AP Inter 2nd Year Zoology Study Material Pdf | Intermediate 2nd Year Zoology Textbook Solutions

Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Zoology Study Material Textbook Solutions Guide PDF Free Download, TS AP Inter 2nd Year Zoology Blue Print Weightage 2022-2023, Telugu Academy Intermediate 2nd Year Zoology Textbook Pdf Download, Questions and Answers Solutions in English Medium and Telugu Medium are part of AP Inter 2nd Year Study Material Pdf.

Students can also read AP Inter 2nd Year Botany Syllabus & AP Inter 2nd Year Zoology Important Questions for exam preparation. Students can also go through AP Inter 2nd Year Zoology Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Zoology Study Material Pdf Download | Sr Inter 2nd Year Zoology Textbook Solutions

TS AP Inter 2nd Year Zoology Weightage Blue Print 2022-2023

TS AP Inter 2nd Year Zoology Weightage 2022-2023 | TS AP Inter 2nd Year Zoology Blue Print 2022

TS AP Inter 2nd Year Zoology Weightage Blue Print

Intermediate 2nd Year Zoology Syllabus

TS AP Inter 2nd Year Zoology Syllabus

Unit I Human Anatomy and Physiology – I (22 Periods)

Unit IA: Digestion and Absorption
Alimentary canal and digestive glands; Role of digestive enzymes and gastrointestinal hormones; Peri¬stalsis, digestion, absorption, and assimilation of proteins, carbohydrates, and fats, egestion. The calorific value of proteins, carbohydrates, and fats (for box item – not to be evaluated); Nutritional disorders: Protein Energy Malnutrition (PEM), indigestion, constipation, vomiting, jaundice, diarrhea, Kwashiorkor.

Unit IB: Breathing and Respiration
Respiratory organs in animals; Respiratory system in humans; Mechanism of breathing and its regulation in humans – Exchange of gases, transport of gases and regulation of respiration; Respiratory volumes; Respiratory disorders: Asthma, Emphysema, Occupational respiratory disorders – Asbestosis, Silicosis, Siderosis, Black Lung Disease in coal miners.

Unit II Human Anatomy and Physiology – II (22 Periods)

Unit IIA: Body Fluids and Circulation
Covered in I year composition of lymph and functions; Clotting of blood; Human circulatory system- the structure of the human heart and blood vessels; Cardiac cycle, cardiac output, double circulation; regulation of cardiac activity; Disorders of circulatory system: Hypertension, coronary artery disease, angina pectoris, heart failure.

Unit IIB: Excretory Products and their Elimination
Modes of excretion – Ammonotelism, Ureotelism, Uricotelism; Human excretory system – the structure of kidney and nephron; Urine formation, osmoregulation; Regulation of kidney function – Renin – Angiotensin – Aldosterone system, Atrial Natriuretic Factor, ADH and diabetes insipidus; Role of other organs in excretion; Disorders: Uraemia, renal failure, renal calculi, nephritis, dialysis using artificial kidney.

Unit III Human Anatomy and Physiology – III (20 Periods)

Unit IIIA: Muscular and Skeletal System
Skeletal muscle – ultrastructure; Contractile proteins & muscle contraction; Skeletal system and its functions; Joints, (to be dealt with relevance to practical syllabus); Disorders of the muscular and skeletal system: myasthenia gravis, tetany, muscular dystrophy, arthritis, osteoporosis, gout, Gregor Mortis.

Unit IIIB: Neural Control and Co-ordination
The nervous system in human beings – Centralnfervous system. Peripheral nervous system and Visceral nervous system; Generation and conduction of nerve impulse; Reflex action: Sensory perception; Sense organs; Brief description of other receptors; Elementary structure and functioning of eye and ear.

Unit IV Human Anatomy and Physiology – IV (15 Periods)

Unit IVA: Endocrine System and Chemical Co-ordination
Endocrine glands and hormones; Human endocrine system – Hypothalamus, Pituitary, Pineal, Thyroid, Parathyroid, Adrenal, Pancreas; Gonads; Mechanism of hormone action (Elementary idea only); Role of hormones as messengers and regulators) Hypo and Hyperactivity and related disorders: Common disorders – Dwarfism, acromegaly, cretinism, goiter, exophthalmic goiter, diabetes, Addison’s disease, Cushing’s syndrome. (Diseases & disorders to be dealt in brief).

Unit IVB: Immune System
Basic concepts of Immunology – Types of Immunity – Innate Immunity, Acquired Immunity, Active and Passive Immunity, Cell-mediated Immunity and Humoral Immunity, Interferon, HIV, and AIDS.

Unit V Human Reproduction (22 Periods)

Unit VA: Human Reproductive System
Male and female reproductive systems; Microscopic anatomy of testis & ovary; Gametogenesis is Sper-matogenesis & Oogenesis; Menstrual cycle; Fertilization, Embryo development up to blastocyst formation. Implantation; Pregnancy, placenta formation. Parturition, Lactation (elementary idea).

Unit VB: Reproductive Health
Need for reproductive health and prevention of sexually transmitted diseases (STD); Birth control – need and methods, contraception and medical termination of pregnancy (MTP); Amniocentesis; infertility and assisted reproductive technologies – IVF-ET, ZIFT, GIFT (Elementary idea for general awareness).

Unit VI Genetics (20 Periods)
Heredity and variation: Mendel’s laws of inheritance with reference to Drosophila. (Drosophila melanogaster Grey, Black body colour; Long, Vestigial wings), Pleiotropy; Multiple alleles: Inheritance of blood groups and Rh-factor; Co-dominance (Blood groups as an example); Elementary idea of polygenic inher¬itance: Skin colour in humans (refer Sinnott, Dtinn and Dobzhansky); Sex determination – in humans, birds, Fumea moth, genic balance theory of sex determination in Drosophila melanogaster and honey bees; Sex-linked inheritance – Haemophilia, Colour blindness; Mendelian disorders in humans: Thalassemia, Haemophilia, Sickle celled anemia, cystic fibrosis PKU, Alkaptonuria; Chromosomal disorders – Down’s syndrome. Turner’s syndrome and Klinefelter syndrome; Genome, Human Genome Project and DNA Finger Printing.

Unit VII Organic Evolution (15 Periods)
Origin of Life, Biological evolution and Evidence for biological evolution (palaeontological, comparative anatomical, embryological and molecular evidence); Theories of evolution: Lamarckism (in brief), Darwin’s theory of Evolution – Natural Selection with example (Kettlewell’s experiments on Biston Bulgaria). Mutation Theory of Hugo De Vries; Modern synthetic theory of Evolution – Hardy- Weinberg law; Types of Natural Selection; Geneflow and genetic drift; Variations (mutations and genetic recombination); Adaptive radiation – viz., Darwin’s finches and adaptive radiation in marsupials; Human evolution; Speciation – Allopatric, sym- Patric; Reproductive isolation.

Unit VIII Applied Biology (15 Periods)
Apiculture; Animal Husbandry:’Pisciculture, Poultry management. Dairy management; Animal breeding; Bio-medical Technology: Diagnostic Imaging (X-Ray, CT scan, MRI), ECG, EEG; Application of Biotechnology in health: Human insulin and vaccine production; Gene Therapy; Transgenic Animals; ELISA; Vaccines, MABs, Cancer biology, stem cells.

We hope that this Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Zoology Study Material Textbook Solutions Guide PDF Free Download 2022-2023 in English Medium and Telugu Medium helps the student to come out successful with flying colors in this examination. This Sr Inter 2nd Year Zoology Study Material will help students to gain the right knowledge to tackle any type of questions that can be asked during the exams.

AP Inter 2nd Year Botany Notes

Students can go through Telangana & Andhra Pradesh BIEAP TS AP Inter 2nd Year Botany Notes Pdf Download in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP Sr Inter 2nd Year Botany Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics.

Students can also go through AP Inter 2nd Year Botany Study Material and AP Inter 2nd Year Botany Important Questions for exam preparation.

AP Intermediate 2nd Year Botany Notes

TS AP Inter 2nd Year Botany Weightage Blue Print

These TS AP Intermediate 2nd Year Botany Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations. These Inter 2nd Year Botany Notes will enable students to study smartly and get a clear idea about each and every concept discussed in their syllabus.

AP Inter 2nd Year Botany Important Questions Chapter Wise Pdf 2022-2023 | Sr Inter Botany Important Questions

TS AP Intermediate 2nd Year Botany Important Questions Chapter Wise 2022: Here we have created a list of Telangana & Andhra Pradesh BIEAP TS AP Intermediate Sr Inter 2nd Year Botany Important Questions Chapter Wise with Answers 2022-2023 Pdf Download just for you. Those who are preparing for Inter exams should practice the Intermediate 2nd Year Botany Important Questions Pdf and do so will clear their doubts instantly. These Senior Inter Botany Important Questions with Answers enhance your conceptual knowledge and prepares you to solve different types of questions in the exam.

Students must practice these AP Inter 2nd Year Botany Important Questions Pdf to boost their preparation for the exam paper. These AP Intermediate 2nd Year Botany Important Questions with Answers are prepared as per the latest exam pattern. Each of these chapters contains a set of solved questions and additional questions for practice.

Students can also read AP Inter 2nd Year Botany Study Material for exam preparation. Students can also go through AP Inter 2nd Year Botany Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Botany Important Questions with Answers Chapter Wise 2022

Intermediate 2nd Year Botany Important Questions Chapter Wise 2022

Unit I Plants Physiology

  • Chapter 1 Transport in Plants Important Questions
  • Chapter 2 Mineral Nutrition Important Questions
  • Chapter 3 Enzymes Important Questions
  • Chapter 4 Photosynthesis in Higher Plants Important Questions
  • Chapter 5 Respiration in Plants Important Questions
  • Chapter 6 Plant Growth and Development Important Questions

Unit II Microbiology

  • Chapter 7 Bacteria Important Questions
  • Chapter 8 Viruses Important Questions

Unit III Genetics

  • Chapter 9 Principles of Inheritance and Variation Important Questions

Unit IV Molecular Biology

  • Chapter 10 Molecular Basis of Inheritance Important Questions

Unit V Biotechnology

  • Chapter 11 Biotechnology: Principles and Processes Important Questions
  • Chapter 12 Biotechnology and its Applications Important Questions

Unit VI Microbes and Human Welfare

  • Chapter 13 Strategies for Enhancement in Food Production Important Questions
  • Chapter 14 Microbes in Human Welfare Important Questions

TS AP Inter 2nd Year Botany Weightage Blue Print

We are providing well-organized Botany Important Questions Inter 2nd Year that will help students in their exam preparation. These Botany Inter 2nd Year Important Questions are designed by subject experts. So Students should utilise the Intermediate 2nd Year Botany Important Questions with Answers 2022 to pass their board exams with flying colours.

The questions given in the Inter Second Year Botany Important Questions are designed and laid out chronologically and as per the syllabus. Students can expect that these TS AP Intermediate Inter 2nd Year Botany Important Questions Chapter Wise Pdf 2022-2023 might be covered in the final exam paper.

AP Inter 2nd Year Botany Study Material Pdf | Intermediate 2nd Year Botany Textbook Solutions

Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Botany Study Material Textbook Solutions Guide PDF Free Download, TS AP Inter 2nd Year Botany Blue Print Weightage 2022-2023, Telugu Academy Intermediate 2nd Year Botany Textbook Pdf Download, Questions and Answers Solutions in English Medium and Telugu Medium are part of AP Inter 2nd Year Study Material Pdf.

Students can also read AP Inter 2nd Year Botany Syllabus & AP Inter 2nd Year Botany Important Questions for exam preparation. Students can also go through AP Inter 2nd Year Botany Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Botany Study Material Pdf Download | Sr Inter 2nd Year Botany Textbook Solutions

Unit I Plants Physiology

Unit II Microbiology

Unit III Genetics

Unit IV Molecular Biology

Unit V Biotechnology

Unit VI Microbes and Human Welfare

TS AP Inter 2nd Year Botany Weightage Blue Print 2022-2023

TS AP Inter 2nd Year Botany Weightage 2022-2023 | TS AP Inter 2nd Year Botany Blue Print 2022

  • TS AP Inter 2nd Year Botany Weightage Blue Print

Intermediate 2nd Year Botany Syllabus

TS AP Inter 2nd Year Botany Syllabus

Unit I Plants Physiology

Chapter 1 Transport in Plants
Means of Transport – Diffusion, Facilitated Diffusion, Passive symports and antiports, Active Transport, Comparison of Different Transport Processes, Plant-Water Relations – Water Potential, Osmosis, Plasmolysis, Imbibition, Long Distance Transport of Water – Water Movement up a Plant, Root Pressure, Transpiration pull, Transpiration – Opening and Closing of Stomata, Transpiration and Photosynthesis, Uptake and Transport of Mineral Nutrients – Uptake of Mineral Ions, Translocation of Mineral Ions, Phloem Transport: Flow from Source to Sink – The Pressure Flow or Mass Flow Hypothesis.

Chapter 2 Mineral Nutrition
Methods to Study the Mineral Requirements of Plants, Essential Mineral Elements – Criteria for Essentiality, Macronutrients, Micronutrients, Role of Macro- and Micro- nutrients, Deficiency Symptoms of Essential Elements, Toxicity of Micronutrients, Mechanism of Absorption of Elements, Translocation of Solutes, Soil as Reservoir of Essential Elements, Metabolism of Nitrogen -Nitrogen Cycle, Biological Nitrogen Fixation, Symbiotic nitrogen fixation, Nodule Formation.

Chapter 3 Enzymes
Chemical Reactions, Enzymatic Conversions, Nature of EnzymeAction, Factors Affecting Enzyme Activity, Temperature and pH, Concentration of Substrate, Classification and Nomenclature of Enzymes, Co-factors.

Chapter 4 Photosynthesis in Higher Plants
Early Experiments, Site of Photosynthesis, Pigments Involved in Photosynthesis, Light Reaction, The Electron TransportSplitting of Water, Cyclic and Non- cyclic Photo-phosphorylation, Chemiosmotic Hypothesis, Biosynthetic phase – The Primary Acceptor of CO2, The Calvin Cycle, The C4 Pathway, Photorespiration, Factors affecting Photosynthesis.

Chapter 5 Respiration of Plants
Cellular respiration, Glycolysis, Fermentation, Aerobic Respiration – Tricarboxylic Acid Cycle, Electron Transport System (ETS) and Oxidative Phosphorylation, The Respiratory Balance Sheet, Amphibolic Pathway, Respiratory Quotient.

Chapter 6 Plant Growth and Development
Growth- Plant Growth, Phases of Growth, Growth Rates, Conditions for Growth, Differentiation, Dedifferentiation and Redifferentiation, Development, Plant Growth Regulators – Physiological Effects of Plant Growth Regulators, Auxins, Gibberellins, Cytokinins, Ethylene, Abscisic acid, Seed Dormancy, Photoperiodism, Vernalisation.

Unit II Microbiology

Chapter 7 Bacteria
Morphology of Bacteria, Bacterial cell structure – Nutrition, Reproduction – Sexual Reproduction, Conjugation, Transformation, Transduction, The importance of Bacteria to Humans.

Chapter 8 Viruses
Discovery, Classification of Viruses, structure of Viruses, Multiplication of Bacteriophages – The Lysogenic Cycle, Viral diseases in Plants, Viral diseases in Humans.

Unit III Genetics

Chapter 9 Principles of Inheritance and Variation
Mendel’s Experiments, Inheritance of one gene (Monohybrid Cross) – Back cross and Test cross, Law of Dominance, Law of Segregation or Law of purity of gametes, Deviations from Mendelian concept of dominance – Incomplete Dominance, Co-dominance, Explanation of the concept of dominance, Inheritance of two genesLaw of Independent Assortment, Chromosomal Theory of Inheritance, Linkage and Recombination, Mutations – Significance of mutations.

Unit IV Molecular Biology

Chapter 10 Molecular Basis of inheritance
The DNA – Structure of Polynucleotide Chain, Packaging of DNA Helix, The Search for Genetic Material, Transforming Principle, Biochemical Characterisation of Transforming Principle, The Genetic Material is DNA, Properties of Genetic Material (DNA versus RNA), RNA World, Replication – The Experimental Proof, The Machinery and the Enzymes, Transcription – Transcription Unit, Transcription Unit and the Gene, Types of RNA and the process of Transcription, GeneticCodeMutations and Genetic Code, tRNA– the Adapter Molecule, Translation, Regulation of Gene Expression – The Lac operon.

Unit V Biotechnology

Chapter 11 Principles and Processes of Biotechnology
Principles of Biotechnology – Construction of the first artificial recombinant DNA molecule, Tools of Recombinant DNA Technology – Restriction Enzymes, Cloning Vectors, Competent Host (For Transformation with Recombinant DNA), Processes of Recombinant DNA Technology – Isolation of the Genetic Material (DNA), Cutting of DNA at Specific Locations, Separation and isolation of DNA fragments, Insertion of isolated gene into a suitable vector, Amplification of Gene of Interest using PCR, Insertion of Recombinant DNA into the Host, Cell/Organism, Selection of Transformed host cells, Obtaining the Foreign Gene Product, Downstream Processing.

Chapter 12 Biotechnology and it’s Applications
Biotechnological Applications In Agriculture – Bt Cotton, Pest Resistant Plants, Other applications of Biotechnology Insulin, Gene therapy, Molecular Diagnosis, ELISA, DNA fingerprinting, Transgenic plants, Bio-safety and Ethical issues – Biopiracy.

Unit VI Plants, Microbes and Human Welfare

Chapter 13 Strategies for Enhancement in Food Production
Plant Breeding – What is Plant Breeding?, Wheat and Rice, Sugarcane, Millets, Plant Breeding for Disease Resistance, Methods of breeding for disease resistance, Mutation, Plant Breeding for Developing Resistance to Insect Pests, Plant Breeding for Improved Food Quality, Single Cell Protein (SCP), Tissue Culture.

Chapter 14 Microbes in Human Welfare
Microbes in Household Products, Microbes in Industrial Products – Fermented Beverages, Antibiotics, Chemicals, Enzymes and other Bioactive Molecules, Microbes in Sewage Treatment, Primary treatment, Secondary treatment or Biological treatment, Microbes in Production of Biogas, Microbes as Biocontrol Agents, Biological control of pests and diseases, Microbes as Biofertilisers, Challenges posed by Microbes.

We hope that this Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Botany Study Material Textbook Solutions Guide PDF Free Download 2022-2023 in English Medium and Telugu Medium helps the student to come out successful with flying colors in this examination. This Sr Inter 2nd Year Botany Study Material will help students to gain the right knowledge to tackle any type of questions that can be asked during the exams.

AP Inter 2nd Year Physics Notes

Students can go through Telangana & Andhra Pradesh BIEAP TS AP Inter 2nd Year Physics Notes Pdf Download in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP Sr Inter 2nd Year Physics Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics.

Students can also go through AP Inter 2nd Year Physics Study Material and AP Inter 2nd Year Physics Important Questions for exam preparation.

AP Intermediate 2nd Year Physics Notes

TS AP Inter 2nd Year Physics Weightage Blue Print

These TS AP Intermediate 2nd Year Physics Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations. These Inter 2nd Year Physics Notes will enable students to study smartly and get a clear idea about each and every concept discussed in their syllabus.

AP Inter 2nd Year Physics Important Questions Chapter Wise Pdf 2022-2023 | Sr Inter Physics Important Questions

TS AP Intermediate 2nd Year Physics Important Questions Chapter Wise 2022: Here we have created a list of Telangana & Andhra Pradesh BIEAP TS AP Intermediate Sr Inter 2nd Year Physics Important Questions Chapter Wise with Answers 2022-2023 Pdf Download just for you. Those who are preparing for Inter exams should practice the Intermediate 2nd Year Physics Important Questions Pdf and do so will clear their doubts instantly. These Senior Inter Physics Important Questions with Answers enhance your conceptual knowledge and prepares you to solve different types of questions in the exam.

Students must practice these AP Inter 2nd Year Physics Important Questions Pdf to boost their preparation for the exam paper. These AP Intermediate 2nd Year Physics Important Questions with Answers are prepared as per the latest exam pattern. Each of these chapters contains a set of solved questions and additional questions for practice.

Students can also read AP Inter 2nd Year Physics Study Material for exam preparation. Students can also go through AP Inter 2nd Year Physics Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Physics Important Questions with Answers Chapter Wise 2022

Intermediate 2nd Year Physics Important Questions Chapter Wise 2022

TS AP Inter 2nd Year Physics Weightage Blue Print

We are providing well-organized Physics Important Questions Inter 2nd Year that will help students in their exam preparation. These Physics Inter 2nd Year Important Questions are designed by subject experts. So Students should utilise the Intermediate 2nd Year Physics Important Questions with Answers 2022 to pass their board exams with flying colours.

The questions given in the Inter Second Year Physics Important Questions are designed and laid out chronologically and as per the syllabus. Students can expect that these TS AP Intermediate Inter 2nd Year Physics Important Questions Chapter Wise Pdf 2022-2023 might be covered in the final exam paper.

AP Inter 2nd Year Physics Study Material Pdf | Intermediate 2nd Year Physics Textbook Solutions

Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Physics Study Material Textbook Solutions Guide PDF Free Download, TS AP Inter 2nd Year Physics Blue Print Weightage 2022-2023, Telugu Academy Intermediate 2nd Year Physics Textbook Pdf Download, Questions and Answers Solutions in English Medium and Telugu Medium are part of AP Inter 2nd Year Study Material Pdf.

Students can also read AP Inter 2nd Year Physics Syllabus & AP Inter 2nd Year Physics Important Questions for exam preparation. Students can also go through AP Inter 2nd Year Physics Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Physics Study Material Pdf Download | Sr Inter 2nd Year Physics Textbook Solutions

TS AP Inter 2nd Year Physics Weightage Blue Print 2022-2023

TS AP Inter 2nd Year Physics Weightage 2022-2023 | TS AP Inter 2nd Year Physics Blue Print 2022

TS AP Inter 2nd Year Physics Weightage Blue Print

Intermediate 2nd Year Physics Syllabus

TS AP Inter 2nd Year Physics Syllabus

Chapter 1 Waves

  • Introduction
  • Transverse and longitudinal waves
  • Displacement relation in a progressive wave
  • The speed of a traveling wave
  • The principle of superposition of waves
  • Reflection of waves
  • Beats
  • Doppler effect

Chapter 2 Ray Optics and Optical Instruments

  • Introduction
  • Reflection of Light by Spherical Mirrors
  • Refraction
  • Total Internal Reflection
  • Refraction at Spherical Surfaces and by Lenses
  • Refraction through a Prism
  • Dispersion by a Prism
  • Some Natural Phenomena due to Sunlight
  • Optical Instruments

Chapter 3 Wave Optics

  • Introduction
  • Huygens Principle
  • Refraction and reflection of plane waves using the Huygens Principle
  • Coherent and Incoherent Addition of Waves
  • Interference of Light Waves and Young’s Experiment
  • Diffraction
  • Polarisation

Chapter 4 Electric Charges and Fields

  • Introduction
  • Electric Charges
  • Conductors and Insulators
  • Charging by Induction
  • Basic Properties of Electric Charge
  • Coulomb’s Law
  • Forces between Multiple Charges
  • Electric Field
  • Electric Field Lines
  • Electric Flux
  • Electric Dipole
  • Dipole in a Uniform External Field
  • Continuous Charge Distribution
  • Gauss’s Law
  • Application of Gauss’s Law

Chapter 5 Electrostatic Potential and Capacitance

  • Introduction
  • Electrostatic Potential
  • Potential due to a Point Charge
  • Potential due to an Electric Dipole
  • Potential due to a System of Charges
  • Equipotential Surfaces
  • Potential Energy of a System of Charges
  • Potential Energy in an External Field
  • Electrostatics of Conductors
  • Dielectrics and Polarisation
  • Capacitors and Capacitance
  • The Parallel Plate Capacitor
  • Effect of Dielectric on Capacitance
  • Combination of Capacitors
  • Energy Stored in a Capacitor
  • Van de Graaff Generator

Chapter 6 Current Electricity

  • Introduction
  • Electric Current
  • Electric Currents in Conductors
  • Ohm’s law
  • The drift of Electrons and the Origin of Resistivity
  • Limitations of Ohm’s Law
  • The resistivity of various Materials
  • Temperature Dependence of Resistivity
  • Electrical Energy, Power
  • Combination of Resistors – Series and Parallel
  • Cells, emf, Internal Resistance
  • Cells in Series and in Parallel
  • Kirchhoff’s Laws
  • Wheatstone Bridge
  • Meter Bridge
  • Potentiometer

Chapter 7 Moving Charges and Magnetism

  • Introduction
  • Magnetic Force
  • Motion in a Magnetic Field
  • Motion in Combined Electric and Magnetic Fields
  • Magnetic Field due to a Current Element, Biot-SavartLaw
  • Magnetic Field on the Axis of a Circular Current Loop
  • Ampere’s Circuital Law
  • The Solenoid and the Toroid
  • The force between Two Parallel Currents, the Ampere
  • Torque on Current Loop, Magnetic Dipole
  • The Moving Coil Galvanometer

Chapter 8 Magnetism and Matter

  • Introduction
  • The Bar Magnet
  • Magnetism and Gauss’s Law
  • The Earth’s Magnetism
  • Magnetization and Magnetic Intensity
  • Magnetic Properties of Materials
  • Permanent Magnets and Electromagnets

Chapter 9 Electromagnetic Induction

  • Introduction
  • The Experiments of Faraday and Henry
  • Magnetic Flux
  • Faraday’s Law of Induction
  • Lenz’s Law and Conservation of Energy
  • Motional Electromotive Force
  • Energy Consideration: A Quantitative Study
  • Eddy Currents
  • Inductance
  • AC Generator

Chapter 10 Alternating Current

  • Introduction
  • AC Voltage Applied to a Resistor
  • Representation of AC Current and Voltage by Rotating Vectors – Phasors
  • AC Voltage Applied to an Inductor
  • AC Voltage Applied to a Capacitor
  • AC Voltage Applied to a Series LCR Circuit
  • Power in AC Circuit: The Power Factor
  • LC Oscillations
  • Transformers

Chapter 11 Electromagnetic Waves

  • Introduction
  • Displacement Current
  • Electromagnetic Waves
  • Electromagnetic Spectrum

Chapter 12 Dual Nature of Radiation and Matter

  • Introduction
  • Electron Emission Photoelectric Effect
  • Experimental Study of Photoelectric Effect
  • Photoelectric Effect and Wave Theory of Light
  • Einstein’s Photoelectric Equation: Energy Quantum of Radiation
  • Particle Nature of Light: The Photon
  • Wave Nature of Matter
  • Davisson and Germer Experiment

Chapter 13 Atoms

  • Introduction
  • Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom
  • Atomic Spectra
  • Bohr Model of the Hydrogen Atom
  • The Line Spectra of the Hydrogen Atom
  • DE Broglie’s Explanation of Bohr’s Second Postulate of Quantisation

Chapter 14 Nuclei

  • Introduction
  • Atomic Masses and Composition of Nucleus
  • Size of the Nucleus
  • Mass-Energy and Nuclear Binding Energy
  • Nuclear Force
  • Radioactivity
  • Nuclear Energy

Chapter 15 Semiconductor Electronics: Materials, Devices and Simple Circuits

  • Introduction
  • Classification of Metals, Conductors and Semiconductors
  • Intrinsic Semiconductor
  • Extrinsic Semiconductor
  • p-n Junction
  • Semiconductor diode
  • Application of Junction Diode as a Rectifier
  • Special Purpose p-n Junction Diodes
  • Junction Transistor
  • Digital Electronics and Logic Gates
  • Integrated Circuits

Chapter 16 Communication Systems

  • Introduction
  • Elements of a Communication System
  • Basic Terminology Used in Electronic Communication Systems
  • Bandwidth of Signals
  • The bandwidth of Transmission Medium
  • Propagation of Electromagnetic Waves
  • Modulation and its Necessity
  • Amplitude Modulation
  • Production of Amplitude Modulated Wave
  • Detection of Amplitude Modulated Wave

We hope that this Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Physics Study Material Textbook Solutions Guide PDF Free Download 2022-2023 in English Medium and Telugu Medium helps the student to come out successful with flying colors in this examination. This Sr Inter 2nd Year Physics Study Material will help students to gain the right knowledge to tackle any type of questions that can be asked during the exams.

AP Inter 2nd Year Chemistry Notes

Students can go through Telangana & Andhra Pradesh BIEAP TS AP Inter 2nd Year Chemistry Notes Pdf Download in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP Sr Inter 2nd Year Chemistry Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics.

Students can also go through AP Inter 2nd Year Chemistry Study Material and AP Inter 2nd Year Chemistry Important Questions for exam preparation.

AP Intermediate 2nd Year Chemistry Notes

TS AP Inter 2nd Year Chemistry Weightage Blue Print

These TS AP Intermediate 2nd Year Chemistry Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations. These Inter 2nd Year Chemistry Notes will enable students to study smartly and get a clear idea about each and every concept discussed in their syllabus.

AP Inter 2nd Year Chemistry Important Questions Chapter Wise Pdf 2022-2023 | Sr Inter Chemistry Important Questions

TS AP Intermediate 2nd Year Chemistry Important Questions Chapter Wise 2022: Here we have created a list of Telangana & Andhra Pradesh BIEAP TS AP Intermediate Sr Inter 2nd Year Chemistry Important Questions Chapter Wise with Answers 2022-2023 Pdf Download just for you. Those who are preparing for Inter exams should practice the Intermediate 2nd Year Chemistry Important Questions Pdf and do so will clear their doubts instantly. These Senior Inter Chemistry Important Questions with Answers enhance your conceptual knowledge and prepares you to solve different types of questions in the exam.

Students must practice these AP Inter 2nd Year Chemistry Important Questions Pdf to boost their preparation for the exam paper. These AP Intermediate 2nd Year Chemistry Important Questions with Answers are prepared as per the latest exam pattern. Each of these chapters contains a set of solved questions and additional questions for practice.

Students can also read AP Inter 2nd Year Chemistry Study Material for exam preparation. Students can also go through AP Inter 2nd Year Chemistry Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Chemistry Important Questions with Answers Chapter Wise 2022

Intermediate 2nd Year Chemistry Important Questions Chapter Wise 2022

TS AP Inter 2nd Year Chemistry Weightage Blue Print

We are providing well-organized Chemistry Important Questions Inter 2nd Year that will help students in their exam preparation. These Chemistry Inter 2nd Year Important Questions are designed by subject experts. So Students should utilise the Intermediate 2nd Year Chemistry Important Questions with Answers 2022 to pass their board exams with flying colours.

The questions given in the Inter Second Year Chemistry Important Questions are designed and laid out chronologically and as per the syllabus. Students can expect that these TS AP Intermediate Inter 2nd Year Chemistry Important Questions Chapter Wise Pdf 2022-2023 might be covered in the final exam paper.

AP Inter 2nd Year Chemistry Study Material Pdf | Intermediate 2nd Year Chemistry Textbook Solutions

Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Chemistry Study Material Textbook Solutions Guide PDF Free Download, TS AP Inter 2nd Year Chemistry Blue Print Weightage 2022-2023, Telugu Academy Intermediate 2nd Year Chemistry Textbook Pdf Download, Questions and Answers Solutions in English Medium and Telugu Medium are part of AP Inter 2nd Year Study Material Pdf.

Students can also read AP Inter 2nd Year Chemistry Syllabus & AP Inter 2nd Year Chemistry Important Questions for exam preparation. Students can also go through AP Inter 2nd Year Chemistry Notes to understand and remember the concepts easily.

AP Intermediate 2nd Year Chemistry Study Material Pdf Download | Sr Inter 2nd Year Chemistry Textbook Solutions

TS AP Inter 2nd Year Chemistry Weightage Blue Print 2022-2023

TS AP Inter 2nd Year Chemistry Weightage 2022-2023 | TS AP Inter 2nd Year Chemistry Blue Print 2022

TS AP Inter 2nd Year Chemistry Weightage Blue Print

Intermediate 2nd Year Chemistry Syllabus

TS AP Inter 2nd Year Chemistry Syllabus

Chapter 1 Solid State

  • 1.1 General characteristics of solid state
  • 1.2 Amorphous and crystalline solids
  • 1.3 Classification of crystalline solids based on different binding forces (molecular, ionic, metallic, and covalent solids)
  • 1.4 Probing the structure of solids: X-ray crystallography
  • 1.5 Crystal lattices and unit cells, Bravais lattices primitive and centered unit cells
  • 1.6 Number of atoms in a unit cell (primitive, body-centered, and face-centered cubic unit cell)
  • 1.7 Close packed structures: Close packing in one dimension, in two dimensions, and in three dimensions- tetrahedral and octahedral voids- formula of a compound and number of voids filled- locating tetrahedral and octahedral voids
  • 1.8 Packing efficiency in simple cubic, bcc, and in hcp, ccp lattice.
  • 1.9 Calculations involving unit cell dimensions- density of the unit cell.
  • 1.10 Imperfections in solids-types of point defects-stoichiometric and non-stoichiometric defects
  • 1.11 Electrical properties-conduction of electricity in metals, semiconductors, and insulators band theory of metals
  • 1.12 Magnetic properties

Chapter 2 Solutions

  • 2.1 Types of solutions
  • 2.2 Expressing concentration of solutions-mass percentage, volume percentage, mass by volume percentage, parts per million, mole fraction, molarity, and molality
  • 2.3 Solubility: Solubility of a solid in a liquid, solubility of a gas in a liquid, Henry’s law
  • 2.4 Vapour pressure of liquid solutions: vapour pressure of liquid-liquid solutions. Raoult’s law is a special case of Henry’s law – vapour pressure of solutions of solids in liquids
  • 2.5 Ideal and non-ideal solutions
  • 2.6 Colligative properties and determination of molar mass-relative lowering of vapour pressure-elevation of boiling point-depression of freezing point-osmosis and osmotic pressure-reverse osmosis and water purification.
  • 2.7 Abnormal molar masses-van’t Hoff factor

Chapter 3 Electrochemistry And Chemical Kinetics
Electrochemistry

  • 3.1 Electrochemical cells
  • 3.2 Galvanic cells measurement of electrode potentials
  • 3.3 Nernst equation-equilibrium constant from Nernst equation-electrochemical cell and Gibbs energy of the cell reaction
  • 3.4 Conductance of electrolytic solutions- measurement of the conductivity of ionic solutions- a variation of conductivity and molar conductivity with concentration-strong electrolytes and weak electrolytes-applications of Kohlrausch’s law
  • 3.5 Electrolytic cells and electrolysis: Faraday’s laws of electrolysis-products of electrolysis
  • 3.6 Batteries: primary batteries and secondary batteries
  • 3.7 Fuel cells
  • 3.8 Corrosion of metals-Hydrogen economy

Chemical Kinetics

  • 3.9 Rate of a chemical reaction
  • 3.10 Factors influencing the rate of a reaction: dependence of rate on concentration- rate expression and rate constant- order of a reaction, molecularity of a reaction
  • 3.11 Integrated rate equations-zero order reactions-first order reactions-half life of a reaction
  • 3.12 Pseudo first-order reaction
  • 3.13 Temperature dependence of the rate of a reaction-effect of catalyst
  • 3.14 Collision theory of chemical reaction rates

Chapter 4 Surface Chemistry

  • 4.1 Adsorption and absorption: Distinction between adsorption and absorption-mechanism of adsorption-types of adsorption- characteristics of physisorption- characteristics of chemisorptions- adsorption isotherms- adsorption from solution phase- applications of adsorption
  • 4.2 Catalysis: Catalysts, promoters, and poisons-auto catalysis- homogeneous and heterogeneous catalysis- adsorption theory of heterogeneous catalysis- important features of solid catalysts: (a) activity (b) selectivity- shape-selective catalysis by zeolites- enzyme catalysis- characteristics and mechanism- catalysts in industry
  • 4.3 Colloids
  • 4.4 Classification of colloids: Classification based on the physical state of the dispersed phase and dispersion medium- classification based on nature of the interaction between the dispersed phase and dispersion medium- classification based on the type of particles of the dispersed phase- multi molecular, macromolecular, and associated colloids-cleansing action of soaps-preparation of colloids-purification of colloidal solutions-properties of colloidal solutions: Tyndal effect, colour, Brownian movement-charge on colloidal particles, electrophoresis
  • 4.5 Emulsions
  • 4.6 Colloids Around us- application of colloids

Chapter 5 General Principles of Metallurgy

  • 5.1 Occurance of metals
  • 5.2 Concentration of ores- levigation, magnetic separation, froth floatation, leaching
  • 5.3 Extraction of crude metal from concentrated ore-conversion to oxide, reduction of oxide to the metal
  • 5.4 Thermodynamic principles of metallurgy-Ellingham diagram-limitations-applications-extraction of iron, copper, and zinc from their oxides
  • 5.5 Electrochemical principles of metallurgy
  • 5.6 Oxidation and reduction
  • 5.7 Refining of crude metal distillation, liquation poling, electrolysis, zone refining, and vapour phase refining
  • 5.8 Uses of aluminium, copper, zinc, and iron

Chapter 6 P-Block Elements
Group-15 Elements

  • 6.1 Occurance- electronic configuration, atomic and ionic radii, ionization energy, electronegativity, physical and chemical properties
  • 6.2 Dinitrogen- preparation, properties, and uses
  • 6.3 Compounds of nitrogen-preparation and properties of ammonia
  • 6.4 Oxides of nitrogen
  • 6.5 Preparation and properties of nitric acid
  • 6.6 Phosphorous-allotropic forms
  • 6.7 Phosphine-preparation and properties
  • 6.8 Phosphorous halides
  • 6.9 Oxoacids of phosphorous

Group-16 Elements

  • 6.10 Occurance- electronic configuration, atomic and ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, physical and chemical properties
  • 6.11 Dioxygen-preparation, properties, and uses
  • 6.12 Simple oxides
  • 6.13 Ozone preparation, properties, structure and uses
  • 6.14 Sulphur-allotropic forms
  • 6.15 Sulphur dioxide preparation, properties and uses
  • 6.16 Oxoacids of sulphur
  • 6.17 Sulphuric acid-industrial process of manufacture, properties and uses

Group-17 Elements

  • 6.18 Occurance, electronic configuration, atomic and ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, physical and chemical properties
  • 6.19 Chlorine preparation, properties, and uses
  • 6.20 Hydrogen chloride- preparation, properties and uses
  • 6.21 Oxoacids of halogens
  • 6.22 Interhalogen compounds

Group-18 Elements

  • 6.23 Occurance, electronic configuration, ionisation enthalpy,atomic radii electron gain enthalpy, physical and chemical properties (a) Xenon-fluorine compounds – XeF2, XeF4 and XeF6 – preparation,hydrolysis and formation of fluoro anions- structures of XeF2, XeF4 and XeF6 (b) Xenon-oxygen compounds XeO3 and XeOF4 – their formation and structures

Chapter 7 d and f Block Elements & Coordination Compounds
d And f Block Elements

  • 7.1 Position in the periodic table
  • 7.2 Electronic configuration of the d-block elements
  • 7.3 General properties of the transition elements (d-block) -physical properties, variation in atomic and ionic sizes of transition series, ionization enthalpies, oxidation states, trends in the M2+/M and M3+/M2+ standard electrode potentials, trends in the stability of higher oxidation states, chemical reactivity and EJ values, magnetic properties, formation of colored ions, formation of complex compounds, catalytic properties, formation of interstitial compounds, alloy formation
  • 7.4 Some important compounds of transition elements-oxides and oxoanions of metals-preparation and properties of potassium dichromate and potassium permanganate-structures of chromate, dichromate, manganate, and permanganate ions
  • 7.5 Inner transition elements(f-block)-lanthanoids- electronic configuration-atomic and ionic sizes-oxidation states- general characteristics
  • 7.6 Actinoids-electronic configuration atomic and ionic sizes, oxidation states, general characteristics, and comparison with lanthanoids
  • 7.7 Some applications of d and f block elements

Coordination Compounds

  • 7.8 Werner’s theory of coordination compounds
  • 7.9 Definitions of some terms used in coordination compounds
  • 7.10 Nomenclature of coordination compounds- IUPAC nomenclature
  • 7.11 Isomerism in coordination compounds-(a)Stereo isomerism- Geometrical and optical isomerism (b)Structural isomerism- linkage, coordination, ionization, and solvate isomerism
  • 7.12 Bonding in coordination compounds. (a)Valence bond theory – magnetic properties of coordination compounds-limitations of valence bond theory (b) Crystal field theory (i) Crystal field splitting in octahedral and tetrahedral coordination entities (ii) Colour in coordination compounds-limitations of crystal field theory
  • 7.13 Bonding in metal carbonyls
  • 7.14 Stability of coordination compounds
  • 7.15 Importance and applications of coordination compounds

Chapter 8 Polymers

  • 8.1 Classification of Polymers -Classification based on source, structure, mode of polymerization, molecular forces, and growth polymerization
  • 8.2 Types of polymerization reactions- addition polymerization or chain growth polymerization- ionic polymerization, free radical mechanism-preparation of addition polymers- polythene, Teflon, and polyacrylonitrile-condensation polymerization or step growth polymerization-polyamides- preparation of Nylon 6,6 and nylon 6-poly esters- terylene- bakelite, melamine, formaldehyde polymer- copolymerization- Rubber- natural rubber-vulcanization of rubber-Synthetic rubbers- preparation of neoprene and buna-N
  • 8.3 Molecular mass of polymers-number average and weight average molecular masses- polydispersity index(PDI)
  • 8.4 Biodegradable polymers- PHBV, Nylon 2-nylon 6
  • 8.5 Polymers of commercial importance- poly propene, polystyrene, polyvinyl chloride(PVC), urea-formaldehyde resin, glyptal, bakelite- their monomers, structures, and uses

Chapter 9 Biomolecules

  • 9.1 Carbohydrates – Classification of carbohydrates- Monosaccharides: preparation of glucose from sucrose and starch- Properties and structure of glucose- D, L and (+), (-) configurations of glucose- Structure of fructose Disaccharides: Sucrose- preparation, structure-Invert sugar- Structures of maltose and lactose-Polysaccharides: Structures of starch cellulose and glycogen- Importance of carbohydrates
  • 9.2 Aminoacids: Natural amino acids- classification of amino acids – structures and D and L forms-Zwitter ions Proteins: Structures, classification, fibrous and globular- primary, secondary, tertiary, and quaternary structures of proteins- Denaturation of proteins
  • 9.3 Enzymes: Enzymes, mechanism of enzyme action
  • 9.4 Vitamins: Explanation- names- classification of vitamins – sources of vitamins-deficiency diseases of different types of vitamins
  • 9.5. Nucleic acids: chemical composition of nucleic acids, structures of nucleic acids, DNA fingerprinting biological functions of nucleic acids
  • 9.6 Hormones: Definition, different types of hormones, their production, biological activity, diseases due to their abnormal activities.

Chapter 10 Chemistry in Everyday Life

  • 10.1 Drugs and their classification: (a) Classification of drugs on the basis of pharmacological effect(b) Classification of drugs on the basis of drug action (c) Classification of drugs on the basis of chemical structure (d) Classification of drugs on the basis of molecular targets
  • 10.2 Drug-Target interaction-Enzymes as drug targets (a) Catalytic action of enzymes (b) Drug-enzyme interaction Receptors as drug targets
  • 10.3 Therapeutic action of different classes of drugs: antacids, antihistamines, neurologically active drugs: tranquilizers, analgesics- non-narcotic, narcotic analgesics, antimicrobials-antibiotics, antiseptics, and disinfectants- antifertility drugs
  • 10.4 Chemicals in food- artificial sweetening agents, food preservatives, antioxidants in food
  • 10.5 Cleansing agents-soaps and synthetic detergents

Chapter 11 Halo Alkanes and Halo Arenes

  • 11.1 Classification and nomenclature
  • 11.2 Nature of C-X bond
  • 11.3 Methods of preparation: Alkyl halides and aryl halides- from alcohols, from hydrocarbons (a) by free radical halogenation (b) by electrophilic substitution (c) by replacement of diazonium group(Sand- Meyer reaction) (d) by the addition of hydrogen halides and halogens to alkenes-by halogen exchange(Finkelstein reaction)
  • 11.4 Physical properties- melting and boiling points, density and solubility
  • 11.5 Chemical reactions: Reactions of haloalkanes (i)Nucleophilic substitution reactions (a) SN2 mechanism (b) SN1 mechanism (c) stereochemical aspects of nucleophilic substitution reactions -optical activity (ii) Elimination reactions (iii) Reaction with metals-Reactions of haloarenes: (i) Nucleophilic substitution (ii)Electrophilic substitution and (iii) Reaction with metals
  • 11.6 Polyhalogen compounds: Uses and environmental effects of dichloro methane, trichloromethane, triiodomethane, tetrachloro methane, freons, and DDT.

Chapter 12 Organic Compounds Containing C, H, and O (Alcohols, Phenols, Ethers, Aldehydes, Ketones, and Carboxylic Acids)
Alcohols, Phenols, and Ethers

  • 12.1 Alcohols, phenols and ethers-classification
  • 12.2 Nomenclature: (a) Alcohols, (b) phenols and (c) ethers
  • 12.3 Structures of hydroxy and ether functional groups
  • 12.4 Methods of preparation: Alcohols from alkenes and carbonyl compounds- Phenols from haloarenes, benzene sulphonic acid, diazonium salts, cumene
  • 12.5 Physical properties of alcohols and phenols
  • 12.6 Chemical reactions of alcohols and phenols (i) Reactions involving cleavage of O-H bond-Acidity of alcohols and phenols, esterification (ii) Reactions involving cleavage of C-O bond- reactions with HX, PX3, dehydration, and oxidation (iii) Reactions of phenols- electrophilic aromatic substitution, Kolbe’s reaction, Reimer – Tiemann reaction, reaction with zinc dust, oxidation
  • 12.7 Commercially important alcohols (methanol, ethanol)
  • 12.8 Ethers-Methods of preparation: By dehydration of alcohols, Williamson synthesis-Physical properties-Chemical reactions: Cleavage of C-O bond and electrophilic substitution of aromatic ethers.

Aldehydes and Ketones

  • 12.9 Nomenclature and structure of carbonyl group 12.10Preparation of aldehydes and ketones-(1) by oxidation of alcohols (2) by dehydrogenation of alcohols (3) from hydrocarbons
  • 12.10 Preparation of aldehydes (1) from acyl chlorides (2) from nitriles and esters (3) from hydrocarbons-Preparation of ketones (1) from acyl chlorides (2) from nitriles (3) from benzene or substituted benzenes
  • 12.11 Physical properties of aldehydes and ketones
  • 12.12 Chemical reactions of aldehydes and ketones-nucleophilic addition, reduction, oxidation, reactions due to Hydrogen, and other reactions (Cannizzaro reaction, electrophilic substitution reaction)
  • 12.13 Uses of aldehydes and ketones

Carboxylic Acids

  • 12.14 Nomenclature and structure of carboxyl group
  • 12.15 Methods of preparation of carboxylic acids- (1)from primary alcohols and aldehydes (2) from alkylbenzenes(3)from nitriles and amides (4)from Grignard reagents (5) from acyl halides and anhydrides (6) from esters
  • 12.16 Physical properties
  • 12.17 Chemical reactions: (i) Reactions involving cleavage of O-H bond-acidity, reactions with metals and alkalies (ii) Reactions involving cleavage of C-OH bond-formation of anhydride, reactions with PCl5, PCl3, SOCl2, esterification, and reaction with ammonia (iii) Reactions involving -COOH group-reduction, decarboxylation (iv) Substitution reactions in the hydrocarbon part – halogenation and ring substitution
  • 12.18 Uses of carboxylic acids

Chapter 13 Organic Compounds Containing Nitrogen
I. Amines

  • 13.1 Structure of amines
  • 13.2 Classification
  • 13.3 Nomenclature
  • 13.4 Preparation of amines: reduction of nitro compounds, ammonolysis of alkyl halides, reduction of nitriles, reduction of amides, Gabriel phthalimide synthesis, and Hoffmann bromamide degradation reaction
  • 13.5 Physical properties
  • 13.6 Chemical reactions: the basic character of amines, alkylation, acylation, carbonyl amine reaction, reaction with nitrous acid, reaction with aryl sulphonyl chloride, the electrophilic substitution of aromatic amines-bromination, nitration and sulphonation

II. DIazonium Salts

  • 13.7 Methods of preparation of diazonium salts (by diazotization)
  • 13.8 Physical properties
  • 13.9 Chemical reactions: Reactions involving

III. Cyanides and Isocyanides

  • 13.10 Structure and nomenclature of cyanides and isocyanides Preparation, physical properties, and chemical reactions of cyanides and isocyanides

We hope that this Telangana & Andhra Pradesh BIEAP TS AP Intermediate Inter 2nd Year Chemistry Study Material Textbook Solutions Guide PDF Free Download 2022-2023 in English Medium and Telugu Medium helps the student to come out successful with flying colors in this examination. This Sr Inter 2nd Year Chemistry Study Material will help students to gain the right knowledge to tackle any type of questions that can be asked during the exams.

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Practicing the Intermediate 1st Year Maths 1B Textbook Solutions Inter 1st Year Maths 1B Applications of Derivatives Solutions Exercise 10(h) will help students to clear their doubts quickly.

Intermediate 1st Year Maths 1B Applications of Derivatives Solutions Exercise 10(h)

I.

Question 1.
Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function.
i) f(x) – x², ∀ x ∈ R.
Solution:
f(x) = x²
f'(x) = 2x ⇒ f”(x) = 2
For maximum or minimum f'(x) = 0
2x = 0
x = 0
Now f”(x) = 2 > 0 ,
∴ f(x) has minimum at x = 0
Point of local minimum x = 0
Local minimum = 0.

ii) f(x) = sin x, [0, 4π)
Solution:
Given f(x) = sinx
⇒ f'(x) = cosx
⇒ f”(x) = -sinx
For max on min,
f'(x) = 0
cos x = 0
⇒ x = [latex]\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\frac{7\pi}{2}[/latex]

i) f”([latex]\frac{\pi}{2}[/latex]) = -sin[latex]\frac{\pi}{2}[/latex] = -1 < 0
f(x) = sin [latex]\frac{\pi}{2}[/latex] = 1
∴ Point of local maximum x = [latex]\frac{\pi}{2}[/latex]
local maximum – 1

ii) f”([latex]\frac{3\pi}{2}[/latex]) = – sin [latex]\frac{3\pi}{2}[/latex] = -1 > 0
f(x) = sin [latex]\frac{3\pi}{2}[/latex] = -1
∴ Point of local minimum x = [latex]\frac{3\pi}{2}[/latex]
local minimum x = -1

iii) f”([latex]\frac{5\pi}{2}[/latex]) = – sin [latex]\frac{5\pi}{2}[/latex] = -1 > 0
f(x) = sin [latex]\frac{5\pi}{2}[/latex] = 1
∴ Point of local maximum x = [latex]\frac{5\pi}{2}[/latex]
local maximum = 1

iv) f”([latex]\frac{7\pi}{2}[/latex]) = – sin [latex]\frac{7\pi}{2}[/latex] = -1 > 0
f(x) = sin [latex]\frac{7\pi}{2}[/latex] = -1
∴ Point of local maximum x = [latex]\frac{7\pi}{2}[/latex]
local maximum = 1

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

iii) f (x) = x³ – 6x² + 9x + 15 ∀ x ∈ R.
Solution:
f (x) = 3x² – 12x + 9 and f'(x) = 6x – 12
For maximum or minimum f(x) = 0
⇒ 3x² – 12x + 9 = 0
⇒ x² – 4x + 3 = 0
⇒ (x – 1) (x – 3) = 0
⇒ x = 1 or 3
Now f”(1) = 6(1) – 12 = – 6 < 0
∴ f(x) has maximum value at x = 1
Max. valueis f(1)= 1³ – 6(1)² + 9(1) + 15
= 1 – 6 + 9 + 15 = 19

f”(3) = 6(3) – 12 = 18 – 12 = 6 > 0
∴ f(x) has minimum value at x = 3
Min. value is f(3) = 33 – 6.32 + 9.3 + 15
= 27 – 54 + 27+ 15
= 15

iv) f(x) = [latex]\sqrt{1-x}[/latex] ∀ x ∈ (0, 1)
Solution:
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 1
For max. or min. f'(x) = 0
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 2

v) f(x) = 1/x² + 2 ∀ x ∈ R
Solution:
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 3
∴ For maximum or minimum f (x) = 0
⇒ [latex]\frac{-2x}{(x^{2}+2)^{2}}[/latex] = 0 ⇒ x = 0
f”(0) = [latex]\frac{2(0-2)}{(0+2^{3})}=\frac{-4}{8}=\frac{-1}{2}[/latex] < 0
∴ f(x) has max. value at x = 0
Max. value is f(0) = [latex]\frac{1}{0+2}=\frac{1}{2}[/latex]

vi) f(x) = x²- 3x ∀ x ∈ R
Solution:
f(x) = 3x² – 3 and f”(x) = 6x
∴ For maximum or minimum f(x) = 0
⇒ 3x² – 3 = 0
⇒ x² – 1 = 0
⇒ x = ± 1
Now f”(1) = 6(1) = 6 > 0
∴ f(x) has minimum at x = 1
Minimum value is f(1) = 1³ – 3(1) = -2
f”(-1) = 6(-1) = -6 < 0
∴ f(x) has maximum value at x = -1
Maximum value is f(-1) = (-1)³ – 3(-1)
= -1 + 3 = 2

vii) f(x) = (x -1) (x + 2)² ∀ x ∈ R
Solution:
f(x) = (x – 1) (x + 2)²
f(x) = (x – 1) 2(x + 2) + (x + 2)²
= 2(x – 1) (x + 2) + (x + 2)²
f”(x) = 2(x – 1) + 2(x + 2) + 2(x + 2)
= 2(3x + 3) = 6(x + 1)
∴ For maximum or minimum f'(x) = 0
2(x – 1) (x + 2) + (x + 2)² = 0
(x + 2) [2(x – 1) + (x + 2)] = 0
⇒ (x + 2) (3x) = 0
⇒ x = 0, x = -2
Now f”(0) = 6(0 + 1) = 6 > 0
∴ f(x) has min. value at x = 0
Min. value is f(0) = (0 – 1) (0 + 2)² = -4
f'(-2) = 6 (-2 + 1) = -6 < 0
∴ f(x) has max. value at x = -2
Max. value is f(-2) = (-2 -1) (-2 + 2)² = 0

viii) f(x) = [latex]\frac{x}{2}+\frac{2}{x}[/latex] ∀ x ∈ (0, ∞)
Solution:
f'(x) = [latex]\frac{1}{2}-\frac{2}{x^{2}}[/latex] and f”(x) = [latex]\frac{4}{x^{3}}[/latex]
∴ For max. or min. f'(x) = 0
⇒ [latex]\frac{1}{2}-\frac{2}{x^{2}}[/latex] = 0 ⇒ x² – 4 = 0 ⇒ x = ± 2
f”(2) = [latex]\frac{4}{2^{3}}[/latex] = [latex]\frac{1}{2}[/latex] > 0 (Since x > 0)
∴ f(x) has min. value at x = 2
Min. value is f(2) = [latex]\frac{2}{2}+\frac{2}{2}[/latex] = 1 + 1 = 2.

ix) f(x) = – (x – 1)³ (x + 1)² ∀ x ∈ R
Solution:
f(x) = -(x – 1)³ (x + 1)² = (1 – x)³ (x + 1)²
f”(x) = (1 – x)³ 2(x + 1) + 3(1 – x)² (-1) (x + 1)²
= (1 – x)² (x + 1) {2(1 – x) – 3(x + 1)}
= (1 – x)² (x + 1) {2 – 2x – 3x – 3}
= (1 – x)² (x + 1) (-1 – 5x)
f”(x) = (1 – x)² (x + 1) (-5) + (1 – x)² (-1 – 5x) + (x + 1) (-1 -5x) 2(1 – x) (-1)
= -5 (1 -x)² (x+ 1) – (1 + 5x) (1 – x)² + (x + 1) (1 + 5x) 2(1 – x)
∴ For maximum or minimum f(x) = 0
(1 – x)² (x + 1) (-1 – 5x) = 0
⇒ x = ± 1 or -1/5
f”(1) = 0 – 0 + 0 ⇒ critical value at x = 0
f”(1 +1)² (-1) = 0 – (1 – 5) + 0 = 16 > 0
∴ f(x) has min. value at x = -1
Min. value = f(-1) = (1 + 1)³ (-1 + 1)² = 0
f”(- [latex]\frac{1}{5}[/latex]) < o
⇒ f(x) has max. value at x = – [latex]\frac{1}{5}[/latex]
Min. value is f (-[latex]\frac{1}{5}[/latex]) = [latex]\frac{3456}{3125}[/latex]

x) f(x) = x² e3x ∀ x ∈ R
Solution:
f'(x) = x² e3x .3 + e3x. 2x
For maximum or minimum f'(x) = 0
3x² e3x + 2e3x. x = 0
x² e3x (3x + 2) = 0
x = 0, x = [latex]\frac{-2}{3}[/latex] and e = 0 is not possible
Now f”(x) = 3(x² e3x. 3 + e3x 2x)
+ e3x 2 + 2x e3x
f”(x) = 9x²e3x + 6x
e3x+ 2 e3x + 6xe3x
= 9x²e3x + 12xe3x + 2e3x
f”(0) = 2 > 0
∴ Point of local minimum = 0
local minimum = 0
f”([latex]\frac{-2}{3}[/latex]) = [latex]\frac{-2}{e^{2}}[/latex] < 0
∴ point of local maximum = [latex]\frac{-2}{3}[/latex]
local maximum = [latex]\frac{4}{9e^{2}}[/latex]

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Question 2.
Prove that the following functions do not have absoute maximum and absolute minimum.
i) ex in R
Solution:
f(x) = ex and f”(x) = ex
∴ For maxima or minima f'(x) = 0 ⇒ ex = 0
⇒ x value is not defined
Hence it has no maxima or minima.

ii) log x in (0, ∞)
Solution:
f(x) = [latex]\frac{1}{x}[/latex] and f”(x) = – [latex]\frac{1}{x^{2}}[/latex]
f (x) = 0 ⇒ x value is not defined
⇒ f(x) has no maxima or minima.

iii) x³ + x² + x + 1 in R
Solution:
f (x) = 3x² + 2x + 1 gives imaginary values.
⇒ It has no maximum or minimum values.

II.

Question 1.
Find the absolute maximum value and absoulte minimum value of the following functions on the domain specified against the function.
Solution:
f(x) = x³ on (-2, 2)
f(x) = 3x² and f'(x) – 6x
the value f(-2) = (-2)³ = – 8
Max Value f(2) = 2³ = 8

ii) f(x) = (x – 1)²+ 3 on [-3, 1]
Solution:
f(x) = 2(x – 1) and f'(x) = 2
Max. value f(-3) = (-3 – 1)² + 3 = 16 + 3 = 19
Min. value f(l) = 0 + 3 = 3

iii) f(x) = 2|x| on [-1, 6]
Solution:
f'(x) = [latex]\frac{2|x|}{x}[/latex]
For max. or min., f'(x) = 0
[latex]\frac{2|x|}{x}[/latex] = 0 ⇒ x = 0
f(0) = 0
f(-1) – 2|-1| = 2
f(6) = 2(6) = 12
Absolute minimum = 0
Absolute maximum = 12

iv) f(x) = sin x + cos x on [0, π]
Solution:
f'(x) cos x – sin x which exists at all x ∈ (0, π)
Now f'(x) = 0 ⇒ cos x – sin x = 0
⇒ tan x = 1
⇒ x = [latex]\frac{\pi}{4}[/latex] ∈ (0, π)
Now f(0) = sin 0 + cos 0 = 1
f([latex]\frac{\pi}{4}[/latex]) = sin [latex]\frac{\pi}{4}[/latex] + cos [latex]\frac{\pi}{4}[/latex]
= [latex]\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}[/latex]
f(π) = sin π + cos π = 0 – 1 = -1
∴ Minimum value : -1
Maximum value: √2

v) f(x) = x + sin 2x on [0, π]
Solution:
f(x) = x + sin 2x
f(x) = 1 + 2 cos 2x
f (x) = 0 ⇒ 2 cos 2x + 1 = 0
⇒ cos 2x = -[latex]\frac{1}{2}[/latex] = cos [latex]\frac{2 \pi}{3}[/latex]
⇒ 2x = [latex]\frac{2 \pi}{3}[/latex]
⇒ x = [latex]\frac{\pi}{3}[/latex] ∈ (0, 2π)
Now f(0) = 0 + sin 2(0) = 0
f([latex]\frac{\pi}{3}[/latex]) = [latex]\frac{\pi}{3}[/latex] + sin 2.[latex]\frac{\pi}{3}[/latex] = [latex]\frac{\pi}{3}+\frac{\sqrt{3}}{2}[/latex]
f(2π) = 2π + sin 2. 2π = 2π + 0 = 2π
Minimum value = 0
Maximum value is = 2π

Question 2.
Use the first derivative test to find local extrema of f(x) = x³ – 12x on R.
Solution:
f(x) = x³ – 12x
f'(x) = 3x² – 12
f”(x) = 6x
For maximum or minimum, f'(x) = 0
3x² – 12 = 0
3x² = 12
x = ± 2
f”(2) = 12 > 0
Point of local minimum at x = 2
Local minimum = – 16
f”(-2) = -12 < 0
Point of local maximum at x = -1
Local maximum =16

Question 3.
Use the first derivative test to find local extrema of f(x) = x² – 6x + 8 on R.
Solution:
f(x) = x² – 6x + 8
f’(x) = 2x -6 ⇒ f”(x) = 2
For maximum or minimum f'(x) = 0
2x – 6 = 0
⇒ x = 3
f”(3) = 2 > 0
∴ Point of local minimum x = 3
Local minimum = -1

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Question 4.
Use the second derivative test to find local extrema of the function
f(x) =x³ – 9x² – 48x + 72 on R.
Solution:
f(x) =x³ – 9x² – 48x + 72.
⇒ f'(x) = 3x² – 18x – 48
= 3(x – 8) (x + 2)
Thus the stationary point are – 2 & 8
f”(x) = 6x – 18 = 6(x – 3)
At x= 8, f”(8) = 30 > 0
∴ f (8) = (8)³ – 9(8)² – 48(8) + 72
= 512 – 576 – 384 + 72
= – 376
At x= -2, f”(-2) = – 30 < 0
f(-2) = (-2)³ – 9(-2)² – 48(-2)+72
= -8 – 36 + 96 + 72
= 124
Local minimum = -376
Local maximum = 124

Question 5.
Use the second derivative test to find local extrema of the function. f(x) = -x³ + 12x² – 5 on R.
Solution:
f(x) = -x³ + 12x² – 5
⇒ f'(x) = -3x² + 24x
= -3x(x – 8)
Thus the stationary point are 0, 8
f”(x) = – 6x + 24
At x= 0, f”(0) = 24 > 0.
f(0) = -5
At x= 8, f”(8) = -24 < 0
f(8) = -8³ + 12(8)² – 5
= -512 + 768 – 5 = 251
Local minimum = -5
Local maximum = 251

Question 6.
Find local maximum or local minimum of f(x) = -sin 2x – x defined on [-π/2, π/2].
Solution:
f(x) =-sin 2x – x
f'(x) = -2cos 2x – 1
f”(x) = 4 sin 2x
Thus the starting point are x = [latex]\frac{\pi}{3},\frac{-\pi}{3}[/latex]
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 4
Local minimum = -[latex]\frac{\sqrt{3}}{2}-\frac{\pi}{3}[/latex]
Local maximum = [latex]\frac{\sqrt{3}}{2}+\frac{\pi}{3}[/latex]

Question 7.
Find the absolute maximum and absolute minimum of f (x) = 2x³ – 3x² – 36x + 2 on the interval [0, 5].
Solution:
f(x) = 2x³ – 3x² – 36x + 2
f(x) = 6x² – 6x – 36
f(x) = 12x – 6
for maxima or minima, f'(x) = 0
6x² – 6x – 36 = 0
x² – x – 6 = 0
x² -3x + 2x – 6 = 0
x(x – 3) + 2(x – 3) = 0
(x + 2) (x – 3) = 0
x = 3, -2
f”(3) = 30 > 0
f(x) has max/min value at x = 3
f(3) = 2(3)³ – 3(3)² – 36(3) + 2
= 54 – 27 – 108 + 2
= -79
Absolute minimum = – 79
Since 0 ≤ x ≤ 5
∴ f(0) = 0 – 0 – 0 + 2
= 2
∴ Absolute maximum = 2.

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Question 8.
Find the absolute extremum of f(x) = 4x – [latex]\frac{x^{2}}{2}[/latex] on [-2, [latex]\frac{9}{2}[/latex]]
Solution:
f(x) = 4x – [latex]\frac{x^{2}}{2}[/latex]
f'(x) =4 – x
f”(x) = – 1
for maxima or minima f'(x) = 0
4 – x = 0
x = 4
f”(4) = -1 < 0
∴ f has maximum value at x = 4
f(4) = 16 – [latex]\frac{16}{2}[/latex] = 8
Since -2 ≤ x ≤ [latex]\frac{9}{2}[/latex]
∴ f(-2) = -8 – [latex]\frac{4}{2}[/latex]
= -8- 2 = -10
∴ Absolute minimum = -10
Absolute maximum = 8

Question 9.
Find the maximum profit that a company can make, if the profit function is given by P(x) = -41 + 72x – 18x²
Solution:
P(x) = – 41 + 72 x – 18x².
[latex]\frac{dp(x)}{dx}[/latex] = 72 – 36x
for maxima or minima, [latex]\frac{dp}{dx}[/latex] = 0
72 – 36x = 0
x = 2
[latex]\frac{d^{2}p}{dx^{2}}[/latex] = -36 < 0
∴ The profit f(x) is maximum for x = 2
The maximum profit will be P(2) =
= -41 + 72(2) – 18(4)
= 31

Question 10.
The profit function P(x) of a company selling x items is given by P(x) = -x³ + 9x² – 15x – 13 where x represents thousands of units. Find the absolute maximum profits if the company can manufacture a maximum of 6000 units.
Solution:
P(x) = -x³ + 9x² – 15x – 13
[latex]\frac{dp(x)}{dx}[/latex] = -3x² + 18x – 15
for maximum or minimum [latex]\frac{dp}{dx}[/latex] = 0
-3x² + 18x – 15 = 0
x² – 6x + 5 = 0
x² – 5x – x + 5 = 0
x(x- 5) – 1(x- 5) = 0
(x – 1) (x – 5) = 0
x = 1, 5
P(1) = -1 + 9 – 15 – 13 = -10
P(5) = -125 + 225 – 75 – 13 = 12
∴ Maximum profit = 12.

III.

Question 1.
The profit function P(x) of a company selling x items per day is given by P(x) = (150 – x) x – 1000. Find the number of items that the company should manufacture to get maximum profit. Also find the maximum profit.
Solution:
Given that tbe profit function
P(x) = (150 – x)x -1000
for maximum or minimum [latex]\frac{dp}{dx}[/latex] = 0
(150 – x(1) -x (-1) = 0
150 – 2x = 0
x = 75
Now [latex]\frac{d^{2}p}{dx^{2}}[/latex] = -2 < 0
∴ The profit P(x) is maximum for x = 75
The company should sell 75 tems a day the maxma profit will be P (75) = 4625.

Question 2.
Find the absolute maximum and absolute minimum of f(x) = 8x³ + 81x² – 42x – 8 on [-8, 2].
Solution:
f(x) = 8x³ + 81x² – 42x – 8
f'(x) = 24x²+ 162x – 42
For maximum or minimum, f'(x) = 0
24x² + 162x – 42 = 0
4x² + 27x – 7 = 0
4x² + 28x – x – 7 = 0
4x(x + 7) – 1(x + 7) = 0
(x + 7) (4x – 1) = 0
x = – 7 or [latex]\frac{1}{4}[/latex]

f(- 8) = 8(-8)³ + 81(-8)² – 42(-8) -8
= – 8(512) + 81(64) + 336 – 8
= -4096 + 5184 + 336 – 8
= 5520 – 4104
= 1416

f(2) = 8(2)³ + 81 (2)² – 42(2) – 8
= 64 + 324 – 84 – 8
= 296
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 5
f(-7) = 1246
Absolute maximum = 1416
Absolute minimum = [latex]\frac{-216}{16}[/latex]

Question 3.
Find two positive integers whose sum is 16 and the sum of whose squares is minimum.
Solution:
Suppose x and y are the sum value
x + y =16
⇒ y = 16 – x
f(x) = x² + y² = x² + (16 – x)²
= x² + 256 + x² – 32x
f'(x) = 4x – 32
for maximum or minimum f'(x) = 0
⇒ 4x – 32 = 0
4x = 32 x = 8
f”(x) = 4 > 0
∴ f(x) is minimum when x = 8
y = 16 – x = 16 – 8 = 9
∴ Required number are 8, 8.

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Question 4.
Find two positive integers x and y such that x + y = 60 and xy3 is maximum.
Solution:
x + y = 60 ⇒ y = 60 – x ………… (1)
Let p = xy³ = x(60 – x)³
[latex]\frac{dp}{dx}[/latex] = x³(60 – x)²(-1) + (60-x)³
= -3x (60 – x)² + (60 – x)³
= (60 – x)² [-3x + 60 – x]
= (60 – x)² (60 – 4x) = 4(60 – x)² (15 – x)

[latex]\frac{d^{2}p}{dx^{2}}[/latex] = 4[(60-x)² (-1) + (15-x) 2(60-x) (-1)]
= 4(60 – x) [-60 + x – 30 + 2x]
= 4(60 – x) (3x – 90)
= 12(60 – x) (x – 30)
For maximum or minimum [latex]\frac{dp}{dx}[/latex] = 0
⇒ 4(60 – x)2 (15 -x) = 0
⇒ x = 60 or x = 15 ; x cannot be 60
∴ x = 15 ⇒ y = 60 – 15 = 45.
([latex]\frac{d^{2}p}{dx^{2}}[/latex])x = 15 = 12(60 – 15) (15 – 30) < 0
⇒ p is maximum
∴ Required numbers are 15, 45.

Question 5.
From a rectangular sheet of dimensions 30 cm x 80 cm four equal squares of side x cm are removed at the comers and the sides are then turned up so as to form an open rectangular box. Find the value of x, so that the volume of the box is the greatest?
Solution:
Length of the box = 80 – 2x = l
Breadth of the box = 30 – 2x = b
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 6
Height of the box = x = h
Volume = lbh = (80 – 2x) (30 – 2x). x
= x (2400 – 220 x + 4x²)
f(x) = 4x³ – 220 x² + 2400x
f'(x) = 12x² – 440x + 2400
= 4 [3x² – 110 x + 600]
f'(x) = 0
⇒ 3x² – 110 x +600 = 0
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 7
f(x) is maximum when x = [latex]\frac{20}{3}[/latex]
Volume of the box is maximum when x = [latex]\frac{20}{3}[/latex] cm

Question 6.
A window is in the shape of a rectangle surmounted by a semi-circle. If the peri-meter of the window is 20 feet, find the maximum area.
Solution:
Let length of the rectangle be 2x and breadth be y so that radius of the semi-circle is x.
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 8
Perimeter = 2x + 2y + π. x = 20
2y = 20 – 2x – πx.
y = 10 – x – [latex]\frac{\pi}{2}[/latex]. x
Area = 2xy + [latex]\frac{\pi}{2}[/latex]. x²
= 2x(10 – x – [latex]\frac{\pi}{2}[/latex]) + [latex]\frac{\pi}{2}[/latex]x²
= 20x – 2x² – πx² + [latex]\frac{\pi}{2}[/latex] x²
f(x) = 20x – 2x² – [latex]\frac{\pi}{2}[/latex] x²
f'(x) = 0 ⇒ 20 – 4x – πx = 0
(π + 4)x = 20
x = [latex]\frac{20}{\pi+4}[/latex]
f”(x) = -4 – π < 0
f(x) is a maximum when x = [latex]\frac{20}{\pi+4}[/latex]
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 9

Question 7.
If the curved surface of right circular a cylinder inscribed in a sphere of radius r is maximum, show that the height of the cylinder is √2r.
Solution:
Suppose r is the radius and h be the height of the cylinder.
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 10
From ∆OAB, OA² + AB² = OB²
r² + [latex]\frac{h^{2}}{4}[/latex] = R² ; r² = R² – [latex]\frac{h^{2}}{4}[/latex]
Curved surface area = 2πrh
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 11
f(h) is greatest when h = √2 R
i.e., Height of the cylinder = √2 R.

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h)

Question 8.
A wire of length l is cut into two parts which are bent respectively in the form of a square and a circle. What are the lengths of the pieces of the wire respe-ctively so that the sum of the areas is the least?
Solution:
Suppose x is the side of the square and r is the radius of the circle.
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 12
Given 4x + 2πr = l
4x = l – 2πr
r = [latex]\frac{1-2 \pi r}{4}[/latex]
Sum of the area = x² + πr²
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(h) 13
∴ f(r) is least when r = [latex]\frac{l}{ 2(\pi+4)}[/latex]
Sum of the area is least when the wire is cut into pieces of length [latex]\frac{\pi l}{\pi+4}[/latex] and [latex]\frac{4l}{\pi+4}[/latex]

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g)

Practicing the Intermediate 1st Year Maths 1B Textbook Solutions Inter 1st Year Maths 1B Applications of Derivatives Solutions Exercise 10(g) will help students to clear their doubts quickly.

Intermediate 1st Year Maths 1B Applications of Derivatives Solutions Exercise 10(g)

I.

Question 1.
Without using the derivative, show that
i) The function f(x) = 3x + 7 is strictly increasing on R.
Solution:
Let x1, x2 ∈ R with x1 < x2
Then 3x1 < 3x2
Adding 7 on both sides
3x1 + 7 < 3x2 + 7
⇒ f(x1) < f(x2)
∴ x1 < x2 ⇒ f(x1) < f(x2) ∀ x1 x2 ∈ R
∴ The given function is strictly increasing on R

ii) The function f(x) = ([latex]\frac{1}{2}[/latex])x is strictly decreasing on R.
Solution:
f(x) = ([latex]\frac{1}{2}[/latex])x
Let x1, x2 ∈ R
Such that x1 < x2
⇒ ([latex]\frac{1}{2}[/latex])x1 > ([latex]\frac{1}{2}[/latex])x2
⇒ f(x1) > f(x2)
∴ f(x) is strictly decreasing on R.

iii) The function f(x) = e3x is strictly increasing on R.
Solution:
f(x) = e3x
Let x1, x2 ∈ R such that x1 < x2
We know that of a > b then ea > eb
Then e3x < e3x2
⇒ f(x1) < f(x2)
∴ f is strictly increasing on R.

iv) The function f(x) = 5. – 7x is strictly decreasing on R.
Solution:
f(x) = 5 – 7x
Let x1 x2 ∈ R
Such that x1 < x2
Then 7x1 < 7x2
-7x1 > -7x2
Adding 5 on bothsides
5 – 7x1 > 5 – 7x2
f(x1) > (x2)
∴ x1 < x2 ⇒ f(x1) > f(x2) V x1 x2 ∈ R.
The given function f is strictly decreasing on R.

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g)

Question 2.
Show that the function f(x) = sin x. Define on R is neither increasing nor decreasing on (0, π).
Solution:
f(x) = sin x
Since 0 < x < n
Consider 0 < x
f(0) < f(x)
sin 0 < sin x
0 < sin x ……….. (1)
Consider x < n
f(x) < f(π)
sin x < sin π 0 > sin x ………….. (2)
From (1) & (2); f(x) is neither increasing nor decreasing.

II.

Question 1.
Find the intervals in which the following functions are strictly increasing or strictly decreasing.
i) x² + 2x – 5
Solution:
Let f(x) = x² + 2x – 5
f'(x) = 2x + 2
f(x) is increasing if f'(x) > 0
⇒ 2x + 2 < 0 ⇒ x+ 1 > 0
x > -1
f(x) is increasing If x ∈ (-1, ∞)
f(x) is decreasing If f'(x) < 0
⇒ 2x + 2 < 0
⇒ x + 1 < 0
⇒ x < -1 f(x) is decreasing if x ∈ (-∞, -1).

ii) 6 – 9x – x².
Solution:
Let f(x) = 6 – 9x – x²
f'(x) = -9 – 2x
f(x) is increasing if f'(x) > 0
⇒ -9 -2x > 0
⇒ 2x + 9 < 0
x < [latex]\frac{-9}{2}[/latex]
f(x) is increasing if x ∈ (-∞, [latex]\frac{-9}{2}[/latex])
f(x) is decreasing if f'(x) < 0
⇒ 2x + 9 > 0
⇒ x > [latex]\frac{-9}{2}[/latex]
f(x) is decreasing of x ∈ ([latex]\frac{-9}{2}[/latex], ∞)

iii) (x + 1)³ (x – 1)³.
Solution:
Let f(x) = (x + 1)³ (x – 1)³
= (x² – 1)³
x6 – 1 – 3x4 + 3x ²
f'(x) = 6x5 – 12x³ + 6x
= 6(x5 – 2x³ + x)
= 6x(x4 – 2x² +1)
= 6x(x² – 1)²
f'(x) ≤ 0
⇒ 6x(x² – 1)² < 0
f(x) is decreasing when (-∞, -1) ∪ (-1, 0)
f'(x) > 0
f(x) is increasing when (0, 1) ∪ (1, ∞)

iv) x³(x – 2)²
Solution:
f'(x) = x³. 2(x – 2) + (x – 2)².3x²
= x² (x – 2) [2x + 3 (x- 2)]
= x² (x – 2) (2x + 3x – 6)
= x² (x – 2) (5x – 6) ∀ x ∈ R, x² ≥ 0
For increasing, f'(x) = 0
x²(x – 2) (5x – 6) > 0
x ∈ (-∞, [latex]\frac{6}{5}[/latex]) ∪ (2, ∞)
For decreasing, f'(x) < 0
x²(x – 2) (5x – 6) < 0
x ∈ ([latex]\frac{6}{5}[/latex], 2)

v) xex
Solution:
f'(x) = x . ex + ex. 1 = ex(x + 1)
ex is positive for all real values of x
f'(x)>0 ⇒ x + 1 > 6 ⇒ x > – 1
f(x) is increasing when x > – 1
f(x) < 0 ⇒ x + 1 < 0 ⇒ x < -1
f(x) is decreasing when x < – 1

vi) [latex]\sqrt{(25-4x^{2})}[/latex]
Solution:
f(x) is real only when 25 – 4x² > 0
-(4x² – 25) > 0
-(2x + 5) (2x – 5) > 0
∴ x lies between -[latex]\frac{5}{2}[/latex] and [latex]\frac{5}{2}[/latex]
Domain of f = (-[latex]\frac{5}{2}[/latex], [latex]\frac{5}{2}[/latex])
f'(x) = [latex]\frac{1}{2 \sqrt{25-4 x^{2}}}[/latex] (-8x)
= -[latex]\frac{4x}{\sqrt{25-4 x^{2}}}[/latex]
f(x) is increasing when f'(x) > 0
⇒ [latex]\frac{-4x}{\sqrt{25-4 x^{2}}}[/latex] > 0
i.e., x < o
f(x) is increasing when (-[latex]\frac{5}{2}[/latex], 0)
f(x) is decreasing when f'(x) < 0
⇒ -[latex]\frac{4x}{\sqrt{25-4 x^{2}}}[/latex] < 0
∴ x > 0
f(x) is decreasing when (0, [latex]\frac{5}{2}[/latex]).

vii) ln (ln(x)); x > 1.
Solution:
f'(x) = -[latex]\frac{1}{lnx}•\frac{1}{x}[/latex]
f(x) is decreasing when f'(x) > 0
[latex]\frac{1}{x.ln x}[/latex] >0
⇒ x. In x > 0
ln x is real only when x > 0
∴ ln x < 0 = ln 1
i.e., x > 1
f(x) is increasing when x > 1 i.e., in (1, ∞)
f(x) is decreasing when f'(x) < 0 ⇒ ln x > 0 = ln 1
i.e., x < 1
f(x) is decreasing in (0, 1)

viii) x³ + 3x² – 6x + 12.
Solution:
f(x) = x³ + 3x² – 6x + 12
f(x) = 3x² + 6x – 6
= 3(x² + 2x – 2)
= 3((x + 1)² – 3)
= 3[(x + 1) + √3] [(x + 1) – √3]
= 3(x + (1 + √3) (x + (1 – √3 )
f (x) < 0
⇒ x = -(1+ √3 ) or -(1 – √3 )
x = -1 – √3 or √3 – 1
f(x) is decreasing in (-1 -√3 , √3 -1)
f (x) > 0
f(x) increasing when (-∞, -1 – √3 ) ∪ (√3 – 1, ∞)

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g)

Question 2.
Show that f(x) = cos²x is strictly increasing on (0, π/2).
Solution:
f(x) = cos² X
⇒ f(x) = 2 cos x (-sin x)
= -2 sin x cos x
= -sin 2x
Since 0 < x < [latex]\frac{\pi}{2}[/latex]
⇒ 0 < 2x < π
Since ‘sin x’ is +ve between 0 and π
∴ f(x) is clearly -ve.
∴ f'(x) < 0
∴ f(x) is strictly decreasing.

Question 3.
Show that x + [latex]\frac{1}{x}[/latex] is increasing on [1, ∞)
Solution:
Let f(x) = x + [latex]\frac{1}{x}[/latex]
f'(x) = 1 – [latex]\frac{1}{x^{2}}[/latex] = [latex]\frac{x^{2}-1}{x^{2}}[/latex]
Since x ∈ [1, ∞) = [latex]\frac{x^{2}-1}{x^{2}}[/latex] > 0
∴ f'(x) > 0
∴ f(x) is increasing.

Question 4.
Show that [latex]\frac{x}{1+x}[/latex] < ln (1 + x) < x ∀ x > 0
Solution:
Let f(x) = ln(1 + x)- [latex]\frac{x}{1+x}[/latex]
= ln(1 + x) – [latex]\frac{1+x-1}{1+x}[/latex]
= ln(1 + x) – 1 + [latex]\frac{1}{1+x}[/latex]
f'(x) = [latex]\frac{1}{1+x}[/latex] – [latex]\frac{1}{(1+x)^{2}}[/latex]
= [latex]\frac{1+x-1}{(1+x)^{2}}[/latex]
= [latex]\frac{x}{(1+x)^{2}}[/latex] > 0 since x > 0
f(x) is increasing when x > 0
∴ f(x) > f(0)
f(0) = ln 1 – [latex]\frac{0}{1+0}[/latex] = 0 – 0 = 0
Since xe [1, ∞) =
ln (1 + x) – [latex]\frac{x}{1+x}[/latex] > 0
⇒ ln (1 + x) > [latex]\frac{x}{1+x}[/latex] ……… (1)
Let g(x) = x – ln (1 + x)
g'(x) = 1 – [latex]\frac{x}{1+x}=\frac{1+x-1}{1+x}[/latex]
= [latex]\frac{x}{1+x}[/latex] > 0 since x > 0
g(x) is increasing when x > 0
i.e., g(x) > g(0)
g(0) = 0 – ln (1) = 0 – 0 = 0
∴ x – ln (1 + x) > 0
x > ln(1 + x) ………….. (2)
From (1), (2) we get
[latex]\frac{x}{1+x}[/latex] < ln (1 + x) < x ∀ x > 0

III.

Question 1.
Show that [latex]\frac{x}{1+x^{2}}[/latex] < tan-1 x < x when x > 0.
Solution:
Let f(x) = tan-1 x – [latex]\frac{x}{1+x^{2}}[/latex]
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 1
f(x) is increasing when x > 0
f(x) > f(0)
But f(0) = tan-1 0 – 0 = 0 – 0 = 0
i.e., f(x) > 0
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 2
g(x) is increasing when x > 0
g(x) > g(0)
g(0) = 0 – tan-1 0 = 0 – 0 = 0
∴ x – tan-1 x > 0
⇒ x > tan-1 x ………. (2)
From (1), (2) we get
[latex]\frac{x}{1+x^{2}}[/latex] <tan-1 x< x for x > 0

Question 2.
Show that tan x > x for all (0, [latex]\frac{\pi}{2}[/latex])
Solution:
Let f(x) = tan x – x
f'(x) = sec² x – 1 > 0 for every
x ∈ (0, [latex]\frac{\pi}{2}[/latex])
f(x) is increasing for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])
i.e., f(x) > f(0)
f(0) = tan 0 – 0 = 0 – 0 = 0
∴ tan x – x > 0
⇒ tan x > x for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g)

Question 3.
If x ∈ (0, [latex]\frac{\pi}{2}[/latex]) then show that [latex]\frac{2x}{\pi}[/latex] < sin x < x.
Solution:
Let f(x) = x – sin x
f(x) = 1- cos x > 0 for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])
f(x) is increasing for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])
⇒ f(x) > f(0)
f(0) = 0 – sin 0 = 0 – 0 = 0
∴ x – sin x > 0
⇒ x > sin x ………….. (1)
Let g(x) = sin x – [latex]\frac{2x}{\pi}[/latex]
g'(x) = cos x – [latex]\frac{2}{\pi}[/latex] > 0 for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])
g(x) is increasing in (0, [latex]\frac{\pi}{2}[/latex])
g(x) > g(0)
g(0) = sin 0 – 0 = 0 – 0 = 0
∴ sin x – [latex]\frac{2x}{\pi}[/latex] > 0
⇒ sin x > [latex]\frac{2x}{\pi}[/latex] ………… (2)
From (1), (2) we get
[latex]\frac{2x}{\pi}[/latex] < sin x < x for every x ∈ (0, [latex]\frac{\pi}{2}[/latex])

Question 4.
If x e (0,1) then show that 2x < ln [[latex]\frac{(1+x)}{(x-1)}[/latex]] < 2x [1 + [latex]\frac{x^{2}}{2(1+x^{2})}[/latex]] Solution:
Let f(x) = ln [latex]\frac{(1+x)}{1-x}[/latex] – 2x
= ln (1 + x) – ln (1 – x) – 2x
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 3
f(x) is increasing ih (0, 1)
i.e., x > 0 ⇒ f(x) > f(0)
f(0) = ln 1 – 0 = 0 – 0 = 0
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 4
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 5
g(x) is increasing when x > 0
g(x) > g(0)
g(0) = 0 – ln 1 = 0 – 0 = 0
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 6
for x ∈ (0,1)

Question 5.
At what point the slopes of the tangents y = [latex]\frac{x^{3}}{6}-\frac{3x^{3}}{2}+\frac{11x}{2}[/latex] + 12 increases?
Solution:
Equation of the curve is
y = [latex]\frac{x^{3}}{6}-\frac{3}{2}x^{2}+\frac{11x}{2}[/latex] + 12
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 7
Slope = m = [latex]\frac{x^{2}}{c}-3x+\frac{11}{2}[/latex]
[latex]\frac{dm}{dx}[/latex] = [latex]\frac{2x}{2}[/latex] -3 = x – 3
Slope increases ⇒ m > 0
x – 3 > 0
x > 3
The slope increases in (3, ∝)

Question 6.
Show that the functions ln [latex]\frac{(1+x)}{x}[/latex] and [latex]\frac{x}{(1+x)ln(1+x)}[/latex] are decrasing on (0, ∞).
Solution:
i)
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 8
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 9
∴ f(x) is decreasing for x ∈ (0, ∝)

ii) let f(x) = [latex]\frac{x}{(1+x)ln(1+x)}[/latex]
Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g) 10
∴ f(x) is decreasing for x ∈ (0, ∝)

Question 7.
Find the intervals in which the function f (x) = x3 – 3×2 + 4 is strictly increasing all x e R.
Solution:
f(x) = x³ – 3x² + 4
f'(x) = 3x² – 6x
f(x) is increasing if f'(x) > 0
3x² – 6x > 0
3x(x – 2) > 0
(x – 0)(x – 2) > 0
f(x) is increasing if x £ (-∞, 0) u (0, ∞)
f(x) is decreasing if f'(x) < 0
(x – 0) (x – 2) < 0
x ∈ (0, 2)

Inter 1st Year Maths 1B Applications of Derivatives Solutions Ex 10(g)

Question 8.
Find the intervals in which the function f(x) = sin4x + cos4x ∀ x ∈ [0, [latex]\frac{\pi}{2}[/latex]] is increasing and decreasing.
Solution:
f(x) = sin4x + cos4x
f(x) = (sin²x)² + (cos²x)²
= (sin²x + cos²x)² – 2sin²x cos²x
= 1 – [latex]\frac{1}{2}[/latex] sin² 2x
f'(x) = [latex]\frac{-1}{2}[/latex] 2sin 2x. cos 2x(2)
= -2 sin 2x. cos 2x
= -sin 4x
Let 0 < x < [latex]\frac{\pi}{4}[/latex]
∴ f(x) is decreasing if f'(x) < 0
⇒ -sinx < 0 ⇒ sinx > 0
∴ x ∈ (0, [latex]\frac{\pi}{4}[/latex])
f(x) is increasing if f'(x) > 0
⇒ – sinx > 0
⇒ sinx < 0
∴ x ∈ ([latex]\frac{\pi}{4}[/latex], [latex]\frac{\pi}{2}[/latex])