Here we are with SSC PHYSICS BY VIVEK KUMAR for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams. Jigs Solanki provides you with the best chosen study material like Important Current affairs with the list of latest and daily and monthly current affairs which are likely to be asked in the upcoming exams.
Tuesday, 25 September 2018
Biology makes the vital difference between success and failure in all medical entrance examinations. Hence one needs to be thoroughly prepared with this subject. With NEET/AIPMT Study Material, medical aspirants can score more in Biology.
Monday, 24 September 2018
This Study & Master Physical Sciences CAPS Study Guide for Grade 11 has been developed as an aid to support you throughout your year of schooling and down the home stretch leading up to the final examination. Not only does this study guide give you an overview of the content required to successfully master Physical Sciences, it also: explains key concepts you need to fully understand the subject content follows each new concept with a worked example to guide you.
Here we are with QUANTUM PHYSICS NOTES BY J D CRESSER for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams. Jigs Solanki provides you with the best chosen study material like Important Current affairs with the list of latest and daily and monthly current affairs which are likely to be asked in the upcoming exams.
Quantum Theory is the most revolutionary discovery in physics since Newton. This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare.
Horace G. Danner’s A Thesaurus of English Word Roots is a compendium of the most-used word roots of the English language. As Timothy B. Noone notes in his foreword: “Dr. Danner’s book allows you not only to build up your passive English vocabulary, resulting in word recognition knowledge, but also gives you the rudiments for developing your active English vocabulary, making it possible to infer the meaning of words with which you are not yet acquainted.
This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.Updates the leading graduate-level text in mathematical physics.Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering.
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions.
Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems.
Sunday, 23 September 2018
Featuring state-of-the-art computer based technology throughout, this comprehensive book on classical mechanics bridges the gap between introductory physics and quantum mechanics, statistical mechanics and optics—giving readers a strong basis for their work in applied and pure sciences. Introduces Mathcad, using it in to do mathematical calculations, solve problems, make plots and graphs, and generally provide more in-depth coverage and a better understanding of physics.
Here we are with PRINCIPLES OF INHERITANCE AND VARIATION NOTE BY PLANCESS for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.
Electronic Devices and Circuits. Check Electronic Devices and Circuits Notes for GATE and Electronics & Communication Engineering exams preparation. The study notes are perfect approach to aware about which types of questions can be asked and how to make a plan of study to solve the questions easily. Electronic devices and circuits has many topics that can be studied with prepared study plan for upcoming GATE exam. Make sure you have good understanding of all topics and related materials.
The conventional direction of electric current is the direction of motion of positive charge. The current is the same for all cross-sections of a conductor of non-uniform cross-section. Similar to the water flow, charge flows faster where the conductor is smaller in cross-section and slower where the conductor is larger in cross-section, so that charge rate remains unchanged. If a charge q revolves in a circle with frequency f, the equivalent current,(i) Direct Current (DC) Its magnitude and direction do not change with time.
Electrostatic:- It is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges with no acceleration.Coulomb’s Law:- It states that the electro-static force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and varies inversely as the square of the distance between the two bodies.F = Kq1q2/r2
Here, K = 1/4πε0 = 9×109 Nm2C-2 (in free space).
Here, K = 1/4πε0 = 9×109 Nm2C-2 (in free space).
Transmitter(a) It process and encode the information and make it suitable for transmission. (b) The message signal for communication can be analog signals or digital signals.(c) An analog signal can be converted suitably into a digital signal and vice-versa. (d) An analog signal is that in which current or voltage value varies continuously with time.
Communication channel:The medium through which information propagate from transmitter to receiver is called communication channel.
Communication channel:The medium through which information propagate from transmitter to receiver is called communication channel.
Here we are with INORGANIC CHEMISTRY BY R L MADAN AND G D TULI for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams. Jigs Solanki provides you with the best chosen study material like Important Current affairs with the list of latest and daily and monthly current affairs which are likely to be asked in the upcoming exams.
Promeristem or Primordial meristem: The promeristem originates from embryo and, therefore, called primordial or embryonic meristem. It is present in the regions where an organ or a part of plant body is initiated. Primary meristem: A primary meristem originates from promeristem and retains its meristematic activity. It is located in the apices of roots, stems and the leaf primordia. Secondary Meristem: They always arise in permanent tissues and have no typical promeristem.
Saturday, 22 September 2018
What better way is there to learn than by doing? This unusual book enables children to carry out more than 40 experiments and demonstrations, carefully planned to illustrate important principles of modern science. Clear step-by-step instructions, frequent diagrams, and clear statements of conclusions all enable the young student to carry through these experiments with minimal supervision, yet full success.Before embarking on the world of discovery, the reader is introduced to the language of chemistry, including a list of the most common elements and their symbols.
Origin of life: It is generally agreed that all life today evolved by common descent from a single primitive lifeform. We do not know how this early form came about, but scientists think it was a natural process which took place perhaps 3,900 million years ago.
Learning Science does not mean merely gaining of knowledge about facts and principles; rather it is a path which is enlightened by scientific truths, verified experimentally. Keeping these facts in mind, lab manual for Science have been planned, evaluated under subject Enrichment Activities. Basic Concept of Experiments. Before performing the experiments the BASIC CONCEPT section of each experiment helps the students in understanding the aim of experiment and to achieve the result with minimum error.
It is of two types;(i) Spermatogenesis: Formation of sperm. (ii) Oogenesis : Formation of ova (2) Fertilization: It involves the fusion of haploid male and female gametes to form diploid zygote.
Solids constitute a large part of our lives as we utilize solids more than liquids and gases in our day to day activities. Generally a solid is defined as a substance which has rigidity, fixed shape, and size. But what makes solid different from gases and liquids? The nature of particles of matter and the binding force between them varies with solids, liquids, and gases.
Photosynthesis is the process by which plants and other things make food. It is a chemical process that uses sunlight to turn carbon dioxide into sugars that the cell can use as energy. As well as plants, many kinds of algae, protists and bacteria use it to get food. Photosynthesis is very important for all life on Earth.
Thursday, 20 September 2018
New Simplified Physics: A Reference Book - Class 12 is a set of two volumes, which comprehensively covers the entire Physics syllabus of Class 12th. Students who want to excel in their final examinations should study from this guidebook.Physics is an academic discipline which helps us understand how the universe behaves. It can be broadly categorised into two parts, namely Classical Physics and Modern Physics.
The first edition of Objective Chemistry for NEET Vol. 1 is the first of a two-part series written for aspiring doctors who seek to crack the medical entrance test. Designed as a one-stop solution to revise topics in chemistry pertinent to popular medical entrance examinations, the book provides a comprehensive and systematic coverage of the subject supported by numerous practice questions in every chapter.
PROBLEMS AND SOLUTION IN INTRODUCTORY AND ADVANCED MATRIX CALCULUS 2ND EDITION BY WILL-HANS STEEB AND YORICK HARDY
This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices.
Tuesday, 18 September 2018
Here we are with MODERN PHYSICS:-UNSTRUCTURE SOLUTIIN MANUAL for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.Jigs Solanki provides you with the best chosen study material like Important Current affairs with the list of latest and daily and monthly current affairs which are likely to be asked in the upcoming exams.
A Textbook of Fluid Mechanics and Hydraulic Machines is an ultimate book for students of mechanical engineering. Revised and updated, this book contains all the chapters and topics matching the latest syllabus of mechanical engineering. Popular nationwide, this book helps students to gain comprehensive knowledge about the subject. Clear and easy-to- understand language of the book makes it ideal for all.
The book is an elementary treatise covering a part of Real Analysis that would be beneficial for the undergraduate students of Mathematics; the discussion of each topic has been supplemented by a good number of examples so that the readers can learn and understand the basic principles of Analysis. The book includes important topics in Real Analysis that are explained and discussed in a simple manner which is easy to follow.
In this new edition of Fluid Mechanics, which is a revised and substantially expanded version of the first edition, several new topics like open channel flow, hydraulic turbines, hydraulic transients, flow measurements and pumps and fans have been added. The chapter on one-dimensional viscous flow has also been expanded. With the addition of five new chapters, the treatment is now more indepth and comprehensive.
ELEMENTARY DIFFERENTIAL EQUATION AND BOUNDARY VALUE PROBLEMS 10TH EDITION BY WILLIAM E BOYCE AND RICHARD C DIPRIMA
The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between.
PreTest is the closest you can get to seeing the USMLE Step 1 before you take it! 500 USMLE-style questions and answers! "e;Biochemistry and Genetics: PreTest is a valuable resource for students in their board preparation. The author does a good job of presenting complicated information in an easily accessible format with clinically relevant questions and detailed basic science answers."e; -- Daniel Eskenazi, Fourth Year MD/PhD Candidate, University of Washington School of Medicine "e;.
More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice.Outline format facilitates quick and easy review of college physics.
Book Modern Physics for Science and Engineering Pdf download Book Modern Physics for Science and Engineering by Marshall L. Burns Pdf download Author Marshall L. Burns written the book namely Modern Physics for Science and Engineering Author Marshall L. Burns Pdf download Study material of Modern Physics for Science and Engineering Pdf download Lacture Notes of Modern Physics for Science and Engineering.
Sunday, 16 September 2018
The Grammar and Language Workbook offers sequential language instruction along with extensive drill and practice in grammar, usage, and mechanics. The important tool includes a handbook as well as vocabulary, spelling, and composition lessons. The material provided here is being provided and made by the teachers of the top most coaching institutes which provides coaching for competitive exams.
Here we are with CONCEPTUAL INORGANIC CHEMISTRY:-A TEXT BOOK FOR JEE MAIN AND ADVANCED for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams. Jigs Solanki provides you with the best chosen study material like Important Current affairs with the list of latest and daily and monthly current affairs which are likely to be asked in the upcoming exams.
Understanding Mechanics (Vol-I) is meant for aspirants of engineering entrance examinations and aims at making the subject of Mechanics easy for the student. It covers all the topics with a strong conceptual approach- relevant theory being followed by plenty of solved examoles. The new edition has been further enriched with theory and questions to increase its usefulness for students.
Here we are with ORGANIC METALLIC CHEMISTRY HAND WRITTEN NOTE for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.
Saturday, 15 September 2018
"Some shortcuts are good to take as they lead to success. Introducing one of its unique kind Math Formula eBook, where you will learn about applying shortcuts and formulas in order to solve any problem related to mathematics. Whether you want to solve a quadratic equation or ratio and proportion problem, these shortcuts will help you to crack any question in no time at all with 100% accuracy.
Succeed in the course and connect with the microscopic world with CHEMISTRY IN FOCUS. Thoroughly updated with the latest research and developments, this student-friendly book emphasizes the fundamental role the molecular world plays in your daily life. By clearly identifying and explaining connections between the molecular world and microscopic world, the book helps you understand the major scientific, technological, and environmental issues affecting our society today.
Aldehydes and ketones undergo nucleophilic substitution reaction. In nucleophilic substitution, a species that has extra electron or lone pair of electron attacks the carbonyl carbon of the ketone or the aldehyde leading to an alkoxide intermediate as shown in the middle figure below. This alkoxide intermediate can capture a proton to produce a neutral species. Reactivity of aldehyde vs ketone: Aldehydes are usually more reactive than Ketones for two reasons.
Friday, 14 September 2018
The ideal review for your matrix operations course.More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems.
More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. 508 fully worked problems of varying difficulty. 694 additional practice problems.
A Clear And Reliable Guide To Students Of Practical Organic Chemistry At The Undergraduate And Postgraduate Levels. This Edition S Special Emphasis Is On Semi Micro Methods And Modern Techniques And Reactions. Here we are with PRACTICAL ORGANIC CHEMISTRY for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.
This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields.
This book is both a tutorial and a textbook. It is based on over 15 years of lectures in senior level calculus based courses in probability theory and mathematical statistics at the University of Louisville, USA. This book presents an introduction to probability and mathematical statistics and it is intended for students already having some mathematical background. This book contains more than 350 completely worked out examples and over 165 illustrations. Moreover.
This text is intended for a one- or two-semester undergraduate course in abstract algebra and covers the traditional theoretical aspects of groups, rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included.This text is intended for a one or two-semester undergraduate course in abstract algebra.
This is a very good book for Engineering and medical Entrance examination, especially the book is useful for AIEEE candidates. This book includes all types of problems related to the topics along with their simple solution. Each topic has been explained in a lucid way for every level of students.Proper hints have been given wherever necessary to solve unsolved problems.
Isomerism is the phenomenon whereby certain compounds, with the same molecular formula, exist in different forms owing to their different organisations of atoms. The concept of isomerism illustrates the fundamental importance of molecular structure and shape in organic chemistry. This course contains exclusive material for the students preparing for IITJEE and ther engineering entrance exams.
General Organic Chemistry is divided into two parts (a) Electronic Displacement in Covalent Bonds and (b) Acid and Base Strength in Organic Compounds. Electronic effects operates in covalent bonds (a)Inductive effect, (b) Mesomeric and Resonance effect (c) Electromeric effects (d) Hyperconjugation. Without a clear understanding of GOC Mastery of Organic Chemistry is not possible.
Thursday, 13 September 2018
IIT-JEE Super Course in Chemistry: Organic Chemistry is a class-tested course content package for sure-shot success at the IIT-JEE. Each volume in this series is meticulously planned and structured to help the user imbibe and absorb concepts and apply them to IIT problems. Part of the Super Course series that follows a unique, user-friendly approach, with features such as concept strands, concept connectors, topic grip, IIT assignment exercise, which make the learning and application for the coveted IIT-JEE circuit both easy and enjoyable.
Tuesday, 11 September 2018
This title provides the latest information on nuclear physics. Based on a course entitled Applications of Nuclear Physics. Written from an experimental point of view this text is broadly divided into two parts, firstly a general introduction to Nuclear Physics and secondly its applications. Includes chapters on practical examples and problems. Contains hints to solving problems which are included in the appendix.
For close to 30 years, “Basic Electrical Engineering” has been the go-to text for students of Electrical Engineering. Emphasis on concepts and clear mathematical derivations, simple language coupled with systematic development of the subject aided by illustrations makes this text a fundamental read on the subject. Divided into 17 chapters, the book covers all the major topics such as DC Circuits, Units of Work, Power and Energy, Magnetic Circuits.
The All New “Objective Chemistry for JEE Main with Boards Score Booster” is a 2-colour book encapsulating the formula for cracking Boards & JEE Main simultaneously. Salient features of the book are:Exhaustive theory, with solved examples, explaining all fundamentals/ concepts to build a strong base. Illustrations to master applications of concepts & sharpen problem solving skills. levels of graded exercises to ensure sufficient practice. 1200+ NCERT based Questions (Boards Score Booster) for Board exams covered in a separate exercise.
Incorporating new problems and examples, the second edition of Linear Systems and Signals features MATLAB® material in each chapter and at the back of the book. It gives clear descriptions of linear systems and uses mathematics not only to prove axiomatic theory, but also to enhance physical and intuitive understanding. Incorporating new problems and examples, the second edition of Linear Systems and Signals features MATLAB® material in each chapter and at the back of the book.
Here we are with CHEMISTRY ASSERTION AND REASON NOTE BY ALLEN for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.
International A/AS-level Science Revision Guides provide exam-focused texts to guide students through the content and skills of the course to prepare them for their AS and A-level exams.The Introduction provides an overview of the course and how it is assessed, advice on revision and taking the examination papers.
Monday, 10 September 2018
During recent years, stereochemistry has undergone a phenomenal growth both in theory and practice, with a concomitant increase of interest among the organic chemists, biological chemists, medicinal chemists and pharmacologists. The present text provides an up-to-date, coherent; and comprehensive account of the subject starting from the fundamentals and leading up to the latest developments as far as practicable.
Sunday, 9 September 2018
"Working problems,"writes Fuzhen Zhang in the preface, "is a crucial part of learning mathematics. A good problem should be one through which one learns methods, uses techniques, and gains insights into the subject.
Suitable for advanced undergraduate courses in abstract algebra, each chapter in this text consists of definitions, therorem, proofs and collaries. Worked-out exercises after each section provide techniques of problem solving.
These negatively charged particles were discovered by J. J. Thomson in 1897. In the experiment, a gas at low pressure was taken in a discharge tube made up of glass. At the ends of the discharge tube two electrodes were placed, connected to a battery for high voltage supply.
Here we are with COMPLETE INORGANIC CHEMISTRY HAND WRITTEN NOTE for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams.
It is the simplest form of the matter. Smallest unit of an element is known as atom. Total number of the known elements is 118 out of which 98 elements occur naturally and 20 are formed by artificial transmutation.
The first thing which comes in a student’s mind that what are the differences of syllabus if he or she wants study engineering in IIT, NIIT etc. So a student must know the syllabus and how to prepare for it. So here we are having a brief discussion about the necessary differences of the syllabus.
For those of you who plan to pursue a career in the field of Science, cracking class 12 physics is extremely important. A good score in class 12 will set the base for admission in a good institution.The key to getting good marks is studying the entire syllabus thoroughly followed by practice of last year question paper of CBSE class 12 Physics.
concise revision of the concepts followed by ample number of practice questions arranged in an ascending order of difficulty. The book includes sections like 'facts to remember' and 'important guidelines' to help the students prepare for the examination in a better way.
Joint Admission Test for M.Sc is the IIT JAM exam. A large number of students appear for the JAM Physics paper each year to compete for seats in the Indian Institutes of Technology.
CSIR NET June 2018 Exam was successfully conducted on 17th June 2018. CSIR Aspirants will be eagerly awaiting to know CSIR NET Exam June 2018 Expected Cut Off Marks. Biotecnika Experts after analyzing the question paper has calculated the Expected Cut Off Marks. Extreme care is being taken so as to provide you with the most accurate CSIR NET June 2018 Answer Key along with CSIR NET Exam Expected Cut Off Marks with proper Explanations & References so that you can verify the answers.
The Solid state class notes PDF by Allen Institute for IIT JEE and CBSE Class 12 preparation are combined in PDF format and available to download. So, guys, you can download the solid state class notes PDF for IIT JEE by Allen Institute Kota from the download tab given the last of the post.These class notes are basically prepared from the class room course of IIT JEE Main and Advance from Allen Institute Kota.
The basic principle in writing of this CSIR-NET-GATE book is to create a guiding text for students- a text which represents the material in a way that encourages the students for the logical thinking about what they have learned theoretically in their bachelors / masters.
Friday, 7 September 2018
Available for the first time in paperback, The Quantum Theory of Fields is a self-contained, comprehensive, and up-to-date introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume I introduces the foundations of quantum field theory.
Thursday, 6 September 2018
This new addition to the International Series in Pure and Applied Mathematics is for the two-term advanced undergraduate course in abstract algebra. Each chapter consists of definitions, theorems, proofs, and corollaries.
A revision guide tailored to the AS and A Level Chemistry syllabus (9701) for first examination in 2016. This Revision Guide offers support for students as they prepare for their AS and A Level Chemistry (9701) exams.
“Photosynthesis is a process used by plants in which energy from sunlight is used to convert carbon dioxide and water into molecules needed for growth. These molecules include sugars, enzymes and chlorophyll. Light energy is absorbed by the green chemical chlorophyll.”
Wednesday, 5 September 2018
The range of genetic varieties and of cultural practices associated with rice have made the Jeypore tract a globally important reserve of genetic diversity and accumulated traditional knowledge of rice cultivation.
Toppers handwritten notes are a comprehensive package for the preparation of NEET, AIIMS and other medical entrance examinations, which are designed by Top rankers in NEET & AIIMS. These notes cover all the important topics which are required to crack the exam of NEET.
Tuesday, 4 September 2018
In June and July 2018, a widely publicised cave rescue successfully extracted members of a junior football team trapped in Tham Luang Nang Non cave in Chiang Rai Province, Thailand. Twelve members of the team, aged eleven to seventeen, and their 25-year-old assistant coach entered the cave on 23 June after football practice. Shortly afterwards, heavy rains partially flooded the cave, trapping the group inside.
Monday, 3 September 2018
Physics Errorless JEE (Main) JEE (Advanced) AIPMT - Volume 1 & 2, published by Universal Book Depot, contains exhaustive theory with sub-chapter-wise division and level-wise grading of questions.