 833-846 9. Sets, Relations and Functions 847-860 10. Linear Inequality 861-866 11. Trigonometry 867-897 12. Rectangular Coordinates and Straight Line 898-913 13. The Circle 914-928 14. Conic Sections 929-952 15. Three Dimensional Geometry 953-967  THE #1 BEST SELLING 16. Limits, Continuity and Differentiability 968-986 17. Differential Coefficients 987-998 18. Application of Derivatives 999-1013 19. Indefinite Integral 1014-1024 20. Definite Integral and Its Applications 1025-1039 21. Differential Equations 1040-1053 22. Probability 1054-1069 23. Vector Algebra 1070-1085 24. Statistics 1086-1096 25. Linear Programming 1097-1102 Ÿ English Proficiency 1105-1143 Ÿ Logical Reasoning 1147-1191 Ÿ Practice Sets (1-5) 1195-1251 Ÿ Solved Paper 2017 1-29 Ÿ Solved Paper 2018 1-34 Ÿ Solved Paper 2019 1-31  THE #1 BEST SELLING SYLLABUS PART I PHYSICS 1. Units & Measurement 6. Rotational Motion 1.1 Units (Different systems of units, SI 6.1 Description of rotation (angular units, fundamental and derived units) displacement, angular velocity and 1.2 Dimensional Analysis angular acceleration) 1.3 Precision and significant figures 6.2 Rotational motion with constant 1.4 Fundamental measurements in Physics angular acceleration (Vernier calipers, screw gauge, 6.3 Moment of inertia, Parallel and Physical balance etc.) perpendicular axes theorems, rotational kinetic energy 2. Kinematics 6.4 Torque and angular momentum 2.1 Properties of vectors 6.5 Conservation of angular momentum 2.2 Position, velocity and acceleration 6.6 Rolling motion vectors 2.3 Motion with constant acceleration 7. Gravitation 2.4 Projectile motion 7.1 Newton’s law of gravitation 2.5 Uniform circular motion 7.2 Gravitational potential energy, Escape 2.6 Relative motion velocity 7.3 Motion of planets – Kepler’s laws, 3. Newton’s Laws of Motion satellite motion 3.1 Newton’s laws (free body diagram, resolution 8. Mechanics of Solids and Fluids of forces) 8.1 Elasticity 3.2 Motion on an inclined plane 8.2 Pressure, density and Archimedes’ 3.3 Motion of blocks with pulley systems principle 3.4 Circular motion – centripetal force 8.3 Viscosity and Surface Tension 3.5 Inertial and non-inertial frames 8.4 Bernoulli’s theorem 4. Impulse and Momentum 9. Oscillations 4.1 Definition of impulse and momentum 9.1 Kinematics of simple harmonic motion 4.2 Conservation of momentum 9.2 Spring mass system, simple and compound pendulum 4.3 Collisions 9.3 Forced & damped oscillations, 4.4 Momentum of a system of particles resonance 4.5 Center of mass 10. Waves 5. Work and Energy 10.1 Progressive sinusoidal waves 5.1 Work done by a force 10.2 Standing waves in strings and pipes 5.2 Kinetic energy and work-energy 10.3 Superposition of waves, beats theorem 10.4 Doppler Effect 5.3 Power 5.4 Conservative forces and potential 11. Heat and Thermodynamics energy 11.1 Kinetic theory of gases 5.5 Conservation of mechanical energy 11.2 Thermal equilibrium and temperature  THE #1 BEST SELLING 11.3 Specific heat, Heat Transfer - 15.4 Alternating current (peak and rms Conduction, convection and radiation, value) thermal conductivity, Newton’s law of 15.5 AC circuits, LCR circuits cooling 11.4 Work, heat and first law of 16. Optics thermodynamics 16.1 Laws of reflection and refraction 11.5 2nd law of thermodynamics, Carnot 16.2 Lenses and mirrors engine Efficiency and Coefficient of 16.3 Optical instruments – telescope and performance. microscope 16.4 Interference – Huygen’s principle, 12. Electrostatics Young’s double slit experiment 12.1 Coulomb’s law 16.5 Interference in thin films 12.2 Electric field (discrete and continuous 16.6 Diffraction due to a single slit charge distributions) 16.7 Electromagnetic waves and their 12.3 Electrostatic potential and characteristics (only qualitative ideas), Electrostatic potential energy Electromagnetic spectrum 12.4 Gauss’ law and its applications 16.8 Polarization – states of polarization, 12.5 Electric dipole Malus’ law, Brewster’s law 12.6 Capacitance and dielectrics (parallel plate capacitor, capacitors in series 17. Modern Physics and parallel) 17.1 Dual nature of light and matter – Photoelectric effect, De-Broglie 13. Current Electricity wavelength 13.1 Ohm’s law, Joule heating 17.2 Atomic models – Rutherford’s 13.2 D.C circuits – Resistors and cells in experiment, Bohr’s atomic model series and parallel, Kirchoff’s laws, 17.3 Hydrogen atom spectrum potentiometer and Wheatstone bridge, 17.4 Radioactivity 13.3 Electrical Resistance (Resistivity, origin and temperature dependence of 17.5 Nuclear reactions Fission and fusion, resistivity). binding energy 14. Magnetic Effect of Current 18. Electronic Devices 14.1 Biot-Savart’s law and its applications 18.1 Energy bands in solids (qualitative 14.2 Ampere’s law and its applications ideas only), conductors, insulators and semiconductors; 14.3 Lorentz force, force on current carrying conductors in a magnetic 18.2 Semiconductor diode – I-V field characteristics in forward and reverse 14.4 Magnetic moment of a current loop, bias, diode as a rectifier; torque on a current loop, I-V characteristics of LED, photodiode, Galvanometer and its conversion to solar cell, and Zener diode; Zener voltmeter and ammeter diode as a voltage regulator. 18.3 Junction transistor, transistor action, 15. Electromagnetic Induction characteristics of a transistor; 15.1 Faraday’s law, Lenz’s law, eddy transistor as an amplifier (common currents emitter configuration) and oscillator 15.2 Self and mutual inductance 18.4 Logic gates (OR, AND, NOT, NAND 15.3 Transformers and generators and NOR). Transistor as a switch.  THE #1 BEST SELLING PART II CHEMISTRY 1. States of Matter 2.2 Quantum Mechanics Wave-particle 1.1 Measurement Physical quantities and SI duality de-Broglie relation, Uncertainty units, Dimensional analysis, Precision, principle; Hydrogen atom: Quantum Significant figures. numbers and wavefunctions, atomic orbitals and their shapes (s, p, and d), 1.2 Chemical Reactions Laws of chemical Spin quantum number. combination, Dalton’s atomic theory; 2.3 Many Electron Atoms Pauli exclusion Mole concept; Atomic, molecular and principle; Aufbau principle and the molar masses; Percentage composition electronic configuration of atoms, Hund’s empirical & molecular formula; Balanced rule. chemical equations & stoichiometry 2.4 Periodicity Brief history of the 1.3 Three states of matter, intermolecular development of periodic tables Periodic interactions, types of bonding, melting law and the modern periodic table; Types and boiling points Gaseous state: Gas of elements: s, p, d, and f blocks; Periodic Laws, ideal behavior, ideal gas equation, trends: ionization energy, atomic, and empirical derivation of gas equation, ionic radii, inter gas radii, electron Avogadro number, Kinetic theory – affinity, electro negativity and valency. Maxwell distribution of velocities, Nomenclature of elements with atomic Average, root mean square and most number greater than 100. probable velocities and relation to temperature, Diffusion; Deviation from 3. Chemical Bonding & ideal behaviour – Critical temperature, Molecular Structure Liquefaction of gases, van der Waals’ 3.1 Valence Electrons, Ionic Bond Lattice equation. Energy and Born-Haber cycle; Covalent 1.4 Liquid State Vapour pressure, surface character of ionic bonds and polar tension, viscosity. character of covalent bond, bond 1.5 Solid State Classification; Space lattices parameters & crystal systems; Unit cell in two 3.2 Molecular Structure Lewis picture & dimensional and three dimensional resonance structures, VSEPR model & lattices, calculation of density of unit cell molecular shapes – Cubic & hexagonal systems; Close 3.3 Covalent Bond Valence Bond Theory- packing; Orbital overlap, Directionality of bonds & hybridization (s, p & d orbitals only), Crystal Structures Simple AB and AB2 Resonance; Molecular orbital theory- type ionic crystals, covalent crystals – Methodology, Orbital energy level diamond & graphite, metals. Voids, diagram, Bond order, Magnetic properties number of atoms per unit cell in a cubic for homonuclear diatomic species unit cell, Imperfections- Point defects, (qualitative idea only). non-stoichiometric crystals; Electrical, magnetic and dielectric properties; 3.4 Metallic Bond Qualitative description. Amorphous solids qualitative 3.5 Intermolecular Forces Polarity; Dipole description. Band theory of metals, moments; Hydrogen Bond. conductors, semiconductors and insulators, and n- and p- type 4. Thermodynamics semiconductors. 4.1 Basic Concepts Systems and surroundings; State functions; Intensive 2. Atomic Structure & Extensive Properties; Zeroth Law and 2.1 Introduction Radioactivity, Subatomic Temperature particles; Atomic number, isotopes and 4.2 First Law of Thermodynamics Work, isobars, Thompson’s model and its internal energy, heat, enthalpy, heat limitations, Rutherford’s picture of atom capacities andspecific heats, and its limitations; Hydrogen atom measurements of ΔU and ΔH, Enthalpies spectrum and Bohr model and its of formation, phase transformation, limitations. ionization, electron gain;  THE #1 BEST SELLING Thermochemistry; Hess’s Law, cell reactions; Standard electrode Enthalpy of bond dissociation, potentials; EMF of Galvanic cells; combustion, atomization, sublimation, Nernst equation; Factors affecting the solution and dilution electrode potential; Gibbs energy 4.3 Second Law Spontaneous and change and cell potential; Secondary reversible processes; entropy; Gibbs cells; dry cells, Fuel cells; Corrosion free energy related to spontaneity and and its prevention. non-spontaneity, non-mechanical work; 6.2 Electrolytic Conduction Electrolytic Standard free energies of formation, Conductance; Specific and molar free energy change and chemical conductivities; variations of equilibrium conductivity with concentration , 4.4 Third Law Introduction Kolhrausch’s Law and its application, Electrolysis, Faraday’s laws of 5. Physical and Chemical Equilibria electrolysis; Coulometer; Electrode 5.1 Concentration Units Mole Fraction, potential and electrolysis, Commercial Molarity, and Molality production of the chemicals, NaOH, Na, Al, Cl2 & F2. 5.2 Solutions Solubility of solids and gases in liquids, Vapour Pressure, Raoult’s 7. Chemical Kinetics law, Relative lowering of vapour 7.1 Aspects of Kinetics Rate and Rate pressure, depression in freezing point; expression of a reaction; Rate constant; elevation in boiling point; osmotic Order and molecularity of the reaction; pressure, determination of molecular Integrated rate expressions and half life mass; solid solutions, abnormal for zero and first order reactions. molecular mass, van’t Hoff factor. Equilibrium: Dynamic nature of 7.2 Factor Affecting the Rate of the equilibrium, law of mass action Reactions Concentration of the reactants, catalyst; size of particles, 5.3 Physical Equilibrium Equilibria Temperature dependence of rate involving physical changes (solid- constant concept of collision theory liquid, liquid-gas, solid-gas), Surface (elementary idea, no mathematical chemistry, Adsorption, Physical and treatment); Activation energy; Chemical adsorption, Langmuir Catalysis, Surface catalysis, enzymes, Isotherm, Colloids and emulsion, zeolites; Factors affecting rate of classification, preparation, uses. collisions between molecules. 5.4 Chemical Equilibria Equilibrium 7.3 Mechanism of Reaction Elementary constants (KP, KC), Factors affecting reactions; Complex reactions; equilibrium, Le- Chatelier’s principle. Reactions involving two/three steps 5.5 Ionic Equilibria Strong and Weak only. electrolytes, Acids and Bases 7.4 Surface Chemistry Adsorption (Arrhenius, Lewis, Lowry and Bronsted) Physisorption and chemisorption; and their dissociation; degree of factors affecting adsorption of gasses ionization, Ionization of Water; on solids; catalysis: homogeneous and ionization of polybasic acids, pH; Buffer heterogeneous, activity and selectivity: solutions; Henderson equation, Acid- enzyme catalysis, colloidal state: base titrations; Hydrolysis; Solubility distinction between true solutions, Product of Sparingly Soluble Salts; colloids and suspensions; lyophillic, Common Ion Effect. lyophobic multi molecular and 5.6 Factors Affecting Equilibria macromolecular colloids; properties of Concentration, Temperature, Pressure, colloids; Tyndall effect, Brownian Catalysts, Significance of DG and DG0 movement, electrophoresis, in Chemical Equilibria. coagulations; emulsions – types of emulsions. 6. Electrochemistry 6.1 Redox Reactions Oxidation-reduction 8. Hydrogen and s-block Elements reactions (electron transfer concept); 8.1 Hydrogen Element Unique position in Oxidation number; Balancing of redox periodic table, occurrence, isotopes; reactions; Electrochemical cells and Dihydrogen: preparation, properties,  THE #1 BEST SELLING reactions, and uses; Molecular, saline, nitrogen fixation; Compound of nitrogen; ionic, covalent, interstitial hydrides; Ammonia: Haber’s process, properties Water: Properties; Structure and and reactions; Oxides of nitrogen and aggregation of water molecules; Heavy their structures; Properties and Ostwald’s water; Hydrogen peroxide: preparation, process of nitric acid production; reaction, structure & use, Hydrogen as a Fertilizers – NPK type; Production of fuel. phosphorus; Allotropes of phosphorus; 8.2 s-block Elements Abundance and Preparation, structure and properties of occurrence; Anomalous properties of the hydrides, oxides, oxoacids (elementary first elements in each group; diagonal idea only) and halides of phosphorus, relationships; trends in the variation of phosphine. properties (ionization energy, atomic & 9.5 Group 16 Elements Isolation and ionic radii). chemical reactivity of dioxygen; Acidic, 8.3 Alkali Metals Lithium, sodium and basic and amphoteric oxides; potassium: occurrence, extraction, Preparation, structure and properties of reactivity, and electrode potentials; ozone; Allotropes of sulphur; Biological importance; Reactions with Preparation/production properties and oxygen, hydrogen, halogens water and uses of sulphur dioxide and sulphuric liquid ammonia; Basic nature of oxides acid; Structure and properties of oxides, and hydroxides; Halides; Properties and oxoacids (structures only), hydrides and uses of compounds such as NaCl, halides of sulphur. Na2CO3, NaHCO3, NaOH, KCl 9.6 Group 17 and group 18 Elements and KOH. Structure and properties of hydrides, 8.4 Alkaline Earth Metals Magnesium and oxides, oxoacids of halogens (structures calcium: Occurrence, extraction, only); preparation, properties & uses of reactivity and electrode potentials; chlorine & HCl; Inter halogen Reactions with O2, H2O, H2 and halogens; compounds; Bleaching Powder; Uses of Solubility and thermal stability of oxo Group 18 elements, Preparation, salts; Biological importance of Ca and structure and reactions of xenon Mg; Preparation, properties and uses of fluorides, oxides, and oxoacids. important compounds such as CaO, Ca(OH)2, plaster of Paris, MgSO4, MgCl2, 9.7 d - Block Elements General trends in the CaCO3, and CaSO4; Lime and limestone, chemistry of first row transition elements; cement. Metallic character; Oxidation state; ionization enthalpy; Ionic radii; Color; 9. p - , d - and f - block Elements Catalytic properties; Magnetic properties; 9.1 General Abundance, distribution, Interstitial compounds; Occurrence and physical and chemical properties, extraction of iron, copper, silver, zinc, and isolation and uses of elements; Trends in mercury; Alloy formation; Steel and some chemical reactivity of elements of a important alloys; preparation and group; electronic configuration, oxidation properties of CuSO4, K2Cr2O7, KMnO4, states; anomalous properties of first Mercury halides; Silver nitrate and silver element of each group. halides; Photography. 9.2 Group 13 Elements Boron, Properties 9.8 f - Block Elements Lanthanoids and and uses of borax, boric acid, boron actinoids;Oxidation states and chemical hydrides & halides. Reaction of reactivity of lanthanoids compounds; aluminium with acids and alkalis; Lanthanide contraction and its consequences, Comparison of actinoids 9.3 Group 14 Elements Carbon, carbon and lanthanoids. catenation, physical & chemical properties, uses, allotropes (graphite, 9.9 Coordination Compounds Coordination diamond, fullerenes), oxides, halides and number; Ligands; Werner’s coordination sulphides, carbides; Silicon: Silica, theory; IUPAC nomenclature; Application silicates, silicone, silicon tetrachloride, and importance of coordination Zeolites, and their uses compounds (in qualitative analysis, 9.4 Group 15 Elements Dinitrogen; extraction of metals and biological Preparation, reactivity and uses of systems e.g. chlorophyll, vitamin B12, and nitrogen; Industrial and biological hemoglobin); Bonding: Valence-bond approach, Crystal field theory  THE #1 BEST SELLING (qualitative); Stability constants; 11.2 Conformations Ethane conformations; Shapes, color and magnetic properties; Newman and Sawhorse projections. Isomerism including stereoisomerisms; 11.3 Geometrical isomerism in alkenes Organometallic compounds. 12. Organic Compounds with 10. Principles of Organic Chemistry Functional Groups Containing and Hydrocarbons Oxygen and Nitrogen 10.1 Classification General Introduction, 12.1 General Nomenclature, electronic classification based on functional structure, important methods of groups, trivial and IUPAC preparation, identification, important nomenclature. Methods of purification: reactions, physical and chemical qualitative and quantitative. properties, uses of alcohols, phenols, 10.2 Electronic Displacement in a ethers, aldehydes, ketones, carboxylic Covalent Bond Inductive, resonance acids, nitro compounds, amines, effects, and hyperconjugation; free diazonium salts, cyanides and radicals; carbocations, carbanions, isocyanides. nucleophiles and electrophiles; types 12.2 Specific Reactivity of a-hydrogen in of organic reactions, free radial carbonyl compounds, effect of halogenations. substituents on alphacarbon on acid 10.3 Alkanes and Cycloalkanes Structural strength, comparative reactivity of acid isomerism, general properties and derivatives, mechanism of nucleophilic chemical reactions, free redical addition and dehydration, basic helogenation, combustion and character of amines, methods of pyrolysis. preparation, and their separation, 10.4 Alkenes and Alkynes General importance of diazonium salts in methods of preparation and reactions, synthetic organic chemistry. physical properties, electrophilic and free radical additions, acidic character 13. Biological, Industrial and of alkynes and (1,2 and 1,4) addition Environmental Chemistry to dienes. 13.1 The Cell Concept of cell and energy 10.5 Aromatic Hydrocarbons Sources; cycle. properties; isomerism; resonance 13.2 Carbohydrates Classification; delocalization; aromaticity; Monosaccharides; Structures of polynuclear hydrocarbons; IUPAC pentoses and hexoses; Anomeric nomenclature; mechanism of carbon; Mutarotation; Simple chemical electrophilic substitution reaction, reactions of glucose, Disaccharides: directive influence and effect of reducing and nonreducing sugars – substituents on reactivity; sucrose, maltose and lactose; carcinogenicity and toxicity. Polysaccharides: elementary idea of 10.6 Haloalkanes and Haloarenes structures of starch, cellulose and Physical properties, nomenclature, glycogen. optical rotation, chemical reactions 13.3 Proteins Amino acids; Peptide bond; and mechanism of substitution Polypeptides; Primary structure of reaction. Uses and environmental proteins; Simple idea of secondary , effects; di, tri, tetrachloromethanes, tertiary and quarternary structures of iodoform, freon and DDT. proteins; Denaturation of proteins and enzymes. 10.7 Petroleum Composition and refining, uses of petrochemicals. 13.4 Nucleic Acids Types of nucleic acids; Primary building blocks of nucleic 11. Stereochemistry acids (chemical composition of DNA & 11.1 Introduction Chiral molecules; optical RNA); Primary structure of DNA and activity; polarimetry; R,S and D,L its double helix; Replication; configurations; Fischer projections; Transcription and protein synthesis; enantiomerism; racemates; Genetic code. diastereomerism and meso structures. 13.5 Vitamins Classification, structure, functions in biosystems; Hormones  THE #1 BEST SELLING 13.6 Polymers Classification of polymers; bases; pH measurements of some General methods of polymerization; solutions obtained from fruit juices, Molecular mass of polymers; solutions of known and varied Biopolymers and biodegradable concentrations of acids, bases and polymers; methods of polymerization salts using pH paper or universal (free radical, cationic and anionic indicator; Lyophilic and lyophobic sols; addition polymerizations); Dialysis; Role of emulsifying agents in Copolymerization: Natural rubber; emulsification. Vulcanization of rubber; Synthetic Equilibrium studies involving ferric rubbers. Condensation polymers. and thiocyanate ions (ii) [Co(H2O)6]2+ 13.7 Pollution Environmental pollutants; and chloride ions; Enthalpy soil, water and air pollution; Chemical determination for strong acid vs. reactions in atmosphere; Smog; Major strong base neutralization reaction atmospheric pollutants; Acid rain; (ii) hydrogen bonding interaction Ozone and its reactions; Depletion of between acetone and chloroform; ozone layer and its effects; Industrial Rates of the reaction between (i) air pollution; Green house effect and sodium thiosulphate and hydrochloric global warming; Green Chemistry, acid, (ii) potassium iodate and sodium study for control of environmental sulphite (iii) iodide vs. hydrogen pollution. peroxide, concentration and 13.8 Chemicals in medicine, health-care temperature effects in these reactions. and food: Analgesics, Tranquilizers, 14.4 Purification Methods Filtration, antiseptics, disinfectants, anti- crystallization, sublimation, microbials, anti-fertility drugs, distillation, differential extraction, and antihistamines, antibiotics, antacids; chromatography. Principles of melting Preservatives, artificial sweetening point and boiling point determination; agents, antioxidants, soaps and principles of paper chromatographic detergents. separation – Rf values. 14.5 Qualitative Analysis of Organic 14. Theoretical Principles of Compounds Detection of nitrogen, Experimental Chemistry sulphur, phosphorous and halogens; 14.1 Volumetric Analysis Principles; Detection of carbohydrates, fats and Standard solutions of sodium proteins in foodstuff; Detection of carbonate and oxalic acid; Acidbase alcoholic, phenolic, aldehydic, ketonic, titrations; Redox reactions involving carboxylic, amino groups and KI, H2SO4, Na2SO3, Na2S2O3 and H2S; unsaturation. Potassium permanganate in acidic, 14.6 Quantitative Analysis of Organic basic and neutral media; Titrations of Compounds Basic principles for the oxalic acid, ferrous ammonium quantitative estimation of carbon, sulphate with KMnO4, K2 hydrogen, nitrogen, halogen, sulphur Cr2O7/Na2S2O3, Cu(II)/Na2S2O3. and phosphorous; Molecular mass 14.2 Qualitative Analysis of Inorganic determination by silver salt and Salts Principles in the determination of chloroplatinate salt methods; the cations Pb2+, Cu2+, As3+, Mn2+, Al3+, Calculations of empirical and Zn2+, Co2+, Ca2+, Sr2+, Ba2+, Mg2+, molecular formulae. NH4 +, Fe3+, Ni2+ and the anions CO32–, 14.7 Principles of Organic Chemistry S2–, SO42–, SO32–, NO2–, NO3–, Cl–, Br–, I–, Experiments Preparation of iodoform, PO43–, CH3COO–, C2O42–. acetanilide, p-nitro acetanilide, di- 14.3 Physical Chemistry Experiments benzayl acetone, aniline yellow, Preparation and crystallization of b-naphthol; Preparation of acetylene alum, copper sulphate. Benzoic acid and study of its acidic character. ferrous sulphate, double salt of alum 14.8 Basic Laboratory Technique Cutting and ferrous sulphate, potassium ferric glass tube and glass rod, bending a sulphate; Temperature vs. solubility; glass tube, drawing out a glass jet, Study of pH charges by common ion boring of cork. effect in case of weak acids and weak  THE #1 BEST SELLING PART III a. English Proficiency, b. Logical Reasoning a. English Proficiency 5. Verbal Reasoning This test is designed to assess the test takers’ 5.1 Analogy Analogy means general proficiency in the use of English correspondence. language as a means of self-expression in real In the questions based on life situations and specifically to test the test analogy, a particular relationship takers’ knowledge of basic grammar, their is given and another similar vocabulary, their ability to read fast and relationship has to be identified comprehend, and also their ability to apply the from the alternatives provided. elements of effective writing. 5.2 Classification Classification 1. Grammar means to assort the items of a 1.1 Agreement, Time and Tense, Parallel given group on the basis of construction, Relative pronouns certain common quality they 1.2 Determiners, Prepositions, Modals, possess and then spot the odd Adjectives option out. 1.3 Voice, Transformation 5.3 Series Completion Here series 1.4 Question tags, Phrasal verbs of numbers or letters are given 2. Vocabulary and one is asked to either complete the series or find out 2.1 Synonyms, Antonyms, Odd Word, One the wrong part in the series. Word, Jumbled letters, Homophones, Spelling 5.4 Logical Deduction – 2.2 Contextual meaning. Reading Passage Here a brief 2.3 Analogy passage is given and based on the passage the candidate is 3. Reading Comprehension required to identify the correct or 3.1 Content/ideas incorrect logical conclusions. 3.2 Vocabulary 5.5 Chart Logic Here a chart or a 3.3 Referents table is given that is partially 3.4 Idioms/Phrases filled in and asks to complete it in 3.5 Reconstruction (rewording) accordance with the information given either in the chart / table or 4. Composition in the question. 4.1 Rearrangement 4.2 Paragraph Unity 6. Non-verbal Reasoning 4.3 Linkers/Connectives 6.1 Pattern Perception Here a certain pattern is given and generally a quarter is left blank. b. Logical Reasoning The candidate is required to The test is given to the candidates to judge their identify the correct quarter from power of reasoning spread in verbal and the given four alternatives. nonverbal areas. The candidates should be able to think logically so that they perceive the data 6.2 Figure Formation and accurately, understand the relationships Analysis The candidate is correctly, figure out the missing numbers or required to analyze and form a words, and to apply rules to new and different figure from various given parts. contexts. These indicators are measured 6.3 Paper Cutting It involves the through performance on such tasks as detecting analysis of a pattern that is missing links, following directions, classifying formed when a folded piece of words, establishing sequences, and completing paper is cut into a definite analogies. design.  THE #1 BEST SELLING 6.4 Figure Matrix In this more than one 6.5 Rule Detection Here a particular set of figures is given in the form of a rule is given and it is required to select matrix, all of them following the same from the given sets of figures, a set of rule. The candidate is required to figures, which obeys the rule and follow the rule and identify the forms the correct series. missing figure. PART IV MATHEMATICS 1. Algebra mappings, binary operation, inverse of function, functions of real variables 1.1 Complex numbers, addition, like polynomial, modulus, signum and multiplication, conjugation, polar greatest integer. representation, properties of modulus and principal argument, triangle 1.10 Mathematical Induction inequality, roots of complex numbers, 1.11 Linear Inequalities, solution of linear geometric interpretations; inequalities in one and two variables. Fundamental theorem of algebra. 1.2 Theory of Quadratic equations, 2. Trigonometry quadratic equations in real and 2.1 Measurement of angles in radians and complex number system and their degrees, positive and negative angles, solutions, relation between roots and trigonometric ratios, functions and coefficients, nature of roots, equations identities. reducible to quadratic equations. 2.2 Solution of trigonometric equations. 1.3 Arithmetic, geometric and harmonic 2.3 Properties of triangles and solutions of progressions, arithmetic, geometric triangles and harmonic means, arithmetico- 2.4 Inverse trigonometric functions geometric series, sums of finite 2.5 Heights and distances arithmetic and geometric progressions, infinite geometric series, sums of 3. Two-dimensional squares and cubes of the first n natural numbers. Coordinate Geometry 3.1 Cartesian coordinates, distance 1.4 Logarithms and their properties. between two points, section formulae, 1.5 Exponential series. shift of origin. 1.6 Permutations and combinations, 3.2 Straight lines and pair of straight lines: Permutations as an arrangement and Equation of straight lines in various combination as selection, simple forms, angle between two lines, applications. distance of a point from a line, lines 1.7 Binomial theorem for a positive through the point of intersection of two integral index, properties of binomial given lines, equation of the bisector of coefficients, Pascal’s triangle the angle between two lines, concurrent lines. 1.8 Matrices and determinants of order two or three, properties and evaluation 3.3 Circles and family of circles : Equation of determinants, addition and of circle in various form, equation of multiplication of matrices, adjoint and tangent, normal & chords, parametric inverse of matrices, Solutions of equations of a circle , intersection of a simultaneous linear equations in two circle with a straight line or a circle, or three variables, elementary row and equation of circle through point of column operations of matrices, intersection of two circles, conditions for two intersecting circles to be 1.9 Sets, Relations and Functions, algebra orthogonal. of sets applications, equivalence relations, mappings, one-one, into and 3.4 Conic sections : parabola, ellipse and onto mappings, composition of hyperbola their eccentricity, directrices  THE #1 BEST SELLING & foci, parametric forms, equations of 6.4 Application of definite integrals to the tangent & normal, conditions for y = determination of areas of regions mx + c to be a tangent and point of bounded by simple curves. tangency. 7. Ordinary Differential Equations 4. Three Dimensional 7.1 Order and degree of a differential Coordinate Geometry equation, formulation of a differential 4.1 Co-ordinate axes and co-ordinate equation whole general solution is planes, distance between two points, given, variables separable method. section formula, direction cosines and 7.2 Solution of homogeneous differential direction ratios, equation of a straight equations of first order and first degree line in space and skew lines. 7.3 Linear first order differential equations 4.2 Angle between two lines whose direction ratios are given, shortest 8. Probability distance between two lines. 8.1 Various terminology in probability, 4.3 Equation of a plane, distance of a point axiomatic and other approaches of from a plane, condition for coplanarity probability, addition and multiplication of three lines, angles between two rules of probability. planes, angle between a line and a 8.2 Conditional probability, total plane. probability and Baye’s theorem 8.3 Independent events 5. Differential Calculus 8.4 Discrete random variables and 5.1 Domain and range of a real valued distributions with mean and variance. function, Limits and Continuity of the sum, difference, product and quotient 9. Vectors of two functions, Differentiability. 9.1 Direction ratio/cosines of vectors, 5.2 Derivative of different types of addition of vectors, scalar functions (polynomial, rational, multiplication, position vector of a trigonometric, inverse trigonometric, point dividing a line segment in a exponential, logarithmic, implicit given ratio. functions), derivative of the sum, difference, product and quotient of two 9.2 Dot and cross products of two vectors, functions, chain rule. projection of a vector on a line. 9.3 Scalar triple products and their 5.3 Geometric interpretation of derivative, Tangents and Normals. geometrical interpretations. 5.4 Increasing and decreasing functions, 10. Statistics Maxima and minima of a function. 10.1 Measures of dispersion 5.5 Rolle’s Theorem, Mean Value Theorem 10.2 Measures of skewness and Central and Intermediate Value Theorem. Tendency, Analysis of frequency distributions with equal means but 6. Integral Calculus different variances 6.1 Integration as the inverse process of differentiation, indefinite integrals of 11. Linear Programming standard functions. 11.1 Various terminology and formulation of 6.2 Methods of integration: Integration by linear Programming substitution, Integration by parts, 11.2 Solution of linear Programming using integration by partial fractions, and graphical method, feasible and integration by trigonometric identities. infeasible regions, feasible and 6.3 Definite integrals and their properties, infeasible solutions, optimal feasible Fundamental Theorem of Integral solutions (upto three nonitrivial Calculus, applications in finding areas constraints) under simple curves. 1 Units, Measurement and Dimensions Introduction Science is a systematic attempt to understand natural phenomena in as much detail and depth as possible and use the knowledge, so gained to predict, modify and control the phenomena. Every natural occurrence around us like the Sun, the wind, the planets, atmosphere, human body etc., follows some basic laws. To understand these laws, by observing natural occurrence is called Physics. These laws of physics are related and applicable to every aspect of life, thus understanding them leads to their applications in several fields for further development of society, which is also known as technology. Physical Quantities All those quantities which can be measured directly or indirectly and in terms of which the laws of Physics can be expressed, are called physical quantities. For example, length, mass, temperature, speed and force, electric current, etc. Units of Physical Quantities Unit of any physical quantity is its measurement compared to certain basic, arbitrarily chosen, internationally accepted reference standard. There are several systems of units like CGS (Centimetre, Gram and Second), FPS (Foot, Pound and Second) and MKS (Metre, Kilogram and Second). Fundamental and Derived Units The number of physical quantities is quite large. Thus, we may define a set of fundamental quantities and all other quantities may be expressed in terms of these fundamental quantities. These all other quantities are known as derived quantities. Units of fundamental and derived quantities are known as the fundamental units and derived units, respectively. A complete set of these units, both fundamental and derived units is known as the system of units. 4 SELF STUDY GUIDE BITSAT System of Units Least Count (LC) The least count of a measuring instrument is the least There are some systems used in units, can be defined as value, that can be measured using the instrument. It is 1. CGS System (Centimetre, Gram, Second) is often used denoted as LC. in scientific work. This system measures, length in centimetre (cm), mass in gram (g) and time in Least Count of Certain Measuring second (s). Instruments 2. FPS System (Foot, Pound, Second) It is also called the 1 mm Vernier calliper, Least count = = 0.1 mm British Unit System. This unit measures, length in foot 10 divisions (foot), mass in gram (pound) and time in second (s). Screw gauge, Least count 3. MKS System (Metre, Kilogram, Second) This system Value of 1 pitch scale reading measures length in metre(m), mass in kilogram (kg)and = Total number of head scale divisions time in second (s). 1 mm 4. SI Units (International System of Units) A variety of Least count = 100 divisions system of units (CGS, FPS and MKS) leads to the need of a unique system of units which is accepted = 0.01 mm world-wide. So, in 1971, a system of units named SI Travelling microscope, (System International in French) was developed and Value of 1 main scale division recommended by general conference on weights and Least count = Total number of vernier scale divisions measures. It is an extended version of the MKS system. SI system has seven fundamental units and two 0.5 mm = = 0.01 mm supplementary units, which are as follows 50 divisions 0.5 degree The two supplementary units of SI system are Spectrometer, Least count = 30 divisions (i) Radian for Plane Angle Angle subtended by an arc 30° at the centre of the circle having length equal to = = 1° radius of circle has unit radians. It is denoted by rad. 30 divisions (ii) Steradian for Solid Angle It is the solid angle which 1 degree (angle) = 60′ has the vertex at the centre of the sphere and cut-off and 1′ = 60′′ an area of the surface of sphere equal to that of square with sides of length equal to radius of sphere. It is expressed in unit steradian and denoted by sr. Errors in Measurement The uncertainty in results of every measurement by any measuring instruments, is called error in measurement. Precision of Measuring There can be several causes of errors like instrumental Instruments errors, imperfection in experimental techniques procedures, error caused by random changes in or Measurement is the foundation of all experimental science temperature, pressure, humidity etc. In systematic errors, and technology. The instruments used for measurement in mean of many separate measurement differs significantly. any experiment is called measuring instruments. Accuracy, Precision and Resolution of Calculation of Magnitude of an Instrument Errors (i) Accuracy An instrument is said to be the accurate, if the physical quantity measured by a (i) True Value measuring instrument resembles very close to its It is the mean of observed values. true value. a + a2 + a3 + K+ an (ii) Precision An instrument is said to have high degree ∴ atrue = amean = 1 n of precision, if the value measured by it remains n unchanged, however large number of times it may = 1 Σ ai have been repeated. n i=1 (iii) Resolution It stands for the minimum reading, where, a1 , a2 , K, an are observed values and n is the number which an instrument can read. of observations.  UNITS, MEASUREMENT AND DIMENSIONS 5 (ii) Absolute Error Significant Figures Absolute error of a particular measurement is the Significant figure in the measured value of a physical difference between mean of observed value and true value. quantity tells the number of digits in which we have Absolute error, confidence. All accurately known digits in a measurement ∆a1 = a mean − a1 , plus the first (only one uncertain digit together in a ∆a2 = a mean − a2 , measured value form significant figures). Larger the number of significant figures obtained in a measurement, M M M greater is the accuracy of the measurement. and ∆an = a mean − an Rules for Counting Significant Figures (iii) Mean Absolute Error (i) All the non-zero digits are significant. In 2.738, the The arithmetic mean of the magnitudes of different values number of significant figures is 4. of absolute errors, is known as the mean absolute error. (ii) All the zeroes between two non-zero digits are ∴ Mean absolute error, significant, no matter where the decimal point is, if at | ∆ a1 | + | ∆ a2 | + K + | ∆ an | all. As examples, 209 and 3.002 have 3 and ∆ amean = n 4 significant figures respectively. The final result of measurement can be written as (iii) If the measurement of number is less than 1, the a = a mean ± ∆a mean. This implies that value of a is likely to zero (es) on the right of decimal point and to the left lie as a mean + ∆a mean and a mean − ∆a mean. of the first non-zero digit are non-significant. In 000807,. first three underlined zeroes are non-significant and the number of significant figures (iv) Relative or Fractional Error is only 3. The ratio of the mean value of absolute error and the true (iv) The terminal or trailing zero (es) in a number value, is known as the mean relative error. without a decimal point are not significant. Thus, Mean absolute error 12.3 = 1230cm = 12300 mm has only 3 significant Mean relative error = Mean value of measurement figures. ∆amean (v) The trailing zero (es) in number with a decimal point = amean are significant. Thus, 3.800 kg has 4 significant figures. (v) Percentage Error (vi) A choice of change of units does not change the number of significant digits or figures in a When relative error is expressed in terms of percentage, measurement. then relative error is called the percentage error. Hence, Percentage error = ∆amean × 100% Rules for Arithmetic amean Operations with Significant Combination of Errors Figures (i) In addition or subtraction, the final results should (i) Sum of errors (Z) of two physical quantities A and B, retain as many decimal places as there are in the where ∆A and ∆B are their absolute errors, is number with the least decimal place. As an example ∆Z = ± ( ∆A + ∆B ) sum of 423.5 g, 164.92 g and 24.381 g is 612.801 g, but (ii) Difference of errors (Z) of two physical quantities A it should be expressed as 612.8 g only because the and B, where ∆A and ∆B are their absolute errors, is least precise measurement (423.5 g) is correct to only one decimal place. ∆Z = ± ( ∆A + ∆B ) (ii) In multiplication or division, the final result should (iii) Errors of a product If Z = AB , then retain as many significant figures, as are there in the ∆Z  ∆A ∆B  original number with the least significant figures. = ± +  Z  A B  For example, suppose an expression is performed like A 24.3 × 1243 (iv) Errors of a quotient If Z = , then = 676.481522 B 44. 65 ∆Z  ∆A   ∆B  Rounding the above result upto three significant =  +  Z  A  B  figures, the result would become 676. 6 SELF STUDY GUIDE BITSAT Rules for Rounding off the i.e. dimensions of all the terms in a physical expression must be same. Uncertain Digits LHS = RHS Result of arithmetic computation, we get a number having Dimensional analysis can be used in conversion of units, to more digits than the appropriate number of significant figures, then these uncertain digits are rounded off as per check the dimensional correctness of physical relation and the rules given ahead. to establish relation among various physical quantities. (i) The preceding digit is raised by 1, if the insignificant digit to be dropped is more than 5 and is left Dimensional Analysis and unchanged, if the latter is less than 5. Its Applications e.g.18.764 will be rounded off to 18.8 and 18.74 to 18.7. Dimensional analysis help us in deducing certain relations (ii) If the insignificant figure is 5 and the preceding digit among different quantities. Main applications of is even, then the insignificant digit is simply dropped. dimensional analysis are as follows: However, if the preceding digit is odd, then it is raised by one, so as to make it even. e.g. 17.845 will be To check the correctness of a given rounded off to 17.84 and 17.875 to 17.88. physical equation If both sides of a physical relation have same dimensions, Dimensions of Physical then the relation is dimensionally correct. Dimensional analysis is also used to deduce relation among the physical Quantities quantities, i.e. if the dimensions of physical quantities on The dimensions of a physical quantity are the power to both sides is known, then we can deduce relations which the base quantities are raised to represent that correlating the quantities with these dimensions. quantity. The expression which shows how and which base quantities represent the dimensions of a physical quantity, To convert a physical quantity from is called the dimensional formula. e.g. for volume, one system to another dimensional formula is [M0L3T0 ]. An equation, where a Let dimensional formula of a given physical quantity be physical quantity is equated with its dimensional formula is called dimensional equation. e.g. dimensional equation for [M aLbT c ]. If a physical quantity is known in one system of force is unit (n 1 ). Then, we can relate it with another system of unit [ F ] = [MLT −2 ] (n 2 ) as below a b c n 1  M 1   L 1   T1  = Principle of Homogeneity of n 2  M 2  L 2  T2  Dimensions NOTE Here, a system having base units [M1, L1, T1 ] the numerical According to this principle, a correct dimensional equation value of the given quantity be n1, and the numerical value n2 in must be homogeneous, another unit system having the base units M2 ,L 2 , T2. Practice Exercise 1. Which one is not a unit of time? 11. The nearest star to our solar system is 4.29 light year a. Leap year b. Year c. Shake d. Light year away. How much is this distance in terms of parsecs? 2. The height of the building is 50 ft. The same in a. 1.32 b. 3.21 c. 2.31 d. 3.12 millimetre is 12. The concorde is the fastest airlines used for a. 560 mm b. 285 mm commercial service. It can cruise at 1450 mile per c. 1786.8 mm d. 15240 mm hour (about two times the speed of sound or in other words, mach 2). What is it in m/s? 3. Which of the following is the most precise device for measuring length? a. 644.4 m/s b. 80 m/s c. 40 m/s d. None of these a. A vernier calliper with 20 divisions of the sliding scale 13. One light year is defined as the distance travelled by b. An optical instrument that can measure length within light in one year. The speed of light is 3 × 108 m/s. wavelength of light Find the same in metre. c. A screw gauge of pitch 1 mm and 100 divisions on a. 3 × 1012 m b. 9.461 × 1015 m the circular scale c. 3 × 1015 m d. None of these d. None of the above 4. The radius of hydrogen atom in ground state is 14. The acceleration of a car is 10 mile per hour per 5 × 10 −11 m. Find the radius of hydrogen atom in ft second. The same in is fermimetre. (1 fm = 10−15 m). s2 ft ft a. 5 × 104 fm b. 2 × 104 fm a. 1467. b. 14.67 s2 s2 c. 5 × 102 fm d. 5 × 106 fm c. 40 ft / s2 d. None of these 5. One nautical mile is 6080 ft. The same in kilometre is 15. The speed of light in vacuum is 3 × 108 m/s. How a. 0.9 km b. 0.8 km many nanosecond does it take to travel one metre in a c. 1.85 km d. None of these vacuum? 6. The area of a room is 10 m2. The same in ft 2 is a. 8 ns b. 10 ns a. 107.6 ft 2 b. 77 ft 2 3 c. 77.6 ft 2 d. None of these c. 3.34 ns d. None of these 3 7. The density of iron is 7.87 g/cm. If the atoms are 16. The time taken by an electron to go from ground state spherical and closely packed. The mass of iron atom to excited state is one shake (one shake = 10−8 s). is 9.27 × 10−26kg. What is the volume of an iron atom? Find this time in nanosecond. a. 1.18 × 10−29 m3 b. 2.63 × 10−29 m3 a. 10 ns b. 4 ns c. 2 ns d. 25 ns. × 10−28 m3 c. 173 d. 0.53 × 10−29 m3 17. The time between human heart beat is 8 × 10−1 s. 8. In the previous question, what is the distance between How many heart beats are measured in one minute? the centres of adjacent atoms? a. 75 b. 60 c. 82 d. 64 a. 2.82 × 10−9 m b. 0.282 × 10−9 m 17 18. The age of the universe is 5 × 10 s. Find the age of c. 0.63 × 10−9 m d. 6.33 × 10−9 m universe in year. 9. The world’s largest cut diamond is the first start of a. 158 × 106 year b. 158 × 109 year Africa (mounted in the British Royal Sceptre and kept c. 158 × 108 year d. 158 × 1011 year in the tower of London). Its volume is 1.84 cubic inch. 19. Assuming the length of the day uniformly increases What is its volume in cubic metre? by 0.001 second per century. Calculate the net a. 30.2 × 10−6 m3 b. 33.28 m2 effect on the measure of time over 20 centuries. c. 4.8 m3 d. None of these a. 3.2 hour b. 2.1 hour c. 2.4 hour d. 5 hour 10. Crane is British unit of volume. 20. Find the number of molecules of H2O in 90 g of water. (One crane = 170.474 litre). Convert crane into SI unit. a. 35.6 × 1023 molecules. × 1023 molecules b. 4122 a. 0.170474 m3 b. 17.0474 m3 c. 0.0017474 m3 d. 1704.74 m3 c. 27.2 × 1023 molecules d. 30.11 × 1023molecules 8 SELF STUDY GUIDE BITSAT 21. The mass of Earth is 5.98 × 1024 kg. The average 32. 1 revolution is equivalent to 360°. The value of atomic weight of atoms that make up Earth is 40 u. 1 revolution per minute is How many atoms are there in Earth? a. 2π rad/s b. 0.1047 rad/s a. 9 × 1051 b. 9 × 1049 c. 9 × 1046 d. 9 × 1055 c. 3.14 rad/s d. None of these 22. One amu is equivalent to 931 MeV energy. The rest 33. The height of a man is 5.87532 ft. But measurement is mass of electron is 9.1 × 10−31 kg. The mass equivalent correct upto three significant figures. The correct energy is (Here, 1 amu = 1.67 × 10−27 kg) height is a. 0.5073 MeV b. 0.693 MeV a. 5.86 ft b. 5.87 ft c. 4.0093 MeV d. None of these c. 5.88 ft d. 5.80 ft. × 10−27 kg. The 23. One atomic mass unit in amu = 166 34. 4.32 × 2.0 =......... atomic weight of oxygen is 16. Find the mass of one a. 8.64 b. 8.6 atom of oxygen. c. 8.60 d. 8.640 a. 26.56 × 10−27 kg b. 10.53 × 10−27 kg 35. 4.338 + 4.835 × 3.88 ÷ 3.0 is equal to c. 74 × 10−27 kg d. 2.73 × 10−27 kg a. 10.6 b. 10.59 24. One horse power is equal to c. 10.5912 d. 10.591267 a. 746 W b. 756 W c. 736 W d. 766 W. × 2.88 is equal to 36. 10 2 25. If E = mc a. 2.88 b. 2.880 where, m = mass of the body, c = speed of light c. 2.9 d. None of these Guess the name of physical quantity E.. × 2.88 is equal to 37. 100 a. Energy b. Power a. 2.88 b. 2.880 c. Momentum d. None of these c. 2.9 d. None of these 26. One calorie of heat is equivalent to 4.2 J. BTU (British 38. If v = velocity of a body, c = speed of light. Thermal Unit) is equivalent to 1055 J. The value of v one BTU in calorie is Then, the dimension of is c a. 251.2 cal b. 200 cal c. 263 cal d. None of these a. [M0L0T 0] b. [MLT −1] c. [ML2T −2] d. None of these 27. It is claimed that the two cesium clocks, if allowed to run for 100 yr, free from any disturbance, may differ by 39. The expression for centripetal force depends upon only about 0.02s. Which of the following is the correct mass of body, speed of the body and the radius of fractional error? circular path. Find the expression for centripetal force. a. 10− 9 b. 10− 5 c. 10− 13 d. 10− 11 mv 2 mv 2 a. F = b. F = 28. Which of the following is the average mass density of 2r 3 r sodium atom assuming, its size to be about 2.5 Å mv 2 m 2v 2 c. F = 2 d. F = (Use the known values of Avogadro's number and the r 2r atomic mass of sodium). 40. The maximum static friction on a body is F = µN. a. 0.64 × 103 kg / m3 b. 8.0 × 102 kg / m3 Here, N = normal reaction force on the body, c. 8.6 × 103 kg / m3 d. 6.4 × 105 kg / m3 µ = coefficient of static friction. The dimensions of µ is 29. Electron volt is the unit of energy (1 eV = 1.6 × 10−19 J). a. [MLT −2] b. [M0L0T 0θ −1] In H-atom, the binding energy of electron in first orbit c. dimensionless d. None of these is 13.6 eV. The same in joule (J) is 41. What are dimensions of Young’s modulus of a. 10 × 10−19 J b. 21.76 × 10−19 J elasticity? c. 13.6 × 10−19 J d. None of these a. [ML−1T −2] b. [MLT −2] 30. 1 mm of Hg pressure is equivalent to one torr and one c. [MLT −1] d. None of these torr is equivalent to 133.3 N/m 2. The atmospheric 42. The surface tension is T = F , then the pressure in mm of Hg pressure is l a. 70 mm b. 760 mm dimensions of surface tension is c. 3.76 mm d. None of these a. [MLT −2] b. [MT −2] 5 2 31. One bar is equivalent to 10 N/m. The atmosphere c. [M0L0T 0] d. None of these pressure is 1.013 × 105 N/m 2 The same in bar is 43. The dimension of heat capacity is a. 1.88 bar b. 1.013 bar a. [L2T −2θ −1] b. [ML2T −2θ −1] c. 2.013 bar d. None of these c. [M−1L2T −2θ −1] d. None of these  UNITS, MEASUREMENT AND DIMENSIONS 9 44. If ∆H = mL, where m is mass of body. 52. The work done by a battery is W = ε ∆q , where ∆H = total thermal energy supplied to the body ∆q = charge transferred by battery ε = emf of the L = latent heat of fusion. battery. What are dimensions of emf of battery? Find the dimensions of latent heat of fusion. a. [A−2M0L0T −2] b. [A−2ML2T −3] a. [ML T ] 2 −2 2 −2 b. [L T ] 0 0 −2 c. [M L T ] d. [ML T ] 0 −1 c. [A0M2T −3] d. [A−1ML2T −3] 45. Solar constant is defined as energy received by Earth J 53. The expression for drift speed is v d =. per cm2 per minute. Find the dimensions of solar ne constant. Here, J = current density, a. [ML2T −3] b. [M2L0T −1] c. [MT −3] d. [MLT −2] n = number of electrons per unit volume, C2. × 10−19unit e = 16 46. The unit of electric permittivity is. Find the Nm 2 The unit and dimensions of e are dimensions of electric permittivity. a. coulomb and [AT] 2 −1 −3 4 a. [A M L T ] −1 −3 4 b. [AM L T ] b. ampere per second and [AT −1] c. no sufficient information c. [A2M−1L−3T 0] d. [A2M0L−3T 4] d. None of the above 47. A physical relation is ε = ε 0εr 54. The unit of current element is ampere-metre. Find the where, ε = electric permittivity of a medium dimensions of current element. ε0 = electric permittivity of vacuum a. [AML] b. [AML2T] εr = relative permittivity of medium c. [MLT 2] d. [AL] What are dimensions of relative permittivity? 55. The magnetic force on a point moving charge is a. [ML2T −2] b. [M0L2T −3] F = q ( v × B). c. [M0L0T 0] d. [M0L0T −1] Here, q = electric charge 1 2 v = velocity of the point charge 48. The dimensions of εE are same as 2 B = magnetic field a. energy density (energy per unit volume) The dimensions of B is b. energy a. [AMLT −1] c. power b. [A−1MLT −2] d. None of the above c. [A−1MT −2] 49. The electric flux is given by scalar product of electric d. None of these field strength and area. What are the dimensions of E electric flux? 56. What are dimensions of ? B a. [A−2ML3T −2] b. [A−1ML3T −2] a. [LT −1] b. [LT −2] c. [A−1ML3T −3] d. [A0M2LT −1] c. [MLT −1] d. [ML2T −1] 50. Electric displacement is given by D = εE 57. What are the dimensions of µ 0ε 0? Here, ε = electric permittivity Here, µ 0 = magnetic permeability in vacuum, E = electric field strength. ε 0 = electric permittivity in vacuum Find the dimensions of electric displacement. a. [ML−2T −2] b. [L−2T −2] −2 −2 −1 a. [AML T] b. [AL T ] c. [L−2T 2] d. None of these c. [AL−2T] d. None of these 58. In the formula, a = 3bc 2 ‘a’ and ‘c’ have dimensions 51. The energy stored in an electric device known as of electric capacitance and magnetic induction, q2 respectively. What are dimensions of ‘b’ in MKS capacitor, is given by U = system? 2C where, U = energy stored in capacitor a. [M−3L−2T 4Q4] b. [M−3T 4Q4] C = capacity of capacitor c. [M−3T 3Q] d. [M−3L2T 4Q−4] q = charge on capacitor R 59. Find the dimensions of. Find the dimensions of capacity of the capacitor L a. [A2M−1L−2T 4] Here, R = electric resistance b. [AM−1L−2T 4] L = self-inductance c. [A2M−2L−2T 4] a. [T −2] b. [T −1] d. [A0M0L−2T 4] c. [ML−1] d. [T] 10 SELF STUDY GUIDE BITSAT 60. The magnetic energy stored in an inductor is given by 67. The dimensions of frequency is 1 a. [T −1] b. [M0L0T] E = La I b. Find the value of ‘a’ and ‘b’. 2 c. [M0L0T −2] d. None of these Here, L = self-inductance, I = electric current. 68. The dimensions of wavelength is a. a = 3, b = 0 b. a = 2, b = 1 a. [M0L0T 0] b. [M0LT 0] c. a = 0, b = 2 d. a = 1, b = 2 c. [M0L−1T 0] d. None of these 61. In L-R circuit, I = I 0 [1 − e −t / λ ] 2π 69. The optical path difference is defined as ∆x =. Here, I = electric current in the circuit. Then, λ a. the dimensions of I 0 and λ are same What are dimensions of optical path difference? b. the dimensions of t and λ are same a. [M0L−1T 0] b. [M1L1T 0] c. the dimensions of I and I 0 are not same c. [ML0T1] d. [ML−2T] d. All of the above W 70. The unit of intensity of a wave is ? What are 62. A physical quantity u is given by the m2 2 B dimensions of intensity of wave