The document contains an answer key for a review test with questions from Chemistry, Physics, and Math. It provides the question numbers, parts, and answers. For some physics questions, it also provides short explanations or solutions. The answer key is organized by subject, section, and part with the corresponding question numbers and answers.
Cpm 14 06 2009 Paper 1 12th (Abcd) Code Bsracy.com
The document contains an answer key for a review test with questions from Chemistry, Physics, and Math. It provides the question numbers, parts, and answers in a structured format. The answer key is for 12th standard students for the date June 14, 2009 for paper 1.
1) The document contains a 25 question placement test covering math and geometry concepts such as rounding, operations with fractions and decimals, word problems, properties of shapes, coordinate geometry, statistics, and more.
2) The questions range from simple computations and word problems to more complex problems involving multiple steps.
3) The test is designed to assess a student's current math skill level and place them in the appropriate math course.
The document provides examples of advanced quantitative questions from the GMAT exam covering topics such as fractions and ratios, percentages, integers, powers, roots, algebra, and word problems. Each section presents 3 sample problems with multiple choice answers and explanations of the correct answers. The questions require setting up and solving equations, factoring expressions, evaluating expressions, approximations, properties of integers and exponents, and interpreting word problems algebraically.
The document describes the transform and quantization processes used in H.264 video compression. It discusses how the discrete cosine transform is approximated using integer arithmetic. The forward and inverse processes are derived from each other. Scaling matrices are incorporated to normalize values and minimize computational complexity while maintaining good compression performance. Quantization values are specified in the standard through scaling matrices.
1. The document contains 42 multiple choice questions about factorizing algebraic expressions and evaluating expressions.
2. The questions cover topics like factorizing quadratic expressions, common factors of expressions, evaluating expressions involving exponents and fractions, and identifying factors of expressions.
3. The multiple choice options provide the possible factored forms or simplified expressions for evaluating each question.
This document provides information about a chemistry GCSE exam involving questions on the periodic table, reactions of elements, preparation of salts, electrolysis, exothermic reactions, and hydrated sodium carbonate. The questions assess knowledge of key concepts like periodic trends, writing balanced equations, describing preparation methods and observations, redox reactions, and stoichiometry calculations. Step-by-step working is shown for multi-part questions involving calculations.
The document summarizes key macromolecules found in living cells, including polysaccharides, lipids, proteins, and nucleic acids. It describes the basic structures and functions of these macromolecules. Specifically, it notes that polysaccharides and lipids are important macromolecules, proteins require specific 3D structures to function, and DNA contains the genetic information in most organisms.
The document discusses the production of ammonia via the Haber process. Key points:
- Ammonia is produced by reacting nitrogen and hydrogen gases over an iron catalyst at high temperature (450°C) and pressure (200 atm).
- The balanced equation for the reaction is: N2 + 3H2 → 2NH3
- Unreacted gases are recycled in the process. Ammonia is then cooled to be liquified.
Cpm 14 06 2009 Paper 1 12th (Abcd) Code Bsracy.com
The document contains an answer key for a review test with questions from Chemistry, Physics, and Math. It provides the question numbers, parts, and answers in a structured format. The answer key is for 12th standard students for the date June 14, 2009 for paper 1.
1) The document contains a 25 question placement test covering math and geometry concepts such as rounding, operations with fractions and decimals, word problems, properties of shapes, coordinate geometry, statistics, and more.
2) The questions range from simple computations and word problems to more complex problems involving multiple steps.
3) The test is designed to assess a student's current math skill level and place them in the appropriate math course.
The document provides examples of advanced quantitative questions from the GMAT exam covering topics such as fractions and ratios, percentages, integers, powers, roots, algebra, and word problems. Each section presents 3 sample problems with multiple choice answers and explanations of the correct answers. The questions require setting up and solving equations, factoring expressions, evaluating expressions, approximations, properties of integers and exponents, and interpreting word problems algebraically.
The document describes the transform and quantization processes used in H.264 video compression. It discusses how the discrete cosine transform is approximated using integer arithmetic. The forward and inverse processes are derived from each other. Scaling matrices are incorporated to normalize values and minimize computational complexity while maintaining good compression performance. Quantization values are specified in the standard through scaling matrices.
1. The document contains 42 multiple choice questions about factorizing algebraic expressions and evaluating expressions.
2. The questions cover topics like factorizing quadratic expressions, common factors of expressions, evaluating expressions involving exponents and fractions, and identifying factors of expressions.
3. The multiple choice options provide the possible factored forms or simplified expressions for evaluating each question.
This document provides information about a chemistry GCSE exam involving questions on the periodic table, reactions of elements, preparation of salts, electrolysis, exothermic reactions, and hydrated sodium carbonate. The questions assess knowledge of key concepts like periodic trends, writing balanced equations, describing preparation methods and observations, redox reactions, and stoichiometry calculations. Step-by-step working is shown for multi-part questions involving calculations.
The document summarizes key macromolecules found in living cells, including polysaccharides, lipids, proteins, and nucleic acids. It describes the basic structures and functions of these macromolecules. Specifically, it notes that polysaccharides and lipids are important macromolecules, proteins require specific 3D structures to function, and DNA contains the genetic information in most organisms.
The document discusses the production of ammonia via the Haber process. Key points:
- Ammonia is produced by reacting nitrogen and hydrogen gases over an iron catalyst at high temperature (450°C) and pressure (200 atm).
- The balanced equation for the reaction is: N2 + 3H2 → 2NH3
- Unreacted gases are recycled in the process. Ammonia is then cooled to be liquified.
The document outlines the syllabus for Paper III of the B.Sc. Chemistry program at Dr. B.R. AMBEDKAR University. The syllabus covers inorganic chemistry, organic chemistry, and physical chemistry over 3 units and 90 hours. Some of the main topics included are coordination chemistry, spectral properties of metal complexes, nitrogen compounds, carbohydrates, chemical kinetics, and photochemistry.
This document contains a 50-question multiple choice test on chemistry concepts. The questions cover topics like chemical formulas, periodic trends, chemical bonding, stoichiometry, acid-base reactions, and organic chemistry. Each question is followed by 4 answer choices labelled A, B, C, or D.
Electrolysis is the process of using electricity to cause a non-spontaneous chemical reaction. During electrolysis, ions migrate towards the electrodes and undergo oxidation or reduction reactions. At the cathode, positively charged ions are reduced and neutral atoms are formed. At the anode, negatively charged ions are oxidized and neutral atoms or molecules are formed. The products of electrolysis depend on factors like the ions present in the electrolyte, their concentration and position in the reactivity series, and the nature of the electrodes. Electrolysis has applications in purifying and extracting metals, and in electroplating.
The document contains a chapter on periodicity of elements with 35 multiple choice questions about periodic tables, properties of elements, groups and periods. It tests knowledge of Mendeleev's periodic table, concepts like atomic number and mass, properties of groups including alkali metals and noble gases, and the discoveries of isotopes and electronic configuration that improved understanding of the periodic table. The answer key is provided at the end.
Definitions and MCQs of Ninth Class Chemistry (chemical bonding)Dr. Sajid Ali Talpur
This document contains definitions and multiple choice questions related to chemical bonding. It defines different types of bonds including ionic bonds, covalent bonds, single/double/triple covalent bonds, hydrogen bonds, and dispersion forces. It also defines related concepts like electronegativity, dipole moment, and bond pairs/lone pairs of electrons. The remainder of the document consists of 36 multiple choice questions testing understanding of these chemical bonding concepts and definitions. The questions cover topics like bond types in different molecules, properties of ionic compounds, and characteristics of different intermolecular forces. An answer key is provided at the end.
1. Alkenes readily undergo addition reactions where carbon-carbon double bonds become single bonds, converting unsaturated hydrocarbons to saturated organic compounds. Common addition reactions include bromination, hydrogenation, and hydration.
2. Cracking is the breaking down of long-chain hydrocarbons into smaller molecules like alkenes. It is done industrially over catalysts like aluminum oxide at high temperatures.
3. Alkenes can also undergo combustion reactions, burning with a smokier flame than alkanes of similar carbon number due to their higher carbon percentages.
Limestone is a naturally occurring resource that is quarried and used to make cement, concrete, and other building materials. It is composed mainly of calcium carbonate, which can be decomposed through heating to calcium oxide and carbon dioxide. Calcium oxide reacts with water to form calcium hydroxide, which is used to neutralize acidic soils. Metals are extracted from metal ores through various processes like heating with carbon or electrolysis depending on the reactivity of the metal. New extraction methods are being developed as metal ores become depleted.
Some basic concepts of chemistry exercise with solutionssuresh gdvm
This document contains sample questions and answers from Class 11 chemistry Chapter 1 on basic chemistry concepts. The questions calculate molecular masses, empirical and molecular formulas, mass percentages of elements in compounds, moles of reactants and products in chemical reactions, molarity and molality calculations. It also defines terms like significant figures, pressure, mass and prefixes related to the International System of Units.
Chemistry Multiple choice questions(50) with answerVibhor Agarwal
This document contains 50 multiple choice questions related to chemistry. The questions cover topics such as the father of modern chemistry, properties of elements in the periodic table, compounds like PVC and gunpowder, types of rocks, octane number, uses of gases like chlorine and ethylene, chemical properties and reactions, and more. Each question is followed by 4 possible answer choices with the correct answer provided at the end in bold. This quiz tests knowledge of basic chemistry concepts and terminology.
1. The document is a chemistry test paper containing multiple choice questions about chemical formulae and equations.
2. It tests students on topics like relative atomic mass, mole calculations, empirical formulae, gas volume calculations and stoichiometry.
3. The questions range in difficulty from calculating moles and masses to balancing chemical equations and solving multi-step stoichiometry problems.
1. The document describes 6 experiments involving chemical reactions and properties. It includes questions about the experiments and reactions.
2. Experiment 1 involves electrolysis of silver nitrate and copper sulfate solutions. Observations and half reactions are asked about.
3. Experiment 2 involves heating lead(II) carbonate and identifying the gas produced. Calculations of moles of gas are required.
The document provides guidelines and answering techniques for the SPM Chemistry examination. It outlines the format of the exam papers, including the number and types of questions in each paper. It also provides tips on scoring highly, such as familiarizing yourself with different question types and mastering core topics. The document gives guidance on how to answer questions in Papers 1, 2 and 3, including matching command words to their requirements. It defines key terms and describes the various elements expected in answers, such as explaining concepts, describing experiments, and planning experiments.
This document contains a 50 question chemistry mcqs test with an answer key. The test covers topics in general chemistry including the building blocks of matter, chemical formulas, chemical equations, states of matter, density, the periodic table, and acid-base chemistry. It is intended as a practice test for entry-level exams. The document was created by Dr. Sajid Ali Talpur and contains additional links to other chemistry and biology tests and study materials also authored by Dr. Talpur.
1st year chemistry 1st chapter short question answers - Malik XufyanMalik Xufyan
This document contains answers to questions about chemistry concepts such as ions, stoichiometry, limiting reactants, atomic mass, and moles. It defines terms like gram atom, gram molecular mass, molar volume, and Avogadro's number. It provides examples to illustrate concepts like how one mole of H2SO4 requires two moles of NaOH for complete neutralization due to each having different numbers of ions. Overall it concisely explains chemistry concepts and uses examples to show how concepts like moles, atoms, and reactions relate based on principles such as the law of conservation of mass.
Pairing scheme first year chemistry 2016- Malik XufyanMalik Xufyan
This document outlines the pairing scheme for the first year chemistry course in 2016. It details that the MCQ questions will cover multiple chapters, short questions will cover specific chapters and include 4 questions, long questions will span multiple chapters in each question, and practical exams will include physical experiments and different types of titration questions. The pairing scheme was created by Malik Xufyan and directs students to a chemistry discussion blog for more information.
1. The document provides a topical test with 6 questions about chemical equations and stoichiometric calculations. It asks the student to write chemical equations for reactions involving sodium, magnesium carbonate, aluminum, copper nitrate, and iron. It also asks the student to calculate relative molecular mass, mass of atoms, relative molecular mass of a gas, a combustion reaction of magnesium, and the volume and number of oxygen molecules from the decomposition of hydrogen peroxide.
This document contains the instructions for three experiments:
1) To compare the reactivity of alkali metals towards oxygen by observing their reactions in different sets. Students are asked to record observations, make predictions, and analyze pH changes.
2) To determine the reaction between barium chloride and potassium chromate solutions by measuring precipitate formation at different volumes. Students must complete a table of results and draw a graph to identify the reacting quantities.
3) To investigate the effect of zinc size on its reaction rate with sulfuric acid by developing a full experiment plan outlining the problem, hypothesis, variables, materials, procedure, and method of collecting data.
Guidelines on answering paper 2 and paper 3 questionsNoor Haslina
This document provides guidelines for students on how to answer questions in Chemistry Paper 2 and Paper 3 exams. It discusses how to write precise yet complete answers, relate answers to question needs, use correct terminology, describe chemical tests, write balanced equations, state changes in observations, show workings for calculations clearly, plot graphs correctly, and draw functional apparatus setup diagrams. The document also provides a suggested format for answering essay questions involving experiments, highlighting the importance of the title, apparatus list, setup diagram, correct procedure, and stating measurements. Overall, the document aims to help students structure their exam answers appropriately and avoid common mistakes to score well.
This document contains a 25 question multiple choice test on the structure of the atom. The questions cover topics like the differences between atoms and ions, kinetic theory, states of matter, phase changes, atomic structure, isotopes, and the number of protons, neutrons and electrons in atoms.
Copy of mpc 22-04-2018 jee adv-p-1 _ 2_cc_ans _ solRAVIPUROHIT22
This document contains answers to questions from JEE-Advanced Test 1 and Test 2 across Mathematics, Physics and Chemistry sections. It provides the question numbers, options selected as answers and some additional hints and explanations for certain questions from the test papers. The summary includes details of 3 questions - Question 13 from Mathematics discusses the properties of a parabola with given formula, Question 14 finds the HCF of three numbers and Question 15 calculates binomial expressions for given values of variables.
JEE Main 2022 Session 1 Physics Paper and Solution 1st shiftALLEN Overseas
Here we present JEE Main 2022 Session 1 Answer Key with Solutions prepared by ALLEN Overseas subject matter experts to help candidates analyze their performance and calculate their tentative score.
Here we present JEE Main 2022 Session 1 Answer Key with Solutions prepared by ALLEN Overseas subject matter experts to help candidates analyze their performance and calculate their tentative score.
The document outlines the syllabus for Paper III of the B.Sc. Chemistry program at Dr. B.R. AMBEDKAR University. The syllabus covers inorganic chemistry, organic chemistry, and physical chemistry over 3 units and 90 hours. Some of the main topics included are coordination chemistry, spectral properties of metal complexes, nitrogen compounds, carbohydrates, chemical kinetics, and photochemistry.
This document contains a 50-question multiple choice test on chemistry concepts. The questions cover topics like chemical formulas, periodic trends, chemical bonding, stoichiometry, acid-base reactions, and organic chemistry. Each question is followed by 4 answer choices labelled A, B, C, or D.
Electrolysis is the process of using electricity to cause a non-spontaneous chemical reaction. During electrolysis, ions migrate towards the electrodes and undergo oxidation or reduction reactions. At the cathode, positively charged ions are reduced and neutral atoms are formed. At the anode, negatively charged ions are oxidized and neutral atoms or molecules are formed. The products of electrolysis depend on factors like the ions present in the electrolyte, their concentration and position in the reactivity series, and the nature of the electrodes. Electrolysis has applications in purifying and extracting metals, and in electroplating.
The document contains a chapter on periodicity of elements with 35 multiple choice questions about periodic tables, properties of elements, groups and periods. It tests knowledge of Mendeleev's periodic table, concepts like atomic number and mass, properties of groups including alkali metals and noble gases, and the discoveries of isotopes and electronic configuration that improved understanding of the periodic table. The answer key is provided at the end.
Definitions and MCQs of Ninth Class Chemistry (chemical bonding)Dr. Sajid Ali Talpur
This document contains definitions and multiple choice questions related to chemical bonding. It defines different types of bonds including ionic bonds, covalent bonds, single/double/triple covalent bonds, hydrogen bonds, and dispersion forces. It also defines related concepts like electronegativity, dipole moment, and bond pairs/lone pairs of electrons. The remainder of the document consists of 36 multiple choice questions testing understanding of these chemical bonding concepts and definitions. The questions cover topics like bond types in different molecules, properties of ionic compounds, and characteristics of different intermolecular forces. An answer key is provided at the end.
1. Alkenes readily undergo addition reactions where carbon-carbon double bonds become single bonds, converting unsaturated hydrocarbons to saturated organic compounds. Common addition reactions include bromination, hydrogenation, and hydration.
2. Cracking is the breaking down of long-chain hydrocarbons into smaller molecules like alkenes. It is done industrially over catalysts like aluminum oxide at high temperatures.
3. Alkenes can also undergo combustion reactions, burning with a smokier flame than alkanes of similar carbon number due to their higher carbon percentages.
Limestone is a naturally occurring resource that is quarried and used to make cement, concrete, and other building materials. It is composed mainly of calcium carbonate, which can be decomposed through heating to calcium oxide and carbon dioxide. Calcium oxide reacts with water to form calcium hydroxide, which is used to neutralize acidic soils. Metals are extracted from metal ores through various processes like heating with carbon or electrolysis depending on the reactivity of the metal. New extraction methods are being developed as metal ores become depleted.
Some basic concepts of chemistry exercise with solutionssuresh gdvm
This document contains sample questions and answers from Class 11 chemistry Chapter 1 on basic chemistry concepts. The questions calculate molecular masses, empirical and molecular formulas, mass percentages of elements in compounds, moles of reactants and products in chemical reactions, molarity and molality calculations. It also defines terms like significant figures, pressure, mass and prefixes related to the International System of Units.
Chemistry Multiple choice questions(50) with answerVibhor Agarwal
This document contains 50 multiple choice questions related to chemistry. The questions cover topics such as the father of modern chemistry, properties of elements in the periodic table, compounds like PVC and gunpowder, types of rocks, octane number, uses of gases like chlorine and ethylene, chemical properties and reactions, and more. Each question is followed by 4 possible answer choices with the correct answer provided at the end in bold. This quiz tests knowledge of basic chemistry concepts and terminology.
1. The document is a chemistry test paper containing multiple choice questions about chemical formulae and equations.
2. It tests students on topics like relative atomic mass, mole calculations, empirical formulae, gas volume calculations and stoichiometry.
3. The questions range in difficulty from calculating moles and masses to balancing chemical equations and solving multi-step stoichiometry problems.
1. The document describes 6 experiments involving chemical reactions and properties. It includes questions about the experiments and reactions.
2. Experiment 1 involves electrolysis of silver nitrate and copper sulfate solutions. Observations and half reactions are asked about.
3. Experiment 2 involves heating lead(II) carbonate and identifying the gas produced. Calculations of moles of gas are required.
The document provides guidelines and answering techniques for the SPM Chemistry examination. It outlines the format of the exam papers, including the number and types of questions in each paper. It also provides tips on scoring highly, such as familiarizing yourself with different question types and mastering core topics. The document gives guidance on how to answer questions in Papers 1, 2 and 3, including matching command words to their requirements. It defines key terms and describes the various elements expected in answers, such as explaining concepts, describing experiments, and planning experiments.
This document contains a 50 question chemistry mcqs test with an answer key. The test covers topics in general chemistry including the building blocks of matter, chemical formulas, chemical equations, states of matter, density, the periodic table, and acid-base chemistry. It is intended as a practice test for entry-level exams. The document was created by Dr. Sajid Ali Talpur and contains additional links to other chemistry and biology tests and study materials also authored by Dr. Talpur.
1st year chemistry 1st chapter short question answers - Malik XufyanMalik Xufyan
This document contains answers to questions about chemistry concepts such as ions, stoichiometry, limiting reactants, atomic mass, and moles. It defines terms like gram atom, gram molecular mass, molar volume, and Avogadro's number. It provides examples to illustrate concepts like how one mole of H2SO4 requires two moles of NaOH for complete neutralization due to each having different numbers of ions. Overall it concisely explains chemistry concepts and uses examples to show how concepts like moles, atoms, and reactions relate based on principles such as the law of conservation of mass.
Pairing scheme first year chemistry 2016- Malik XufyanMalik Xufyan
This document outlines the pairing scheme for the first year chemistry course in 2016. It details that the MCQ questions will cover multiple chapters, short questions will cover specific chapters and include 4 questions, long questions will span multiple chapters in each question, and practical exams will include physical experiments and different types of titration questions. The pairing scheme was created by Malik Xufyan and directs students to a chemistry discussion blog for more information.
1. The document provides a topical test with 6 questions about chemical equations and stoichiometric calculations. It asks the student to write chemical equations for reactions involving sodium, magnesium carbonate, aluminum, copper nitrate, and iron. It also asks the student to calculate relative molecular mass, mass of atoms, relative molecular mass of a gas, a combustion reaction of magnesium, and the volume and number of oxygen molecules from the decomposition of hydrogen peroxide.
This document contains the instructions for three experiments:
1) To compare the reactivity of alkali metals towards oxygen by observing their reactions in different sets. Students are asked to record observations, make predictions, and analyze pH changes.
2) To determine the reaction between barium chloride and potassium chromate solutions by measuring precipitate formation at different volumes. Students must complete a table of results and draw a graph to identify the reacting quantities.
3) To investigate the effect of zinc size on its reaction rate with sulfuric acid by developing a full experiment plan outlining the problem, hypothesis, variables, materials, procedure, and method of collecting data.
Guidelines on answering paper 2 and paper 3 questionsNoor Haslina
This document provides guidelines for students on how to answer questions in Chemistry Paper 2 and Paper 3 exams. It discusses how to write precise yet complete answers, relate answers to question needs, use correct terminology, describe chemical tests, write balanced equations, state changes in observations, show workings for calculations clearly, plot graphs correctly, and draw functional apparatus setup diagrams. The document also provides a suggested format for answering essay questions involving experiments, highlighting the importance of the title, apparatus list, setup diagram, correct procedure, and stating measurements. Overall, the document aims to help students structure their exam answers appropriately and avoid common mistakes to score well.
This document contains a 25 question multiple choice test on the structure of the atom. The questions cover topics like the differences between atoms and ions, kinetic theory, states of matter, phase changes, atomic structure, isotopes, and the number of protons, neutrons and electrons in atoms.
Copy of mpc 22-04-2018 jee adv-p-1 _ 2_cc_ans _ solRAVIPUROHIT22
This document contains answers to questions from JEE-Advanced Test 1 and Test 2 across Mathematics, Physics and Chemistry sections. It provides the question numbers, options selected as answers and some additional hints and explanations for certain questions from the test papers. The summary includes details of 3 questions - Question 13 from Mathematics discusses the properties of a parabola with given formula, Question 14 finds the HCF of three numbers and Question 15 calculates binomial expressions for given values of variables.
JEE Main 2022 Session 1 Physics Paper and Solution 1st shiftALLEN Overseas
Here we present JEE Main 2022 Session 1 Answer Key with Solutions prepared by ALLEN Overseas subject matter experts to help candidates analyze their performance and calculate their tentative score.
Here we present JEE Main 2022 Session 1 Answer Key with Solutions prepared by ALLEN Overseas subject matter experts to help candidates analyze their performance and calculate their tentative score.
1. This document contains a multi-part math exam with questions on solving equations, finding gradients, calculating areas and volumes, probability, and other topics.
2. It provides the questions, spaces for answers, and fully worked out solutions. The first section contains 6 questions, the second section asks the student to answer 4 questions, and the third/alternative sections contain 2 optional questions each.
3. Various question types are used, including free response problems, multiple choice, graphing, word problems, and proofs. Questions involve concepts like functions, geometry, statistics, and trigonometry. Worked solutions or answers are provided to check understanding.
1. The document discusses algebra rules including addition, subtraction, multiplication, and transformation of radicals.
2. Examples are provided of reducing and performing operations with radicals.
3. The document contains practice problems for working with radicals and their operations.
This document contains instructions and questions for a mathematics preliminary examination. It consists of 7 questions testing skills in algebra, trigonometry, geometry, statistics, and problem solving. Students are instructed to show their working, use formulas provided, and give answers to a specified degree of accuracy. A total of 100 marks are available across the exam.
The document appears to contain a marking scheme for a Science exam consisting of Paper 1 and Paper 2. It provides the answers to 50 multiple choice questions for Paper 1. For Paper 2, it lists 5 questions and provides the marking criteria and marks allocated for each question component or part. The marking scheme is intended for examiners and contains the guidelines for awarding marks to students' responses. It also notes that the document is confidential and copyrighted material intended solely for examiners.
The document introduces the Law of Cosines, which can be used to find the length of any side of any triangle given the lengths of the other two sides and the angle between them. It provides examples of using the Law of Cosines to find the length of a diagonal of a parallelogram, the measure of the smallest angle of a triangle, and the measures of all three angles of a triangle.
This document provides a table listing common engineering prefix multipliers used with units of measurement from yocto to yotta, along with their decimal, binary, and hexadecimal representations. The prefixes and their associated multipliers allow expressing very large or small quantities in a standardized way. Notes are included to define common numeric terms like million, billion, and trillion used with the prefixes.
The document provides instructions for a quiz competition with 12 multiple choice questions across 3 sections. Participants have 60 seconds to answer each question and can discuss with teammates. Correct answers score 5 marks within 60 seconds or 2 marks within 30 seconds. Incorrect answers score 0 marks but allow a second chance. The sections cover quadratic equations, indices/logarithms, and coordinate geometry/statistics.
This document consists of a 16 page mathematics exam with multiple choice and free response questions covering topics like algebra, trigonometry, calculus, and geometry. The document provides the standard information for exam takers such as instructions, mathematical formulas, worked examples, and blank pages for solutions.
The document provides information about a physics exam, including sample multiple choice questions and their explanations. Some key details:
- The exam contains two sections - one with single answer multiple choice questions, and one with multiple answer multiple choice questions.
- Sample questions cover topics like optics, mechanics, electromagnetism, and thermodynamics. The explanations show the conceptual steps and mathematical calculations used to arrive at the correct answers.
- Questions involve concepts like reflection, interference, momentum, work, harmonic motion, magnetic fields, electrostatics, and more. Diagrams are provided to illustrate some questions.
The document provides models for the amounts spent on natural gas (N) and electricity (E) in the United States from 1989 to 1993. It asks students to: 1) Find a model for the total amount (A) spent on natural gas and electricity during that period by adding the two models together. 2) According to the combined model, calculate how much will be spent on natural gas and electricity in 2020.
Similar to Cpm 14 06 2009 Paper 2 12th (Abcd) Code B (12)
This document contains solutions to chemistry questions from the IIT-JEE 2009 exam. It includes multiple choice, matrix match, and integer answer questions covering topics like thermodynamics, organic chemistry reactions, and coordination compounds. The questions assess understanding of concepts like reaction mechanisms, isomerism, redox potentials, and calorimetry calculations.
This document contains solutions to chemistry questions from the IIT-JEE 2009 exam. It provides the questions, explanations of the correct answers, and in some cases diagrams. The questions cover topics like electrolytes, isotopes, acid strength, IUPAC naming, gas laws, intermolecular forces, chemical reactions, isomerism, and defects in solids.
1. This section contains 9 multiple choice questions about physics concepts. The questions cover topics like gravitational force, wind force on an advertising board, capacitance of coaxial cylinders, and photon collisions with hydrogen atoms.
2. The second part contains 2 questions with multiple correct options about torque on a gate submerged in water and collision properties between two spheres.
3. The last part presents assertion-reason questions relating to electric fields near conducting planes, magnetic force fields, adiabatic expansion of gases, and cooling rates of metallic spheres. It also includes comprehension questions about magnetic forces on current carrying wires and the height of liquid flowing out of a cylindrical vessel over time.
This section contains multiple choice questions in straight objective type format. There are 9 questions testing concepts related to mathematics, including functions, geometry, probability, limits, and differential equations. The document also includes an assertion-reason type question and a comprehension section containing word problems and geometry concepts related to engineering drawing.
1) The document contains a 9 question multiple choice quiz on chemistry topics. It includes questions on reactions, periodic trends, properties of compounds and complex concepts.
2) Additional sections include comprehension questions that require applying knowledge of concepts like crystal field theory to propose experiments and interpret results.
3) Equilibrium constants and how they relate to reaction entropy are also discussed through examples involving complex formation.
The document outlines a schedule for providing information on the results of JEE-2009. It lists 10 items of information that will be displayed on the IIT-JEE websites on August 1, 2009 for candidates, including the procedure for preparing merit lists, question papers and answers, minimum qualifying marks, marks of candidates with specific ranks, aggregate totals, and category-wise admission details. Candidates will also be able to view their individual marks until August 31, 2009.
This document provides information about a program to prepare students for the IIT-JEE entrance exam.
The program focuses on developing students' fundamental science and math concepts, analytical skills, and ability to solve complex problems. It aims to help students excel not only on the IIT-JEE but also board exams and other engineering entrance exams.
The course is divided into four phases with classes, assignments, tests and other activities. It provides over 400 hours of classroom instruction as well as additional study materials and practice tests. The program is available in both regular and weekend formats.
The document provides an introduction to the Joint Entrance Examination (JEE) process for admissions to the Indian Institutes of Technology (IITs), Indian Institute of Technology BHU, Varanasi, and Indian School of Mines University. Key details include:
- Admissions to 8 new IITs located in Mandi, Himachal Pradesh and Indore, Madhya Pradesh will be made through JEE-2009.
- 3% of total seats in each institute will be reserved for candidates with physical disabilities, allocated randomly across courses and categories to maintain an overall reservation of 3% in each institute and category.
- Institutes will fill vacant seats after the initial admission process by selecting candidates
This document is a practice test for the IIT-JEE 2008 exam. It contains 66 multiple choice questions across physics, chemistry, and mathematics. The instructions provide details on the exam format, allowed and prohibited items, how to fill out the answer sheet, and the marking scheme. Students are asked to read and follow all instructions carefully.
We recently hosted the much-anticipated Community Skill Builders Workshop during our June online meeting. This event was a culmination of six months of listening to your feedback and crafting solutions to better support your PMI journey. Here’s a look back at what happened and the exciting developments that emerged from our collaborative efforts.
A Gathering of Minds
We were thrilled to see a diverse group of attendees, including local certified PMI trainers and both new and experienced members eager to contribute their perspectives. The workshop was structured into three dynamic discussion sessions, each led by our dedicated membership advocates.
Key Takeaways and Future Directions
The insights and feedback gathered from these discussions were invaluable. Here are some of the key takeaways and the steps we are taking to address them:
• Enhanced Resource Accessibility: We are working on a new, user-friendly resource page that will make it easier for members to access training materials and real-world application guides.
• Structured Mentorship Program: Plans are underway to launch a mentorship program that will connect members with experienced professionals for guidance and support.
• Increased Networking Opportunities: Expect to see more frequent and varied networking events, both virtual and in-person, to help you build connections and foster a sense of community.
Moving Forward
We are committed to turning your feedback into actionable solutions that enhance your PMI journey. This workshop was just the beginning. By actively participating and sharing your experiences, you have helped shape the future of our Chapter’s offerings.
Thank you to everyone who attended and contributed to the success of the Community Skill Builders Workshop. Your engagement and enthusiasm are what make our Chapter strong and vibrant. Stay tuned for updates on the new initiatives and opportunities to get involved. Together, we are building a community that supports and empowers each other on our PMI journeys.
Stay connected, stay engaged, and let’s continue to grow together!
About PMI Silver Spring Chapter
We are a branch of the Project Management Institute. We offer a platform for project management professionals in Silver Spring, MD, and the DC/Baltimore metro area. Monthly meetings facilitate networking, knowledge sharing, and professional development. For more, visit pmissc.org.
LinkedIn Strategic Guidelines for June 2024Bruce Bennett
LinkedIn is a powerful tool for networking, researching, and marketing yourself to clients and employers. This session teaches strategic practices for building your LinkedIn internet presence and marketing yourself. The use of # and @ symbols is covered as well as going mobile with the LinkedIn app.
Khushi Saini, An Intern from The Sparks Foundationkhushisaini0924
This is my first task as an Talent Acquisition(Human resources) Intern in The Sparks Foundation on Recruitment, article and posts.
I invitr everyone to look into my work and provide me a quick feedback.
Learnings from Successful Jobs SearchersBruce Bennett
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1. ANSWER KEY
12 th ABCD (Date: 14-06-2009) Review Test-2
Code-B
Paper-2
CHEMISTRY PHYSICS MATHS
SECTION-2 SECTION-3
SECTION-1
PART-A PART-A
PART-A
Q.13 C Q.1 D
Q.1 C
Q.24 D Q.2 A
Q.2 D
Q.35 C Q.3 A
Q.3 B
Q.41 A Q.4 B
Q.4 A
Q.52 D Q.5 B
Q.5 D
Q.66 B Q.6 B
Q.6 C
Q.77 A Q.7 C
Q.7 B
Q.88 A Q.8 C
Q.8 A
Q.99 B Q.9 D
Q.9 D
Q.1010 B Q.10 C
Q.10 B
Q.1111 A Q.11 B
Q.11 B
Q.1215 B Q.12 A, B, C, D
Q.12 A, D
Q.1312 A, C Q.13 A, D
Q.13 B, C, D
Q.1413 A, D Q.14 B, C
Q.14 A, B
Q.1514 A, B, C Q.15 C, D
Q.15 A,B,C,D
PART-B PART-B PART-B
Q.1 (A) T (B) R Q.1 (A) P, R,S (B) P,Q,S Q.1 (A) T ; (B) Q;
(C) P (D) P (C) P,Q,S (D) P,R,S (C) Q, R, S, T ; (D) R, S
PART-C PART-C PART-C
Q.1 0008 Q.1 0005 Q.1 0010
Q.2 0004 Q.2 0024 Q.2 0022
Q.3 0036 Q.3 8400 Q.3 0006
Q.4 0002 Q.4 0024 Q.4 0100
2. PHYSICS
PART-A
Q.1
[Sol. n11 = n22
1 4000Å
n11 = n22 n2 = n1 = 60
6000Å
= 40 ]
2
Q.2
(I) O
[Sol.
D = 25cm
v = –25 cm
f = +10 cm
1 1 1 25.10 50
– =
25 u 10 25 10
u= = ]
7
Q.3
Com
[Sol. x
Greater the value of , lesser the value of x. hence for the sector of angle position of COM will be
farther than the semicircle (sector of angle ) ]
Q.4
[Sol. Fringe width does not depend on distance between the source and plane of slits. ]
Q.5
[Sol. Angular spacing between two consecutive maxima = = =2× ]
D d 180
Q.6
[Sol. Luminous flux per unit area × area of hole
d d 2
2
= ds = × = ]
4r 2 4r 2 2 16r 2
Q.7
T.I.R.
[Sol. S
sin i = µ sin r
1
sin = n sin sin = ]
2 n
Code-B Page # 1
3. PHYSICS
Q.8
[Sol. For TIR >c
90 – > c cos > sin c
n 2 1 1
> n> 2 ]
n n
Q.9
[Sol. Chemical energy of explosive is converted to heat which is connected to K.E. of the cannon-ball ]
Q.10
[Sol. Force on cannon ball = PA – Patm A
( P Patm ) A
acceleration
m
displacement inside ballerl = length of barrel =
v2 = 2as
(P Patm )A 2 (51 1) 105 8 10 3 2.5
2 =
v= = 100 m/s ]
m 20
Q.11
[Sol. PV = nRT
dn dV
= R' & = A.V.
.
dt dt
dV dn
P = RT
T
dt dt
PAv = R' RT v R' ]
Q.12
[Sol. We know VIBGYOR
Since in option V & Y are not given so possible are BG YOR
R > B
R < B By cauchy’s relation
1
sin C =
and by T.I.R.
so (C)B < (C)R
so there is probability of reflection of Blue colour so D must be blue and C nearest to blue which is green
R > y so R < y i.e. A is red B is yellow.
Q.13
R
r
Fv FR
[Sol.
10cm
fR
Code-B Page # 2
4. PHYSICS
From similar triangles,
r fR fv
= f
R R
1 f R 10 100
= f fR =
10 R 9
1 2
f R = (µR – 1) R
2 9
(µR – 1) = µR = 1.27
6 100
fR fv fR fv 100 / 9 10 1
= fy fR = = ~ 0.1 ]
100 / 9 10
Q.14
[Sol. We know
O2 =
5 7
He = ,
3 5
PV = const.
L
5/3
PHe (LA) = 5/3 A
2
PHe
PHe = PHe (2)5/3 ... (1)
PO 2 (LA)7/5 = PO 2 (LA)7/5
L
7/5
L
PO 2 = PO 2 ... (2)
Now PO 2 PHe
PO 2 PHe
L
PO 2 PHe 7/5
1
= =
L
PO 2 PHe 5/3
2
7/5
L7 / 5
(L) =
25 / 3
L L
L = 5/3 5/ 7 =
2 x 2 25 / 21
LA
so volume of O2 = LA = ]
2 25 / 21
Code-B Page # 3
5. PHYSICS
Q.15
[Sol. (A) For convex mirror object is not at focus (focus is on other side). The mirror will cause the
diverging incident beam to diverge even more.
(B) The rays emerging towards left from the lens must be parallel to P.A.
(C) Object is between optic center and focus. Image will be diverging (virtual)
(D) Initial object is at O whose image is formed at pole of mirror by the lens. Hence find image will
also be at O. ]
PART-B
Q.1
[Sol. (1) y1 = n11 = n22 = LCM of 1 and 2
2y1 = 2n11 = 2n22
Hence at this point both maxima again coincide.
1 1
y2 = n1 1 = n 2 2
2 2
n2
1
1 2
2 =
n1
1
2
1 2n 2 1 1 odd
2 = 2n 1 which will have a solution. Iff expressed as a proper fraction will be of form .
1 2 odd
1 odd
Option B & C : is of form . Hence no solution i.e. the two minima will never coincide.
2 even
1 odd
For option A& D : is of form . Hence at some finite y2 the two minima will coincide.
2 odd
At 2y2 the two maxima (and not minima) will coincide.
y = 3y2 is the next nearest point where minima coincide. ]
PART-C
Q.1
[Sol. New volume of flask = 2(1 + 3Glass T) litres (1dm3 = Litre)
New volume of water = 1(1 + Ywater T) litres
New volume of iron = 1(1 + 3iron T) dm3
Volume of water overflow = Vwater + Viron – Vflask
= (Ywater + 3iron – 6Glass)T
= [(180 + 3 × 12 – 6 × 8) × 10–6] × 50
= 168 × 50 × 10–6 = 8400 × 10–6 litres = 8400 mm3 ]
Q.2
[Sol. Heat released by water = Heat absorbed by ice
(15 × 103(gm))(cal/gm) × (80 – 20)°C = ms (20°C – 0°C) + mL
= (100 cal/g) m(gram)
Code-B Page # 4
6. PHYSICS
15 60
m= × 103 gm = 9kg
100
total water = 15 + 9 = 24 kg
minimum volume of vessel = 24 litres. ]
Q.3
dv Adx
[Sol. Temperature is constant E = 0, dW = nRT = nRT
v AL / 2
Q = E + W
dW nRT dx
=
dt L / 2 dt
1 T 2nRT dx
dQ dW
L dt
k =
dt dt 900 L
dx k 27 415.5 27 2 1
900 0.5 8.31 300 200
= = = m/s = 5 mm/s ]
dt 900.nRT
Q.4
[Sol. Heat supplied (1 2 & 2 3)
= nCv9T0 + nCp90T0
Heat rejected (3 4 & 4 1)
= nCv90T0 + nCp9T0
10C v C p
10
= 1 C 10C = 1 –
11.4 3.6 12
=1–
p 1 10
= =
V 15 15 50
%efficiency = 24% ]
Code-B Page # 5
7. CHEMISTRY
PART-A
Q.1
[Sol. H = V + (PV)
V = W = – 4 × – 10 = 40 l-bar
(PV) = P2V2 – P1V1 = 4 × 30 – 2 × 40 = 40 l – bar ]
Q.2
[Sol. (A) nBeH2(g) Cool. (BeH2)n(s)
H H
H –– Be –– H Be Be Be
Hyb. of Be : sp H H
(gas) 3
.. Hyb. of Be : sp
.. (solid)
..
..O O. .
(B) .. [NO2]+ [NO3]+
N–O–N
.. Hyb. of N in NO2+ : sp
..
Hyb. of N in NO3¯ : sp2
. .
O. . O:
..
2 (N2O5 in solid state)
Hyb. of each N:sp
(gaseous state)
(C) XeF6 [XeF5]+ F¯
Gaseous state Solid state
Hyb. sp3d3 Hyb. sp3d2
(D) PF5 PF5
Gaseous state Solid state
Hyb. : sp3d Hyb.: sp3d ]
Q.3
[Sol. q = – E
I law
E = – +
2E =
2CVdT = – PdV
RT
2CVdT = – dV
V
2C V dT dV
– = ]
R T V
Q.4
a
P 2 (V – b) = RT
V
[Sol. T
RT a
– 2
Vb V
P=
PV V a
–
V b VRT
Z= =
RT
Code-B Page # 1
8. CHEMISTRY
a
T
V b
–
Vb V Rb
=
b2
V ( V b)
=1+ ]
Q.5
[Sol. Tertiary alkyl halides can take part in the reaction but prefers disproportionation so the yield of dimerized
product will be less but it can show Wurtz reaction. ]
Paragraph for question nos. 6 to 8
Me CH2 CH3
Me Me
[Sol. + +
Me Me CH3 CH3 CH3 CH3
Me
(X) (R) 3° Free radical (P) 1° Free radical (Q) 2° Free radical
]
CH2–Cl CH3
Me Me Cl
H
Cl CH3 CH3 CH3 CH3
Me
Dia +
Dia + CH3
Me Me H
Cl
Me CH3 CH3
Cl
9
9×1 =9 1°Product = × 100 = 19.86%
45.3
22.8
6 × 3.8 = 22.8 2° Product = × 100 = 50.33%
45.3
13.5
3 × 4.5 = 13.5 3° Product = × 100 = 29.80%
45.3
45.3
Code-B Page # 2
9. CHEMISTRY
Q.9
F
N
[Sol. (A) F F
F
Hybridisation of N : sp3
FNF = 109°
As all substituents are same
Cl
C
(B) Cl Cl
Cl
Hybridisation of c : sp3
l CC = 109°
As all substituents are same.
O¯ O O O
(C) Cl Cl Cl Cl
O O O¯ O O O O O¯
O O O¯ O
Hybridisation of Cl : sp3
OClO : 109° , as well Cl–O bonds are of equal length. ]
Q.10
F F
Br —F
< 90°
[Sol. (A) B
F F F
Hybridisation of B : sp2 Hybridisation of Br : sp3d
Shape : Trigonal planar Shape : Bent 'T' shape.
Cl
I 180°
Cl — Be — Cl
(B)
Cl
Hybridisation : sp3d Hybridisation : sp
Shape : linear Shape : linear
Code-B Page # 3
10. CHEMISTRY
Cl
(C) B P
Cl Cl Cl Cl
Cl
Hybridisation of N : sp3 Hybridisation of P : sp3
Shape : Trigonal planar Shape : Triangular pyramidal
N P
(D) Cl Cl
Cl Cl
Cl Cl
Hybridisation of N : sp3 Hybridisation of P : sp3
Shape : Triangular pyramidal Shape : Triangular pyramidal. ]
Q.11
H C
[Sol. (A) C H (B) H F
H F
Triangular pryamidal
(Planar)
(Nonplanar)
•
C N
(C) F F (D)
O O
Planar (singlet carbene) (Planar)
Q.12
[ B]t k1
[Sol.(A) [C] = 2k = 1
t 2
k1
(B) ln E a for same temp. change
k
0.693
(C) t1/2 = k k = 2.772 sec. ]
1 2
Code-B Page # 4
11. CHEMISTRY
Q.13
[Sol. NCl3 undergoes hydrolysis and H2O attacks at Cl-atoms.
H 2SO3 4HF
SF4 + 3H2O
R .T.
Pr oton donor acids
+
Cl OH2
B B¯
H 2O
Cl Cl Cl Cl
2 Cl
Hyb. sp
3
Hyb. sp
(Transition state)
Q.15
COOH COOH
NO2
[Sol. (A) Ethanol can solvate anion of as compared to anion of
O2N NO2
(B) H H
N N N N
No flipping 2°amine 3°amine l.p.is present in more EN orbital
(C) L.G. tendency does not depend on solvent nature.
(D) Polar Aprotic solvent does not solvate anion. ]
PART-B
Q.1
Potential
Energy
[Sol. (A) As after rearrangement two product are formed.
Reaction progress
(B) No rearrangement
(C) Two products formed.
(D) Two products formed. ]
Code-B Page # 5
12. CHEMISTRY
PART-C
Q.1
[Sol. WAB = WCD = 0 D C
WBC = – nRT = – 1 × R × 300 = 300 R
40
WDA = – nRT = – 1 × R × – 200 = 200 R
V
(L)
Wtotal = – 100 R 20 lit.
A
B
|W| = 8 atm. lit. ]
200 300 400 600
T (K)
Q.2
[Sol. AsCl3 + 3H2O H 3AsO3 3HCl ]
Basicity 3 Basicity 1
Total basicity of products 4
Q.3
[Sol. A(g) B(g) + 2C(g)
P0 – –
P0 – x x 2x
– P0 2P0
if N is pressure of inert gas
P0 + N = 200
3P0 + N = 500
P0 = 150 ; N = 50
at t = 70 sec.
Pt = 350 = P0 + 2x + N
x = 75
t = t1/2 = 70 sec.
0.693
k (hr–1) = t sec × 3600 ]
1/ 2
Q.4
[Sol. Cl –– Be –– Cl
No. of 2C – 2e– bonds = 2 Total no. of 2C – 2e– &
No. of 3C – 4e– bonds = 0 3C – 2e– bonds = 2
]
Code-B Page # 6
13. MATHEMATICS
PART-A
Q.1
x2 t2 x2
[Sol. 2 f ' (2x) = x2 f ' (2x) = ; put 2x = t f ' (t) = f ' (x) = Ans.]
2 8 8
Q.2
dx
Let cos–1x = t –
1 x2
[Sol. = dt
(1 cos t ) sin t 1 sin t
I = – e
t
dt = – e t
1 cos t (1 cos t ) 2 dt
(1 cos t ) 2
1
et e cos x
=C– =C–
1 cos t
Ans. ]
1 x
Q.3
[Sol. Equation of line : y – 1 = m(x – 7)
mx – y + 1 – 7m = 0
r | 7m 1 | r
1 m2
Perpendicular distancer from (0, 0)= = =5
2 2
(7m – 1) 2 = 25(1 + m2)
49m2 – 14m + 1 = 25 + 25m2
24m2 – 14m – 24 = 0 m1m2 = – 1 Ans. ]
Q.4
2 x (5 x 1) (5 x 1) ( 2 x 1) (5 x 1) Lim ( 2 1) (5 1)
x x
l = Lim = Lim
x · x ln (sec x )1 x
[Sol. = x 0 2
x 0 ln (sec x ) x 0 ln (sec x )
x 2 ln 2 · ln 5 (ln 2 · ln 5) x 2
= Lim
x 0 ln (1 (sec x 1))
= Lim = 2 (ln 2 · ln 5) = (ln 4) (ln 5) Ans.]
x 0 (1 cos x )
Q.5
a a
[Sol. 1 r1 = r1 and 1 r2 = r2
a
r2 – r + a = 0
1 r
hence r1 and r2 are the roots of =r r1 + r2 = 1 Ans.]
Code-B Page # 1
14. MATHEMATICS
Paragraph for question nos. 6 to 8
[Sol. y = f (x) = x 2 – 4ax + a2 + 5a + 2
4a
vertex = = 2a
2
(i) f (2a) = 4a2 – 8a2 + a2 + 5a + 2
= – 3a2 + 5a + 2
2 5a 2 5 25 24 49
2
5
2
= – 3 a = – 3 a = 3 a
3 3
6 36 35 12
6
5
f (2a) is maximum if a = Ans.(i)
6
(ii) f (x) 0 x R
x2 – 4ax + a2 + 5a + 2 0
D0
16a2 – 4(a2 + 5a + 2) 0 4a2 – a2 – 5a – 2 0 3a2 – 6a + a – 2 0
(3a + 1)(a – 2) 0 – 1/3 a 2 amax = 2 Ans.(ii)
(iii) Given minimum value of f (x) is 2, for x 0
Case-1: when vertex is 0
i.e. 2a 0 a0
minimum f (x) occurs at x = 2a
f (2a) = 4a2 – 8a2 + a2 + 5a + 2 = – 3a2 + 5a + 2
f (2a) = 2 a(5 – 3a) = 0 a = 0 or a = 5/3
Case-2: when vertex is < 0
i.e. a<0
in this case, minimum occurs when x = 0
f (0) = a2 + 5a + 2 = a(a + 5) = 0 a = 0 or a = – 5
hence a {0, – 5, 5/3} 3 values of 'a' Ans.(iii) ]
Paragraph for question nos. 9 to 11
Sol. We have
r
sin x x (r 1)
n
6 6
r
f1(x) = 2
r 1
cos x (r 1) · cos x
6 6
2 3 2
= 2 · tan x tan x tan x tan x tan x tan x
6 6 6 6 6
n
................ tan x tan x (n 1)
6 6
n
f1(x) = 2 · tan x tan x
6
for n = 3, f1(x) = 2 tan x tan x = 2 cot x tan x = – 2
1
2 sin x cos x
Code-B Page # 2
15. MATHEMATICS
n
2 f2(x) = f1(x) – 2 · tan x
6
Now
n n
= 2 tan x – 2 tan x – 2 tan x
6 6
f2(x) = – tan x
f3(x) = – f2(x), so
f3(x) = tan x
e( e x 1) 1
2·(e x 1)
e ; x 0
Now f 4 ( x ) k1 ; x0
1 | tan x | tan x ; x 0
k2
1
f (0¯) = e 2 e
lne
Clearly
f (0+) = e k 2 & f (0) k1
(i) As f4(x) is continuous at x = 0, so by definition of continuity, we get
f (0¯ ) = f (0+) = f (0)
e = e k 2 = k1
1
k1 e & k2 = (D)
2
(ii) As y = f3(x) = tan x
clearly f3(x) is continuous as well as derivable everywhere in 0, 2 . (C)
(iii) for n = 3,
f1(x) = – 4
sin x cos x
– 2(tan x + cot x) = – 4 cos x sin x = 2 1 = 2 sin x · cos x
0,
4 2
x= (B)]
Q.12
[Sol. (A) f (x) = x – cos x ; f (0) < 0, f (/2) > 0
(B) f (x) = x + sin x – 1
1
f (0) = – 1 < 0; f (/6) = 1 0
6 2
(C) f (x) = a(x – 3) + b(x – 1) in [1, 3]
f (1) = – 2a < 0; f (3) = 2b > 0 f (x) = 0 in (1, 3)
(D) h (x) = f (x) – g (x)
h (a) = f (a) – g (a) > 0
h (b) = f (b) – g (b) < 0
hence using IVT all the four have at least one root in indicated interval. ]
Code-B Page # 3
16. MATHEMATICS
Q.13
[Sol. g ' (x) = aeax + f ' (x)
g ' (0) = a + f ' (0) = a – 5 ....(1)
g '' (x) = a2eax + f '' (x)
g '' (0) = a2 + f '' (0) = a2 + 3 ....(2)
g ' (0) + g '' (0) = 0
a – 5 + a2 + 3 = 0 a2 + a – 2 = 0 (a + 2)(a – 1) = 0 a = 1, – 2 Ans.]
Q.14
= 1 cos 1 cos 1 cos 1 cos
4k 2 4k 2 4k 4k
[Sol. P(k)
= 1 cos 1 sin 1 sin 1 cos
4k 4k 4k 4k
4 sin 2 · cos 2
= 1 cos 1 sin =
2 2 4k 4k
4k 4k 4
1 2
sin · =
1 1 1
2k
P(k) = P(3) = ;
4 4 4 16
2 1 2 1
sin sin 1 cos = 2 2 (B)
8 8 4
P(4) =
4 2k 4 16
1 2 1 2 1 5 1 3 5
= 2 sin = 1 cos 36 = 1
1
sin 4 = 32 (C)
8 10 8
P(5) = 8
4 10
1 2 1 2 1 1 3 2 3
= 2 sin = 1 cos = 1
2 = 16
sin
8 12 8 6 8
P(6) = ]
4 12
Q.15
[Sol. for continuity at x = 0
1
f (0) = 0 ; f (0–) = 0; f (0+) = Lim h sin
n
=0 n>0
h0 h
for derivability at x = 0
1
h n sin
f ' (0–) = 0; f ' (0+) = Lim h for this limit not to exist n 1
h0 h
hence 0 < n 1
n can not be 3/2 or 2 C, D ]
Code-B Page # 4
17. MATHEMATICS
PART-B
Q.1
[Sol.
e ln x ! x!
= 20 = 20 x(x – 1) = 20 x2 – x – 20 = 0 (x – 5)(x + 4) = 0
( x 2)! ( x 2)!
(A)
x = 5 Ans. (T)
(B) 4{x} = x + [x] ....(1)
2x 2x 5
= x + x – {x} 5{x} = 2x {x} = 0 <1 0x<
5 5 2
hence [x] = 0, 1, 2
Again from (1) 4x – 4[x] = x + [x]
3x = 5[x]
Case-I: If x [0, 1) [x] = 0
3x = 0 x0
Case-II: If x [1, 2) [x] = 1
x
5
3x = 5
3
Case-III: If x (2, 5/2] [x] = 2
10
3x = 10 x= (reject)
3
number of solutions = 2 Ans.
Alternatively :
Let x = I + f
2I 2 4
4f = I + f + I f= I = 0, 1 x=0&x=1+ =
3 3 3
(C) Given equation is
x2 + 2x(y + g) + y2 + 2fy + 4 = 0
2 x = – 2 (y + g) ±
4( y g) 2 4( y 2 2fy 4)
x = – (y + g) ± (g 2 4) 2 y(g f ) ....(1)
(1) will represent a pair of lines if its discriminant is zero
+ 4(g – f) = 0 g=f
x = – (y + g) ± g 2 4 . For two real lines
g2 4 g 2 or g – 2 Ans. Q, R, S, T
(D) If d = 6; A = (0, 0); B(6, 0)
Consider a circle with centre A are radius 2(r1) and a
circle with centre B and radius 3(r2). The circles will be
separated. There will 4 common tangents at a distance
of 2 from A and 3 from B 4 lines
|||ly if d = 5; r1 + r2 = 5 circles touches externally
3 common tangents 3 lines R, S
NOTE: |||ly for two intersecting circles
r2 – r1 < d < r1 + r2 i.e. 1 < d < 5 2 common tangents 2 lines
if d = r2 – r1 i.e. if d = 1 circles touches internally 1 lines ]
Code-B Page # 5
18. MATHEMATICS
PART-C
Q.1
[Sol. AAAAA | B B B B B B M
Middle digit must be A (think !)
so that even number of A's and B's are available
Take AABBB on one side of M (6th place) and then their image about M in a unique way
5!
Number of ways = 2!· 3! = 10 Ans.]
Q.2
[Sol. Using L'Hospital's Rule using f g h ' + g h f ' + h f g'
5 cos 4 x (sin x ) cos 3 2x cos 3 3x 3 cos 2 2 x 2 sin 2x cos 5 x cos 3 3x 3 cos 2 3x 3 sin 3x cos 5 x cos 3 2 x
Lim
x 0 2x
6 3 = 22 Ans.
5 9
=
2 2
Alternatively: Using expansion
x2 (2x ) 2 9x 2
5 3 3
5x · cos32x · cos33x = 1 .... · 1 .... · 1 ....
cos
2! 2! 2!
5x 2
1
=
.... 1 6 x 2 ....
27 x 2
1
....
2 2
5 2 27 x 2
1 6 x .... 1
= ....
2 2
27 x 2 5x 2
= 1 6x 2 ......... = 1 – 22x2 + .....
2 2
1 cos5 x · cos3 2 x ·cos3 3x 1 (1 22x 2 ....)
Lim = Lim = 22 Ans. ]
x 0 x2 x 0 x2
Q.3
[Sol. Let the roots are a – 3d, a – d, a + d, a + 3d
sum of roots = 4a = 0 a=0
hence roots are – 3d, – d, d, 3d
m
product of roots = 9d4 = m2 d2 = ....(1)
3
again x 1x 2 = 3d2 – 3d2 – 9d2 – d2 – 3d2 + 3d2
= – 10d2 = – (3m + 2)
= 10d2 = 3m + 2
10m
= = 3m + 2
3
= 10m = 9m + 6
Code-B m = 6 Ans. ] Page # 6
19. MATHEMATICS
Q.4
[Sol. Let P(x) = k(x – 1)(x – 3)(x – 5)(x – r) where r 1, 3, 5
ln P(x) = ln k + ln (x – 1) + ln (x – 3) + ln (x – 5) + ln (x – r)
differentiate w.r.t. x
P' ( x )
1 1 1 1
x 1 x 3 x 5 x r
=
P( x )
put x = 7, as P'(7) = 0 P(7) 0
23 6
1 1 1 1 1 1 11
=0 =0
6 4 2 7r 12 7r r 7 12
12 89 p
r–7= r= = p + q = 100 Ans.]
11 11 q
Code-B Page # 7