The document describes the instructions for a National Entrance Screening Test (NEST) exam with the following key details:
- The exam has 5 sections with a total of 200 marks: Section 1 (General) is compulsory with 60 marks, and the test taker must choose two of sections 2-5 (Biology, Chemistry, Math, Physics) which are each worth 70 marks.
- Section 1 contains 22 multiple choice questions worth either 3 or 2 marks depending on the question. Wrong or unattempted questions receive 0 marks.
- The answer sheet instructions specify how to fill it out correctly including writing identification details, bubbling in answers, and erasing properly if needed. Calculators and
This document provides instructions for a National Entrance Screening Test (NEST) exam. It states that the exam contains 5 sections worth a total of 200 marks. Section 1 is general and compulsory, while sections 2-5 cover specific subjects (biology, chemistry, math, physics) and students must choose 3 of the 4 subject sections. The instructions provide details on answering questions, using the answer sheet, time limits, and prohibited items.
The document discusses solving rational equations by clearing fractions. It explains that to solve an equation with fractional terms, we first multiply both sides of the equation by the lowest common denominator (LCD) of the fractions. This clears the fractions by distributing the LCD. Then the resulting equation can be solved using normal algebraic techniques. Two examples are provided to demonstrate this process.
1. The document is a booklet containing solutions to questions from the JEE (Advanced) 2013 exam. It provides instructions for taking the exam, details on the exam format and marking scheme, and sample questions with solutions.
2. The exam consists of three parts (Physics, Chemistry, and Mathematics) with three sections each. Section 1 has 10 multiple choice questions with a single correct answer. Section 2 has 5 questions with one or more correct answers. Section 3 has 5 questions where the answer is a single digit integer.
3. The document provides sample questions from the Physics portion of the exam, marked with an asterisk. The questions cover topics like mechanics, optics, heat transfer, and thermodynamics.
Formal expansion method for solving an electrical circuit modelTELKOMNIKA JOURNAL
We investigate the validity of the formal expansion method for solving a second order ordinary differential equation raised from an electrical circuit problem. The formal expansion method approximates the exact solution using a series of solutions. An approximate formal expansion solution is a truncated version of this series. In this paper, we confirm using simulations that the approximate formal expansion solution is valid for a specific interval of domain of the free variable. The accuracy of the formal expansion approximation is guaranteed on the time-scale 1.
This document contains 60 math questions from a school competition countdown round. The questions cover a variety of math topics including percentages, probability, geometry, number properties, and algebra. They range in difficulty from basic calculations to multi-step word problems.
The document contains 75 math word problems and their answers. It appears to be from a math competition with questions ranging in difficulty from basic arithmetic to more complex algebra and probability questions. Many questions involve multi-step word problems involving variables, equations, ratios, percentages and geometric shapes.
The document contains 75 math word problems with answers. It is a countdown round from a 2008 MATH COUNTS chapter competition. The problems cover a range of math topics including arithmetic, algebra, geometry, probability, and word problems. The answers are provided in numeric form following each problem statement.
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving triangles. The module is designed to teach students to apply the definition of proportion of segments to find unknown lengths and illustrate and verify the Basic Proportionality Theorem and its Converse. Examples are provided to demonstrate how to express ratios in simplest form, find missing values in proportions, determine if ratios form proportions, and solve problems involving angles and segments in triangles using ratios and proportions.
This document provides instructions for a National Entrance Screening Test (NEST) exam. It states that the exam contains 5 sections worth a total of 200 marks. Section 1 is general and compulsory, while sections 2-5 cover specific subjects (biology, chemistry, math, physics) and students must choose 3 of the 4 subject sections. The instructions provide details on answering questions, using the answer sheet, time limits, and prohibited items.
The document discusses solving rational equations by clearing fractions. It explains that to solve an equation with fractional terms, we first multiply both sides of the equation by the lowest common denominator (LCD) of the fractions. This clears the fractions by distributing the LCD. Then the resulting equation can be solved using normal algebraic techniques. Two examples are provided to demonstrate this process.
1. The document is a booklet containing solutions to questions from the JEE (Advanced) 2013 exam. It provides instructions for taking the exam, details on the exam format and marking scheme, and sample questions with solutions.
2. The exam consists of three parts (Physics, Chemistry, and Mathematics) with three sections each. Section 1 has 10 multiple choice questions with a single correct answer. Section 2 has 5 questions with one or more correct answers. Section 3 has 5 questions where the answer is a single digit integer.
3. The document provides sample questions from the Physics portion of the exam, marked with an asterisk. The questions cover topics like mechanics, optics, heat transfer, and thermodynamics.
Formal expansion method for solving an electrical circuit modelTELKOMNIKA JOURNAL
We investigate the validity of the formal expansion method for solving a second order ordinary differential equation raised from an electrical circuit problem. The formal expansion method approximates the exact solution using a series of solutions. An approximate formal expansion solution is a truncated version of this series. In this paper, we confirm using simulations that the approximate formal expansion solution is valid for a specific interval of domain of the free variable. The accuracy of the formal expansion approximation is guaranteed on the time-scale 1.
This document contains 60 math questions from a school competition countdown round. The questions cover a variety of math topics including percentages, probability, geometry, number properties, and algebra. They range in difficulty from basic calculations to multi-step word problems.
The document contains 75 math word problems and their answers. It appears to be from a math competition with questions ranging in difficulty from basic arithmetic to more complex algebra and probability questions. Many questions involve multi-step word problems involving variables, equations, ratios, percentages and geometric shapes.
The document contains 75 math word problems with answers. It is a countdown round from a 2008 MATH COUNTS chapter competition. The problems cover a range of math topics including arithmetic, algebra, geometry, probability, and word problems. The answers are provided in numeric form following each problem statement.
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving triangles. The module is designed to teach students to apply the definition of proportion of segments to find unknown lengths and illustrate and verify the Basic Proportionality Theorem and its Converse. Examples are provided to demonstrate how to express ratios in simplest form, find missing values in proportions, determine if ratios form proportions, and solve problems involving angles and segments in triangles using ratios and proportions.
- To write fractions as decimals and decimals as fractions, it is helpful to write numbers in different ways. This allows for easier comparisons and calculations.
- Rational numbers can be written as ratios of integers, repeating decimals can be written as fractions, and terminating decimals can be written as fractions.
- Writing numbers in different forms, such as fractions and decimals, allows for easier evaluation of expressions and calculations.
This document contains 19 multiple choice questions with solutions. The questions cover a range of math and logic topics such as geometry, percentages, remainders, and inequalities. For each question, the correct multiple choice answers are indicated based on working through the logic presented in the short solutions. This provides a review of different types of multiple choice questions and reasoning through solutions in brief explanations.
The document contains solutions to 26 multiple choice questions. The solutions provide step-by-step working to arrive at the answer choices A through E for each question. Some key steps involve simplifying fractions and expressions, evaluating probabilities, solving equations, and using logical reasoning to analyze word problems about topics like math, statistics, and probability.
This document provides information about Module 17 on similar triangles. The key points covered are:
1. The module discusses the definition of similar triangles, similarity theorems, and how to determine if two triangles are similar or find missing lengths using properties of similar triangles.
2. Students are expected to learn how to apply the definition of similar triangles, verify the AAA, SAS, and SSS similarity theorems, and use proportionality theorems to calculate lengths of line segments.
3. Several examples and exercises are provided to help students practice determining if triangles are similar, citing the appropriate similarity theorem, finding missing lengths, and applying properties of similar triangles.
This document provides an overview of Chapter 13 from a mathematics textbook on fractions. It includes summaries and examples for 9 lessons:
Lesson 13-1 introduces parts of a whole and identifying fractions for parts of a circle or figure.
Lesson 13-2 covers parts of a set and identifying fractions for parts of groups.
Lesson 13-3 demonstrates using drawings to solve word problems involving fractions.
Lesson 13-4 explains equivalent fractions through multiplication and division.
Lesson 13-5 defines simplest form and writing fractions in their simplest form.
Lesson 13-6 uses a word problem to demonstrate choosing the best problem-solving strategy.
Lesson 13-7 compares and orders fractions using
This document contains a countdown round from the 2009 MATH COUNTS chapter competition, consisting of 62 multiple choice math questions with answers. The questions cover a wide range of math topics including arithmetic, algebra, geometry, probability, and word problems. The summary provides an overview of the type and scope of questions included in the document without reproducing any specific questions or answers.
This document contains information about geometry and measurement from a math textbook. It includes 7 lessons: on congruent figures, symmetry, perimeter, solving simpler problems, area, choosing a problem-solving strategy, and finding the area of complex figures. The lessons provide definitions, standards, examples and exercises related to these geometry and measurement topics.
1. The document contains 10 math problems with solutions. The problems cover topics like arithmetic progressions, rates of change, probability, and geometry.
2. One problem involves finding the value of n given that the sum of even numbers between 1 and n is a specific value. The solution uses the formula for the sum of an arithmetic progression.
3. Another problem asks what fraction of a solution must be replaced if the original solution was 40% and replaced with 25% solution to get a final concentration of 35%. The solution sets up an equation to solve for the fraction replaced.
The document contains solutions to 18 math and probability problems. Some key details:
- Problem 1 involves finding an odd number n such that the sum of even numbers between 1 and n equals 79*80.
- Problem 2 calculates the price at which a bushel of corn costs the same as a peck of wheat, given changing prices.
- Problem 3 determines the minimum number of people needed to have over a 50% chance that one was born in a leap year.
The document contains 22 math word problems. The problems cover a variety of topics including fractions, ratios, percentages, geometry, probability, and algebra. They range in complexity from simple calculations to multi-step problems. The answers provided are numerical values, algebraic expressions, or ratios expressed as common fractions.
The document is about algebra and graphing. It contains 7 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, graphing functions, and a problem-solving investigation. Each lesson contains examples and practice problems to teach the concepts and standards covered in that lesson.
The document is a sample test containing 71 math word problems. It provides the questions, answers, and formatting for a state-level math competition countdown round. The questions cover a range of math topics and vary in difficulty.
This document contains an overview of Chapter 10 from a geometry textbook. It covers the following topics across 10 lessons: solid figures, plane figures, problem-solving strategies like looking for patterns, lines/segments/rays, angles, and problem-solving investigations. The chapter introduces key concepts, provides examples, and aligns topics to state math standards. It aims to teach students to identify, describe, classify and solve problems involving various geometric shapes and their properties.
This document provides examples for estimating square roots and cube roots of numbers that are not perfect squares or cubes. It shows how to estimate the value by finding the largest perfect square or cube below the number and the smallest perfect square or cube above it. The square or cube roots of these numbers are then used to determine an integer estimate between them. Several step-by-step examples are provided to demonstrate this process. Common Core State Standards addressed in the lesson are also listed.
The document is a set of math word problems and their answers from the 2008 MATH COUNTS National Competition Countdown Round. It includes 20 problems covering topics like percentages, ratios, proportions, arithmetic and algebraic sequences, probability, geometry, and more. The problems have a range of difficulties and ask test-takers to determine quantities, values, ratios, and sums based on the information provided.
This document provides information about a mathematics instructional material for Grade 9 learners in the Philippines. It was developed collaboratively by educators and reviewed by DepEd. The material covers variations, including direct, inverse, joint, and combined variations. It encourages teachers to provide feedback to DepEd to help improve the material. The material aims to help learners understand different types of variations and solve problems involving variations.
The document contains 31 multi-step math word problems with solutions. The problems cover a range of topics including percentages, ratios, averages, probability, geometry, and more. The level of difficulty ranges from relatively simple to more complex.
The document provides information on the placement test pattern for Infosys. It consists of two rounds - a written test and final HR round. The written test has two sections - an aptitude reasoning test and a verbal ability test. The aptitude reasoning test covers topics like picture reasoning, statement reasoning, data sufficiency, data interpretation, relation problems and syllogism. The verbal ability test covers topics like sentence correction, phrase insertion, fill in the blanks, theme detection and reading comprehension. Sample questions are provided for the aptitude reasoning section. The document also provides examples and explanations for some of the sample questions.
This document discusses equivalence and solving equations. It begins with defining equivalence as the product of a number and its multiplicative inverse being 1. It then provides examples of solving various equations using properties of equality like addition, subtraction, multiplication and division. These include one-step, two-step and multi-step equations with or without variables on both sides. It also discusses equations having no solutions, one solution, or infinitely many solutions.
The document provides information about the format and marking scheme of the JEE (Advanced) exam from 2013, including:
- The exam has 3 parts (Physics, Chemistry, Mathematics) with 3 sections each: multiple choice with single correct answer, multiple choice with one or more correct answers, and questions with single-digit answers.
- Sections 1 and 3 award marks for correct answers and deduct marks for incorrect answers. Section 2 awards marks only for fully correct answers and deducts marks otherwise.
- An example question is provided for Section 1 of the Physics part of the exam.
Probability and Stochastic Processes A Friendly Introduction for Electrical a...KionaHood
Full download : https://alibabadownload.com/product/probability-and-stochastic-processes-a-friendly-introduction-for-electrical-and-computer-engineers-3rd-edition-yates-solutions-manual/ Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers 3rd Edition Yates Solutions Manual , Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers,Yates,3rd Edition,Solutions Manual
This document provides an overview of analysis of variance (ANOVA). It discusses two-way ANOVA and the design of experiments (DOE) including completely randomized design (CRD) and randomized block design (RBD). CRD is the simplest design where treatments are randomly allocated without blocking. RBD uses blocking to reduce experimental error by making comparisons only between treatments within the same block. The document provides formulas and examples for calculating ANOVA tables for one-way and two-way ANOVA to test for differences between sample means.
- To write fractions as decimals and decimals as fractions, it is helpful to write numbers in different ways. This allows for easier comparisons and calculations.
- Rational numbers can be written as ratios of integers, repeating decimals can be written as fractions, and terminating decimals can be written as fractions.
- Writing numbers in different forms, such as fractions and decimals, allows for easier evaluation of expressions and calculations.
This document contains 19 multiple choice questions with solutions. The questions cover a range of math and logic topics such as geometry, percentages, remainders, and inequalities. For each question, the correct multiple choice answers are indicated based on working through the logic presented in the short solutions. This provides a review of different types of multiple choice questions and reasoning through solutions in brief explanations.
The document contains solutions to 26 multiple choice questions. The solutions provide step-by-step working to arrive at the answer choices A through E for each question. Some key steps involve simplifying fractions and expressions, evaluating probabilities, solving equations, and using logical reasoning to analyze word problems about topics like math, statistics, and probability.
This document provides information about Module 17 on similar triangles. The key points covered are:
1. The module discusses the definition of similar triangles, similarity theorems, and how to determine if two triangles are similar or find missing lengths using properties of similar triangles.
2. Students are expected to learn how to apply the definition of similar triangles, verify the AAA, SAS, and SSS similarity theorems, and use proportionality theorems to calculate lengths of line segments.
3. Several examples and exercises are provided to help students practice determining if triangles are similar, citing the appropriate similarity theorem, finding missing lengths, and applying properties of similar triangles.
This document provides an overview of Chapter 13 from a mathematics textbook on fractions. It includes summaries and examples for 9 lessons:
Lesson 13-1 introduces parts of a whole and identifying fractions for parts of a circle or figure.
Lesson 13-2 covers parts of a set and identifying fractions for parts of groups.
Lesson 13-3 demonstrates using drawings to solve word problems involving fractions.
Lesson 13-4 explains equivalent fractions through multiplication and division.
Lesson 13-5 defines simplest form and writing fractions in their simplest form.
Lesson 13-6 uses a word problem to demonstrate choosing the best problem-solving strategy.
Lesson 13-7 compares and orders fractions using
This document contains a countdown round from the 2009 MATH COUNTS chapter competition, consisting of 62 multiple choice math questions with answers. The questions cover a wide range of math topics including arithmetic, algebra, geometry, probability, and word problems. The summary provides an overview of the type and scope of questions included in the document without reproducing any specific questions or answers.
This document contains information about geometry and measurement from a math textbook. It includes 7 lessons: on congruent figures, symmetry, perimeter, solving simpler problems, area, choosing a problem-solving strategy, and finding the area of complex figures. The lessons provide definitions, standards, examples and exercises related to these geometry and measurement topics.
1. The document contains 10 math problems with solutions. The problems cover topics like arithmetic progressions, rates of change, probability, and geometry.
2. One problem involves finding the value of n given that the sum of even numbers between 1 and n is a specific value. The solution uses the formula for the sum of an arithmetic progression.
3. Another problem asks what fraction of a solution must be replaced if the original solution was 40% and replaced with 25% solution to get a final concentration of 35%. The solution sets up an equation to solve for the fraction replaced.
The document contains solutions to 18 math and probability problems. Some key details:
- Problem 1 involves finding an odd number n such that the sum of even numbers between 1 and n equals 79*80.
- Problem 2 calculates the price at which a bushel of corn costs the same as a peck of wheat, given changing prices.
- Problem 3 determines the minimum number of people needed to have over a 50% chance that one was born in a leap year.
The document contains 22 math word problems. The problems cover a variety of topics including fractions, ratios, percentages, geometry, probability, and algebra. They range in complexity from simple calculations to multi-step problems. The answers provided are numerical values, algebraic expressions, or ratios expressed as common fractions.
The document is about algebra and graphing. It contains 7 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, graphing functions, and a problem-solving investigation. Each lesson contains examples and practice problems to teach the concepts and standards covered in that lesson.
The document is a sample test containing 71 math word problems. It provides the questions, answers, and formatting for a state-level math competition countdown round. The questions cover a range of math topics and vary in difficulty.
This document contains an overview of Chapter 10 from a geometry textbook. It covers the following topics across 10 lessons: solid figures, plane figures, problem-solving strategies like looking for patterns, lines/segments/rays, angles, and problem-solving investigations. The chapter introduces key concepts, provides examples, and aligns topics to state math standards. It aims to teach students to identify, describe, classify and solve problems involving various geometric shapes and their properties.
This document provides examples for estimating square roots and cube roots of numbers that are not perfect squares or cubes. It shows how to estimate the value by finding the largest perfect square or cube below the number and the smallest perfect square or cube above it. The square or cube roots of these numbers are then used to determine an integer estimate between them. Several step-by-step examples are provided to demonstrate this process. Common Core State Standards addressed in the lesson are also listed.
The document is a set of math word problems and their answers from the 2008 MATH COUNTS National Competition Countdown Round. It includes 20 problems covering topics like percentages, ratios, proportions, arithmetic and algebraic sequences, probability, geometry, and more. The problems have a range of difficulties and ask test-takers to determine quantities, values, ratios, and sums based on the information provided.
This document provides information about a mathematics instructional material for Grade 9 learners in the Philippines. It was developed collaboratively by educators and reviewed by DepEd. The material covers variations, including direct, inverse, joint, and combined variations. It encourages teachers to provide feedback to DepEd to help improve the material. The material aims to help learners understand different types of variations and solve problems involving variations.
The document contains 31 multi-step math word problems with solutions. The problems cover a range of topics including percentages, ratios, averages, probability, geometry, and more. The level of difficulty ranges from relatively simple to more complex.
The document provides information on the placement test pattern for Infosys. It consists of two rounds - a written test and final HR round. The written test has two sections - an aptitude reasoning test and a verbal ability test. The aptitude reasoning test covers topics like picture reasoning, statement reasoning, data sufficiency, data interpretation, relation problems and syllogism. The verbal ability test covers topics like sentence correction, phrase insertion, fill in the blanks, theme detection and reading comprehension. Sample questions are provided for the aptitude reasoning section. The document also provides examples and explanations for some of the sample questions.
This document discusses equivalence and solving equations. It begins with defining equivalence as the product of a number and its multiplicative inverse being 1. It then provides examples of solving various equations using properties of equality like addition, subtraction, multiplication and division. These include one-step, two-step and multi-step equations with or without variables on both sides. It also discusses equations having no solutions, one solution, or infinitely many solutions.
The document provides information about the format and marking scheme of the JEE (Advanced) exam from 2013, including:
- The exam has 3 parts (Physics, Chemistry, Mathematics) with 3 sections each: multiple choice with single correct answer, multiple choice with one or more correct answers, and questions with single-digit answers.
- Sections 1 and 3 award marks for correct answers and deduct marks for incorrect answers. Section 2 awards marks only for fully correct answers and deducts marks otherwise.
- An example question is provided for Section 1 of the Physics part of the exam.
Probability and Stochastic Processes A Friendly Introduction for Electrical a...KionaHood
Full download : https://alibabadownload.com/product/probability-and-stochastic-processes-a-friendly-introduction-for-electrical-and-computer-engineers-3rd-edition-yates-solutions-manual/ Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers 3rd Edition Yates Solutions Manual , Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers,Yates,3rd Edition,Solutions Manual
This document provides an overview of analysis of variance (ANOVA). It discusses two-way ANOVA and the design of experiments (DOE) including completely randomized design (CRD) and randomized block design (RBD). CRD is the simplest design where treatments are randomly allocated without blocking. RBD uses blocking to reduce experimental error by making comparisons only between treatments within the same block. The document provides formulas and examples for calculating ANOVA tables for one-way and two-way ANOVA to test for differences between sample means.
The passage describes an experiment involving the diffusion of antibodies through an agarose gel. A central well containing a mixture of antibodies X and Y is surrounded by four outer wells containing different antigens. Based on the pattern of precipitation bands that form, the outer wells can be identified as:
Well M and N contain antigen X.
Wells P and O contain antigens Y and Z respectively.
Guzman, jerome francis r. assignment #3 measures of central tendency, dispers...JeromeFrancis9
This document contains three examples analyzing different data sets using measures of central tendency, dispersion, and location. The first example analyzes students' favorite subjects and calculates the mode. The second examines college freshmen sleep hours and computes mean, median, mode, standard deviation, variance, coefficient of variation, and range. The third looks at test scores, finds the 80th percentile, D5, Q1, and interprets the percentile rank of 82.
This document is the preface to the instructor's manual for Classical Dynamics of Particles and Systems by Stephen T. Thornton and Jerry B. Marion. It provides an overview of the contents of the manual, which contains solutions to the end-of-chapter problems from the textbook. The preface notes there are now 509 problems and the solutions range from straightforward to challenging. It stresses the solutions are only for instructors and should not be shared with students.
For so many years now a lot of scientist have used the series of positive binomial expansion to solve that of Negative binomial expansion, positive fractional binomial expansion and Negative fractional binomial expansion which was generated/derived using Maclaurin series to derive the series of Negative binomial expansion, positive fractional binomial expansion and Negative fractional binomial expansion just as it was used to provide answers to positive binomial expansion but fails for All the other expansion due to a deviation made. This Manuscript contains the correct solution/answers to Negative binomial expansions with proofs through worked examples, with other forms of
solving Negative binomial expansion just as in the case of Pascal’s triangle in positive binomial expansion, in
Negative binomial expansion it is called Anekwe’s triangle and other methods like the combination method of solving Negative binomial expansion.
This document contains a sample paper for the GATE exam with 25 multiple choice questions covering topics such as matrices, complex numbers, differential equations, mechanics, and heat transfer. The questions test concepts like limits, determinants, vector relationships, properties of materials, kinematics of rolling objects, and definitions of terms like Poisson's ratio and Biot number. An explanation or working is provided for each question to explain the reasoning behind the correct answer.
THE MIDLINE THEOREM-.pptx GRADE 9 MATHEMATICS THIRD QUARTERRicksCeleste
1. The document discusses classroom rules which include listening when others are speaking, raising your hand to speak or get up, and being respectful.
2. It then provides an example of using the midline theorem to solve several geometry problems involving triangles. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
3. Finally, it discusses how the midline theorem can be applied in real life contexts like architecture and engineering for structures like rooftops, bridges, and buildings.
This document provides instructions for a test with sections on physics, chemistry, and mathematics. It contains multiple choice questions with one or more correct answers per question (partial marks possible) and numerical response questions (no partial marks). Instructions describe the question formats, time limit, prohibited items, and process for filling out the answer sheet. The test is 183 total marks and takes 3 hours to complete.
This document provides examples and explanations for statistical concepts covered on a final exam, including the normal distribution, hypothesis testing, and probability distributions. It includes sample problems calculating probabilities and critical values for hypothesis tests on means and proportions. Excel templates are referenced for finding probabilities based on the standard normal and Poisson distributions. Step-by-step workings are shown for several problems to illustrate statistical calculations and interpretations.
Mathematics is the study of patterns and quantities. It is used in many fields and is everywhere in daily life. Some key concepts in mathematics include geometric patterns found in nature, Fibonacci numbers, problem solving techniques, and graph theory. Mathematics uses formal language and symbols to express ideas and relationships precisely. Common tools in mathematics include logic, sets, functions, and statistical analysis of data. Mathematicians develop and apply logical reasoning to understand mathematical concepts and solve problems.
The document discusses solving recurrence relations using iterative methods. It provides examples of using forward and backward iteration to predict solutions to recurrence relations given initial conditions. Recurrence relations can be used to model problems involving compound interest, population growth, algorithms like the Tower of Hanoi puzzle, and counting problems. Explicit formulas for the solutions can be derived and proven using induction.
IIT JEE 2012 Solved Paper by Prabhat GauravSahil Gaurav
The document provides instructions for a multiple choice exam paper. It details:
1) General instructions for the exam including not using additional materials and filling out answer sheets.
2) The exam format which includes 3 sections - multiple choice, multiple answer multiple choice, and single digit answer questions.
3) The marking scheme which awards points differently based on the question type and correctness of answers.
11 - 3
Experiment 11
Simple Harmonic Motion
Questions
How are swinging pendulums and masses on springs related? Why are these types of
problems so important in Physics? What is a spring’s force constant and how can you measure
it? What is linear regression? How do you use graphs to ascertain physical meaning from
equations? Again, how do you compare two numbers, which have errors?
Note: This week all students must write a very brief lab report during the lab period. It is
due at the end of the period. The explanation of the equations used, the introduction and the
conclusion are not necessary this week. The discussion section can be as little as three sentences
commenting on whether the two measurements of the spring constant are equivalent given the
propagated errors. This mini-lab report will be graded out of 50 points
Concept
When an object (of mass m) is suspended from the end of a spring, the spring will stretch
a distance x and the mass will come to equilibrium when the tension F in the spring balances the
weight of the body, when F = - kx = mg. This is known as Hooke's Law. k is the force constant
of the spring, and its units are Newtons / meter. This is the basis for Part 1.
In Part 2 the object hanging from the spring is allowed to oscillate after being displaced
down from its equilibrium position a distance -x. In this situation, Newton's Second Law gives
for the acceleration of the mass:
Fnet = m a or
The force of gravity can be omitted from this analysis because it only serves to move the
equilibrium position and doesn’t affect the oscillations. Acceleration is the second time-
derivative of x, so this last equation is a differential equation.
To solve: we make an educated guess:
Here A and w are constants yet to be determined. At t = 0 this solution gives x(t=0) = A,
which indicates that A is the initial distance the spring stretches before it oscillates. If friction is
negligible, the mass will continue to oscillate with amplitude A. Now, does this guess actually
solve the (differential) equation? A second time-derivative gives:
Comparing this equation to the original differential equation, the correct solution was
chosen if w2 = k / m. To understand w, consider the first derivative of the solution:
−kx = ma
a = −
k
m
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
x
d 2x
dt 2
= −
k
m
x x(t) = A cos(ωt)
d 2x(t)
dt 2
= −Aω2 cos(ωt) = −ω2x(t)
James Gering
Florida Institute of Technology
11 - 4
Integrating gives
We assume the object completes one oscillation in a certain period of time, T. This helps
set the limits of integration. Initially, we pull the object a distance A from equilibrium and
release it. So at t = 0 and x = A. (one.
The document contains 16 multiple choice questions about algorithms, data structures, and graph theory. Each question has 4 possible answers and the correct answer is provided. The maximum number of comparisons needed to merge sorted sequences is 358, and depth first search on a graph represented with an adjacency matrix has a worst case time complexity of O(n^2).
The document contains a collection of math and science problems related to topics like calculus, vectors, probability, statistics, and more. It includes over 50 multiple choice questions testing concepts like Laplace transforms, vector operations, differential equations, probability distributions, and calculating averages, means, and standard deviations from data sets. The questions are in Filipino with translations provided and cover a wide range of computational, algebraic, and conceptual problems across several domains of math, science, and engineering.
- Simple linear regression is used to predict values of one variable (dependent variable) given known values of another variable (independent variable).
- A regression line is fitted through the data points to minimize the deviations between the observed and predicted dependent variable values. The equation of this line allows predicting dependent variable values for given independent variable values.
- The coefficient of determination (R2) indicates how much of the total variation in the dependent variable is explained by the regression line. The standard error of estimate provides a measure of how far the observed data points deviate from the regression line on average.
- Prediction intervals can be constructed around predicted dependent variable values to indicate the uncertainty in predictions for a given confidence level, based on the
This document provides instructions for a mathematics scholarship test consisting of 45 multiple-choice questions across 3 sections: Algebra, Analysis, and Geometry. The instructions specify that candidates should answer each question in the provided answer booklet rather than on the question paper. Various mathematical terms and notation are defined for reference. The questions cover a wide range of topics in higher mathematics including algebra, analysis, geometry, and complex analysis.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help enhance one's emotional well-being and mental clarity.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness, happiness and focus.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document provides information about the Post Graduate Common Entrance Test to be held on July 1st, 2017 from 2:30 pm to 4:30 pm for various Masters programs. It lists instructions for candidates regarding filling the answer sheet correctly and details about the structure of the test, which will consist of 75 multiple choice questions worth 100 marks to be completed within 120 minutes. Candidates are advised to carefully read and follow the guidelines for appearing in the exam.
Civil Service 2019 Prelims Previous Question Paper - 2Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Civil Service 2019 Prelims Previous Question Paper - 1Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Civil Service 2018 Prelims Previous Question Paper - 2Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Civil Service 2018 Prelims Previous Question Paper - 1Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Civil Service 2017 Prelims Previous Question Paper - 2Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like depression and anxiety.
Civil Service 2017 Prelims Previous Question Paper - 1Eneutron
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise stimulates the production of endorphins in the brain which elevate mood and reduce stress levels.
This document contains the question paper for SNAP 2013 along with the answers to the 150 multiple choice questions. It directs test takers to an online site to attempt previous SNAP papers and provides information about exam preparation resources available on the site such as daily practice questions, preparation strategies, coaching classes, and current affairs.
This document contains the question paper for SNAP 2014 along with the answers to the 150 multiple choice questions. It provides a link to attempt similar past year papers online and lists exam preparation resources for SNAP like daily practice questions, preparation strategies, coaching class recommendations, and current affairs.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
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Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
2. NATIONAL ENTRANCE SCREENING TEST (NEST – 2010)
Total Marks: 200 Time: 3 hours
General instructions
1. This question booklet contains 5 sections, with mark distribution as follows.
Section 1 General 60 marks Compulsory
Section 2 Biology 70 marks
Section 3 Chemistry 70 marks
Section 4 Mathematics 70 marks
Section 5 Physics 70 marks
Choose any two sections
Total = 60 + 2 × 70 = 200 marks
2. Section 1 is a General section and is compulsory.
3. Sections 2 to 5 are subject sections (Biology, Chemistry, Mathematics and Physics).
Choose any two. That is, omit any two of the four subject sections.
4. Carefully read and follow the instructions given in each section.
5. Answers to the questions are to be marked in the Answer Sheet provided.
6. Ensure that you have received Answer Sheet A.
7. Rough work should be done on the sheets provided.
8. Return the Answer Sheet to the invigilator at the end of the examination.
9. Calculators, log tables, cell phones, etc. are not permitted in the examination hall.
Instructions for writing on Answer Sheet
1. Read and follow the instructions given on the Answer Sheet.
2. Write your name, roll number and other required information with ball point pen in the
appropriate boxes provided. Sign your name with ball point pen in the box provided.
3. Your roll number (given on the admit card) must be entered correctly. If
entered wrongly or not entered, the Answer Sheet may not be graded.
4. In the remaining part of Answer Sheet use HB pencil only as instructed. Make
sure that the bubbles are filled properly (as shown in Answer Sheet).
5. Each question has four options. Fill the appropriate bubble(s). Some questions (as
specified in the question paper) have more than one correct option.
6. Ensure that you are filling up the bubbles corresponding to correct sections.
7. Fill in the answers only when you are sure that you do not need to change the answer.
As far as possible, avoid erasing the answer. In case you have to erase the answer, do so
properly so that there is no black spot inside the bubble.
3. Section 1: GENERAL
Marks for Section 1: 60
This section contains 22 questions.
For each question, only one of the 4 options is a correct answer. For questions 1.1 to 1.16,
a correct answer will earn 3 marks. For questions 1.17 to 1.22, a correct answer will earn
2 marks. For this section, a wrong answer or an unattempted question will earn 0 mark.
Read the following passage carefully and answer questions 1.1 to 1.3.
Metabolism and Life
Living systems are open, non-equilibrium systems which continually exchange energy and mat-
ter with their surroundings through the process of metabolism. The metabolic network of a
living organism consists of a large number of pathways. Each pathway consists of a number of
biochemical reactions. The pathways are integrated with/linked to other pathways to various
extents. There are no stand-alone pathways.
A metabolite is a molecule in a metabolic network. A precursor is a metabolite in a pathway
from which other metabolites are synthesised either in a single step or in multiple steps. An
end-product is a metabolite that is at the dead end of a pathway. Some steps of a metabolic
pathway are committed steps for that pathway (i.e., they are not reversible).
Metabolic pathways are regulated. “Repression” is one type of regulatory mechanism where
the synthesis of the enzyme from DNA is inhibited, i.e., no new molecules of the enzyme which
is under inhibition are synthesised. “Feedback inhibition” is another type where the existing
enzyme molecules are prevented from catalysing the reaction.
In the “common feedback inhibition” mechanism, the end-product of a pathway inhibits the
committed step.
A “sequential feedback inhibition” mechanism is seen in branched pathways. In this mecha-
nism, the intermediate before the branch point inhibits the committed step.
In the “cumulative feedback inhibition” mechanism, multiple end-products partially inhibit a
committed step.
1.1 Suppose all the reactions in a unicellular organism have come to equilibrium. This
(A) signals the birth of the organism.
(B) happens when the organism is at rest.
(C) is true at all the times.
(D) leads to death.
Page 3
4. 1.2 P, Q, R, S, T and U are metabolites. Within this set of metabolites, P is the precursor
of all others. T and U are the only end-products. Q is the precursor of R and S. R is
the precursor of T. Both the metabolites T and U partially inhibit the synthesis of Q.
This is an example of
(A) common feedback inhibition.
(B) cumulative feedback inhibition.
(C) repression.
(D) sequential feedback inhibition.
1.3 In its natural environment, a bacterium E. coli can digest lactose by synthesising β-
galactosidase enzyme. If the medium contains minimal lactose, a specific protein binds
to the nearby region of the gene and inhibits enzyme synthesis. This is an example of
(A) common feedback inhibition.
(B) cumulative feedback inhibition.
(C) repression.
(D) sequential feedback inhibition.
Read the following passage carefully and answer questions 1.4 to 1.6.
Blue sky
Lord Rayleigh was the first to explain the colour of the sky. He showed that the sky looks blue
because of scattering of light by air molecules. When light of wavelength λ traverses a dilute
gaseous medium, its intensity gets attenuated (reduced) according to the law
I(x) = I(0)e−αx
where I(x) is the intensity after it has traversed a distance x. The attenuation coefficient α is
given by
α =
32π3
3nλ4
(µ − 1)
where n and µ are the number density and refractive index of the gaseous medium, respectively.
The intensity decreases because the gas molecules scatter away light.
Let us define η to be the ratio of light intensity at the ground to that at the top of the
atmosphere in a given direction: η =
Iground
Itop
. Making suitable approximations for the variation
of the density of atmosphere as a function of height from ground level, this ratio may be
estimated for different colours (say red, green and blue).
Page 4
5. 1.4 The sky looks blue in directions away from the sun mainly because
(A) ηblue 1 whereas η for other colours is much less than 1.
(B) µblue < µred.
(C) αblue > αgreen > αred.
(D) αblue < αgreen < αred.
1.5 The redness of the sun at sunrise/sunset arises because
(A) αred > αgreen > αblue.
(B) ηred > ηgreen > ηblue at sunrise/sunset in the direction of the sun.
(C) ηred < ηgreen < ηblue at sunrise/sunset in the direction of the sun.
(D) ηred = 1 at sunrise/sunset while η for other colours is much less than 1.
1.6 Let β =
ηred
ηblue
. Considering intensity in the direction of the sun at noontime (nt) and
sunrise/sunset (ss), we have
(A) βnt < βss. (B) βnt > βss. (C) βnt = βss = 1. (D) βnt = βss = 1.
1.7 Using numbers from 1 to 6, the number 9 could be obtained as a sum of three numbers
in six ways: 1+2+6, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3 and the number 10 can be
obtained similarly also in six ways: 1+4+5, 1+3+6, 2+4+4, 2+2+6, 2+3+5, 3+3+4.
In a throw of three dice, let p be the probability of getting the sum 9 and q be the
probability of getting 10 be q. Then
(A) p = q = 1
36
(B) p = q = 1
6
(C) p > q (D) p < q
1.8 The bulk energy of a spherical system of radius R is proportional to its volume and the
surface energy is proportional to its area. The surface energy per unit area, σ, and bulk
energy per unit volume, u, of the system are characteristic properties of the system that
are constant at a given temperature and vary with temperature as σ ∝ T1/2
and u ∝ T.
In estimating the total energy the approximation of neglecting the surface energy is best
when
(A) R is large and T is large.
(B) R is large and T is small.
(C) R is small and T is large.
(D) R is small and T is small.
Page 5
6. 1.9 The expression ylogy(xw)
is
(A) 1
xw
(B) x + w (C) xw (D) (xw)y
1.10 Let M be the product of integers from 1 to 50, which has a factor 2n
. The maximum
value of n is
(A) 19. (B) 33. (C) 47. (D) 50.
1.11 The curve shown in the accompanying figure best approximates
y
x
(A) y = log(1 + x) (B) y = tan x (C) y = x4
(D) y = tan−1
x
1.12 A “straight line” between two points on a sphere is defined to be an arc of the great
circle passing through these points. Given two points on the equator on the Earth
(considered as a perfect sphere), one at longitude 0 degree and the other at longitude
180 degrees, the number of “straight lines” passing through these two points is
(A) 1. (B) 2. (C) 4. (D) infinite.
1.13 Three of the following four figures are related to one another by rotation in the plane
of the paper.
P R SQ
The figure that cannot be related to the others by this operation is:
(A) P (B) Q (C) R (D) S
Page 6
7. 1.14 The continued fraction α is defined as α = 1 +
1
1 + 1
1+···
. The value of α is
(A) 2. (B)
√
5
2
. (C)
√
5 + 1
2
. (D)
√
5 − 1
2
.
1.15 The average x and standard deviation σ of marks xi obtained by students in an exam-
ination are defined as x =
1
N i
fixi and σ =
1
N i
fi(xi − x)2, where
i
fi = N
is the total number of students, fi is the number of students having marks xi, and
i
stands for summation. In an examination of 100 students for a 50-mark paper, the
maximum score obtained was 44. Each student was awarded 6 additional marks and the
resulting marks were scaled up to a total of 100 marks for the paper. Then
(A) xnew = 2 xold + 12 and σnew = 2σold
(B) xnew = xold + 12 and σnew = 2σold
(C) xnew = xold + 6 and σnew = σold
(D) xnew = 2 xold + 12 and σnew = σold
1.16 From the net N, as shown here, one can make a cube by making folds at the appropriate
edges of the squares, such that the dots appear on the outside. No cutting is allowed.
N P R SQ
Which of the cubes shown above can be made from the net N?
(A) P (B) Q (C) R (D) S
1.17 Cerenkov radiation is
(A) the light emitted by a charged particle travelling in a medium with a speed
greater than the speed of light in the medium.
(B) the γ-radiation emitted by an excited heavy nucleus coming to its ground state.
(C) the β-radiation emitted by a radioactive element in the actinide series.
(D) the radiation emitted when α-particles emitted by a radioactive source are
stopped by a target.
Page 7
8. 1.18 The British scientist Rosalind Franklin is known for her work on
(A) gene cloning.
(B) the origin of atmospheric electricity.
(C) X-ray diffraction studies of DNA.
(D) super-heavy elements.
1.19 Consider the four vitamins, A, B, C, D and their properties as listed:
1. Water soluble
2. Curing scurvy
3. Preventing rickets
4. Fat soluble
Choose the correct match from the options below.
(A) A-4, B-1, C-3, D-2
(B) A-4, B-1, C-2, D-3
(C) A-1, B-4, C-2, D-3
(D) A-4, B-3, C-2, D-1
1.20 The famous number 1729 (associated with the great Indian mathematician Ramanujan)
has the interesting property that
(A) it is the cube of a prime number.
(B) it is the difference of squares of two prime numbers.
(C) it is the smallest number that can be expressed as sum of cubes of two integers.
(D) it is the smallest number that can be expressed as sum of cubes of two integers
in two different ways.
1.21 While classifying elements, Mendeleev left some blank spaces in his periodic table. He
believed these elements to exist. He named one such element as ekasilicon and predicted
its properties. The element was discovered later and is now known as
(A) gallium. (B) germanium. (C) scandium. (D) titanium.
1.22 The clue to possible existence of water on the moon from the Chandrayaan-1 mission
came from
(A) spectroscopic studies.
(B) heat-sensing devices.
(C) acoustic interferometry.
(D) chemical analysis.
Page 8
9. Section 2: BIOLOGY
Marks for Section 2: 70
This section contains 20 questions.
For questions 2.1 to 2.15 only one of the 4 options is correct. A correct answer will
earn 3 marks, a wrong answer will earn (−1) mark, and an unattempted question will earn
0 mark.
2.1 Enzymes are biocatalysts that catalyse reactions at very high rates compared to chemical
catalysts. They are specific to the substrate and reaction they catalyse. A few statements
about enzymes are made below:
(i) Not every enzyme is proteinacious in nature.
(ii) Some RNAs also are enzymes.
(iii) The active site of the enzyme is complementary to the transition state.
(iv) Enzymes alter the equilibrium constant of the reaction.
(v) Enzymes catalyse only irreversible reactions.
Which of the above statements are true?
(A) (i), (ii), and (iii).
(B) (ii), (iii), and (iv).
(C) (iii), (iv), and (v).
(D) (i), (ii), and (v).
2.2 An mRNA ready for translation would have
(A) introns, coding exons and non-coding exons.
(B) coding exons and non-coding exons.
(C) only coding exons.
(D) only coding exons and introns.
2.3 During oogenesis in mammals, the second meiotic division occurs
(A) during the formation of primary oocyte.
(B) before ovulation.
(C) after fertilisation.
(D) after implantation.
Page 9
10. 2.4 The Kyoto Protocol specifies regulations on the emission of greenhouse gases. It defines
a term known as “Carbon-Credits”. The following statements pertain to Carbon-Credits:
(i) The mandatory limit of Carbon-Credit for each country is directly proportional to
its size and population.
(ii) One Carbon-Credit defines the emission of one ton of carbon dioxide or equivalent
gases responsible for greenhouse effect.
(iii) Carbon-credits are exchangeable among countries/industries.
(iv) An industry emitting higher than prescribed limit can do so by purchasing Carbon-
Credits.
Which of the above statements are true?
(A) (i) and (ii) only.
(B) (ii) and (iv) only.
(C) (ii), (iii), and (iv) only.
(D) (i), (ii), and (iv) only.
2.5 Which of the following techniques were used by Messelson and Stahl to show that DNA
replication is semi-conservative?
(i) Growing E. coli in defined synthetic medium.
(ii) Use of [3
H]-thymidine and analysis of the products by autoradiography.
(iii) Use of heavy nitrogen and analysis of the products by equilibrium density gradient
centrifugation.
(A) (i) and (ii) only.
(B) (i) and (iii) only.
(C) (ii) and (iii) only.
(D) (i), (ii), and (iii).
2.6 Hormones are regulatory molecules secreted by the endocrine systems in vertebrates.
Which of the following statements is NOT TRUE for hormones?
(A) Hormones are secreted into the blood circulation system and they act on target
organs.
(B) Amino acids are precursors for some hormones.
(C) Hormones can act on the organ that secretes them.
(D) Hormones are always short-lived molecules.
Page 10
11. 2.7 Single locus probe DNA fingerprinting was done for a father and his four children. The
resultant gel electrophoretic pattern is shown below.
Which lanes contain the DNA of the children?
(A) 1, 2, 3, and 4.
(B) 2, 3, 4, and 5.
(C) 1, 2, 4, and 5.
(D) 1, 2, 3, and 5.
2.8 When the lipid content of leaves from two plants was analysed, it was found that the
thylakoid membranes of plant P1 had much more percentage of unsaturated fatty acids
compared to plant P2. What can be deduced from this observation?
(A) P1 is less likely to show low-temperature photoinhibition compared to P2.
(B) P1 will perform photosynthesis at much higher rates compared to P2.
(C) P2 will perform photosynthesis even at very low light intensities compared to
P1.
(D) P2 will perform photosynthesis at very low partial pressures of CO2 compared
to P1.
2.9 In an experiment, mature leaves on the plant were enclosed for a fixed amount of time
in a transparent bag that had radioactive CO2. In which part of the plant will maximum
radioactivity be found after some time?
(A) Actively growing leaves.
(B) Guard cells of all the leaves.
(C) In mature leaves.
(D) Senescing leaves and roots.
Page 11
12. 2.10 The major difference between the mosses and ferns is:
(A) Ferns lack alternation of generation while mosses show the same.
(B) Mosses are facultative aerobes whiles ferns are obligate aerobes.
(C) Vascular bundles of ferns show xylem vessels while those of mosses lack it.
(D) Sporophytes of ferns live much longer as compared to the sporophytes of
mosses.
2.11 The basal metabolic rate (BMR) of a mammal is greatly influenced by its surface area
to volume ratio and environmental temperature. Which graph correctly depicts this
relationship?
(A)
(mLO2/hr)
BMR
Body Mass
(B)
BMR
Body Mass
(mLO2/gm/hr)
(C)
(mLO2/hr)
BMR
Environmental
temperature
(D)
(mLO2/gm/hr)
BMR
Environmental
temperature
2.12 Microbes “GE” and “OG” are facultative aerobes. Their doubling time is comparable
to each other. When grown together, they do not affect the growth of each other. GE
can utilise either glucose or ethanol as carbon source. OG can use only glucose as carbon
source.
An inoculum containing equal number of GE and OG were grown together with glucose
as the sole source of carbon. After a certain duration, only GE was present and not OG.
The reason for this is that culture was grown under
(A) aerobic condition throughout.
(B) anaerobic condition throughout.
(C) anaerobic condition initially and then under aerobic condition.
(D) aerobic condition initially and then under anaerobic condition.
2.13 Lipid molecules have a polar headgroup and one or two hydrophobic tails. A variety
of lipid assemblies are known: they can be lamellar (layer-like) or spherical and they can
be monolayered or bilayered. A lipid molecule has one hydrophobic tail of length l nm.
Suppose that l << a, where a nm2
is the surface area of the headgroup. In an aqueous
medium, molecules of such a lipid assemble to form
(A) monolayered lamellar structures.
(B) monolayered spherical structures.
(C) bilayered lamellar structures.
(D) bilayered spherical structures.
Page 12
13. 2.14 Hemoglobin (Hb) transports oxygen from lungs to tissues. The partial pressure of
oxygen in lungs is different from that in tissues. Each Hb can bind to up to four oxygen
molecules. Suppose we have an equal number of Hb and oxygen molecules and all the
oxygen molecules are in bound form. Then, which of the following is TRUE?
(A) Almost all the Hb molecules have one bound oxygen molecule.
(B) Nearly half of all the Hb molecules are each bound to two oxygen molecules.
(C) Nearly one-fourth of all the Hb molecules are bound to four oxygen molecules
each.
(D) Most of the Hb molecules have one bound oxygen molecule each; the rest either
have no bound oxygen or have two or more bound oxygen molecules.
2.15 Dr. Venkataraman Ramakrishnan is one of the three recipients of the 2009 Nobel Prize
for Chemistry. He worked towards the elucidation of the three-dimensional structure of
ribosomes. Ribosomes are involved in the biosynthesis of proteins and
(A) one of their protein components is the catalyst.
(B) one of their RNA components is the catalyst.
(C) they bind to DNA for the purpose of protein synthesis.
(D) they bind either to tRNA or to mRNA at any given time.
For questions 2.16 to 2.20 one or more than one of the 4 options may be correct. Your
answer is regarded correct only if you choose all the correct option(s) and no incor-
rect option(s). A correct answer will earn 5 marks, a wrong answer or an unattempted
question will earn 0 mark.
2.16 Experiments 1, 2, and 3 were conducted wherein synthetic vesicles containing Fo-F1
ATP synthase were prepared and incubated overnight in a tube. Subsequently, the
vesicles were transferred to another tube which also contained ADP and Pi (inorganic
phosphate).
Page 13
14. Which of the following statements is/are true for the above experiments?
(A) A proton gradient across the vesicular membrane will be present in both ex-
periments 1 and 2 at the time of transfer.
(B) As a consequence of the proton gradient, ATP will be synthesised in both
experiments 1 and 2.
(C) ATP will be synthesised in experiment 3 because Fo-F1 ATP synthase has the
inherent property to catalyse the synthesis of ATP from ADP and Pi.
(D) ATP will be synthesised in experiment 2 because the proton has to flow out
of the vesicles through the Fo-F1 ATP synthase for ATP synthesis.
2.17 Blood osmolalities and the adaptable ranges of environmental salinities of two types
of animals are shown in the graph below.
600
800
400
200
(mOsm/kg)
BloodOsmolality
20 40 60 80 100
I
II
Sea Water (%)
Mark the correct descriptions of these animals.
(A) Type I animals maintain more or less stable internal osmolality by physiological
means.
(B) Type II animals maintain blood osmolality within narrow physiological ranges
under different salinity conditions.
(C) Type I animals are not likely to be found in estuaries or river mouths where
fresh and salt water meet and the salinity fluctuates greatly.
(D) Type II animals gain and lose water at equal rates and have no need to expend
energy expelling water or salt from the body.
Page 14
15. 2.18 Troglobites are animals that spend their entire life in a very stable, unchanging cave
environment. Which of the following adaptations will be seen in these animals?
(A) detrivory or carnivory.
(B) loss of pigmentation.
(C) reduced antennae.
(D) reduced photoreceptors.
2.19 The DNA content of individual cells and the number of cells in each phase of a “cell
cycle” can be determined using flow cytometry. Which of the following combinations of
“phase of a cell cycle and its corresponding DNA content” can be considered normal?
(A) Diploid cells found in the G0 or G1 phase.
(B) Cells with twice the normal DNA content in the early M phase.
(C) Cells with intermediate amounts of DNA in the S phase.
(D) Cells with twice the normal DNA content in the G2 phase.
2.20 The regions of the lac-operon system of E. coli which contain the repressor gene (I),
operator (O), and the structural gene (Z) for β-galactosidase are denoted by the symbols
a, b, and c, but it is not known which symbol represents which region.
The following genotypes of E. coli for the lac-operon were generated. The activity of the
enzyme β-galactosidase was measured separately in the absence and in the presence of
the inducer. The activity of the enzyme β-galactosidase is shown by the symbol (++)
and the absence of the activity is shown by the symbol (−−).
Note that the order in which the symbols are written in the table is not necessarily the
actual sequence in which they occur in the lac-operon. The symbols (+) and (−) written
as superscript on a, b and c represent the wild type and mutant phenotypes, respectively.
Genotype Inducer absent Inducer present
a+
b+
c+
−− ++
a−
b−
c−
−− −−
a−
b+
c+
++ ++
a+
b+
c−
++ ++
a+
b−
c−
−− −−
Which of the following statements is/are correct for the above experiment?
(A) The genotypes a−
b+
c−
and a+
b−
c−
are likely to produce similar results.
(B) Mutations in the region a or c make the lac-operon constitutively expressed.
(C) The symbol b represents the region containing the lac Z gene.
(D) Whether region a contains the lac I or lac O gene cannot be inferred from
these data.
Page 15
16. Section 3: CHEMISTRY
Marks for Section 3: 70
This section contains 20 questions.
For questions 3.1 to 3.15 only one of the 4 options is correct. A correct answer will
earn 3 marks, a wrong answer will earn (−1) mark, and an unattempted question will earn
0 mark.
3.1 The molecular orbital diagram of carbide ion (C2−
2 ) would show the following molecular
orbital occupancy.
(A) σ1s2
σ∗
1s2
σ2s2
σ∗
2s2
π2p4
(B) σ1s2
σ∗
1s2
σ2s2
σ∗
2s2
π2p4
σ2p2
(C) σ1s2
σ∗
1s2
σ2s2
σ∗
2s2
π2p2
σ2p2
π∗
2p2
(D) σ1s2
σ∗
1s2
σ2s2
σ∗
2s2
π2p3
σ2p3
3.2 The activation energies of two reactions are Ea and Ea with Ea > Ea. If the temper-
ature of the reaction systems is increased from T1 to T2, predict which of the following
alternatives is correct for the corresponding rate constants (k) (k1, k1 at T1 and k2, k2
at T2).
(A) k1/k1 = k2/k2
(B) k1/k1 = 2k2/k2
(C) k1/k1 < k2/k2
(D) k1/k1 > k2/k2
3.3 The alcohol that is chiral and can react with acidified dichromate under controlled
conditions to give an aldehyde is
(A) 2-ethyl-1-butanol
(B) 2-pentanol
(C) 2-methyl-1-butanol
(D) 2,2-dimethyl-1-butanol
3.4 Equal volumes of 1.0 M KCl (aq) and 1.0 M AgNO3 (aq) solutions are mixed. The
depression of freezing point of the resulting solution (with respect to water) will be
(assume Kf for water = 1.86 K kg mol−1
and Molarity ≈ Molality)
(A) 1.86 K (B) 3.72 K (C) 0.93 K (D) 7.44 K
Page 16
17. 3.5 Which of the following compounds is the strongest Bronsted base?
(A) NaOH (B) NaF (C) NaCH3 (D) NaNH2
3.6 The standard electrode potentials for the following redox couples are given as:
E0(Fe2+
/Fe) = x V, E0(Fe3+
/Fe2+
) = y V.
The potential E0(Fe3+
/Fe) (in V) will be
(A) (2x + y) (B) (x + y) (C) (x + 2y)/3 (D) (2x + y)/3
3.7 The reaction of 2,4-hexadiene with one equivalent of bromine at 0◦
C gives a mixture of
two compounds X and Y. X is 4,5-dibromo-2-hexene. Y is
(A) 3,4-dibromohexane
(B) 2,5-dibromo-3-hexene
(C) 2,2-dibromo-4-hexene
(D) 1,5-dibromo-3-hexene
3.8 For the compound X shown below, the number of asymmetric centres, and optical
property are
000000
0000000000000000000000
00000000
111111
1111111111111111111111
11111111
Br
Br
CH
CH
3
3
X
(A) 2, optically active.
(B) 2, optically inactive.
(C) 3, optically active.
(D) 3, optically inactive.
3.9 The correct order of decreasing atomic radii is
(A) Rb > Cs > Na > F > Cl
(B) Cs > Rb > Na > I > Cl
(C) Cs > I > Rb > Cl > Na
(D) I > Cl > F > Cs > Rb
Page 17
18. 3.10 The electron in H atom-like species makes a transition from an excited state to the
ground state. In this process, its
(A) kinetic and total energies decrease but potential energy increases.
(B) kinetic energy decreases whereas the potential and total energies remain the
same.
(C) kinetic energy increases but potential and total energies decrease.
(D) kinetic, potential and total energies decrease.
3.11 For the four compounds P, Q, R, and S, shown below, the appropriate relationship is
O
OO
OO
O
O O
P Q R S
OH
(A) P and Q are tautomers.
(B) P and R are tautomers.
(C) P and S are isomers.
(D) Q and R are resonance structures.
3.12 A certain compound X is shown below:
OH
X
On heating with conc. H2SO4, it gives mainly
(A) (B) (C) (D)
Page 18
19. 3.13 The species having tetrahedral shape is
(A) [PdCl4]2−
(B) [Ni(CN)4]2−
(C) [Pd(CN)4]2−
(D) [NiCl4]2−
3.14 MgSO4, on reaction with NH4OH and Na2HPO4, forms a white crystalline precipitate.
The precipitate is
(A) Mg(NH4)PO4 (B) Mg3(PO4)2 (C) Mg(OH)2 (D) MgHPO4
3.15 The ratio of molar heat capacities at constant pressure (Cp) and at constant volume
(Cv) of nitrogen gas at ordinary temperatures is close to
(A) 11/9 (B) 9/7 (C) 7/5 (D) 5/3
For questions 3.16 to 3.20 one or more than one of the 4 options may be correct. Your
answer is regarded correct only if you choose all the correct option(s) and no incor-
rect option(s). A correct answer will earn 5 marks, a wrong answer or an unattempted
question will earn 0 mark.
3.16 The compound(s) which will be oxidised by O3 is/are
(A) KI (B) FeSO4 (C) KMnO4 (D) K2MnO4
3.17 For the cyclic process considered below, which of the following relations is/are correct?
1 2
Reversible
Irreversible
(A) ∆S = S2 − S1 =
2
1
dqrev
T
(B) ∆S = S1 − S2 =
1
2
dqirr
T
(C) ∆Scycle = 0 =
2
1
dqrev
T
+
1
2
dqirr
T
(D) ∆Scycle = 0 >
2
1
dqrev
T
+
1
2
dqirr
T
3.18 Amongst the following, the species having one unpaired electron is/are
(A) BN (B) O−
2 (C) F−
2 (D) XeF
Page 19
20. 3.19 The compounds P, Q, R, and S, shown below, are commercially very important.
C OH
P Q R S
CH2OH
CH2OH
HOCH2
CH2OH
CH2OH OCH3
C OH
P Q R S
CH2OH
CH2OH
HOCH2
CH2OH
CH2OH OCH3
Which of the following statements is/are true regarding the synthesis of these com-
pounds?
(A) P can be prepared by the reaction of acetaldehyde and formaldehyde in the
presence of an alkali.
(B) Q can be prepared from acetaldehyde alone through a series of reactions.
(C) R is formed when a mixture of benzaldehyde and formaldehyde is treated with
an alkali.
(D) S is formed when phenol is reacted with formaldehyde in the presence of HBF4.
3.20 Consider the sequence of reactions shown below.
O (C8H14) (C8
H14
)
Excess HI
Heat
X
alcohol
KOH, Heat
Y
Heat
Z
Which of the following statements is/are true?
(A) X is 5-iodo-2,4-dimethylhexan-1-ol.
(B) Y on reaction with chlorine gives a tetrachloro derivative.
(C) X is a diiodo compound.
(D) Z is 2,4-dimethyl-1,3-hexadiene.
Page 20
21. Section 4: MATHEMATICS
Marks for Section 4: 70
This section contains 20 questions.
For questions 4.1 to 4.15 only one of the 4 options is correct. A correct answer will
earn 3 marks, a wrong answer will earn (−1) mark, and an unattempted question will earn
0 mark.
4.1 If a, b, c, d are positive real numbers such that a+b+c+d = 2, then λ = (1+a+b)(1+c+d)
satisfies
(A) 2 < λ ≤ 3 (B) 3 < λ ≤ 4 (C) 4 < λ ≤ 5 (D) 5 < λ ≤ 6
4.2 In an ellipse, the ratio of the area of the rectangle formed by the end points of its each
latus rectum to that of the ellipse is 1/π. The eccentricity of the ellipse is
(A)
1
√
2
(B)
1
2
(C)
2 ±
√
3
4
(D)
√
3 ± 1
2
√
2
4.3 When all possible four-member committees were formed from a set of people, it was
found that exactly 1/20-th of the committees contained the same two members. The
number of persons in the set was
(A) 20 (B) 17 (C) 16 (D) 15
4.4 The value of the integral
∞
0
5
(x2 + 4)(x2 + 9)
dx
is
(A) π (B)
π
12
(C)
π
6
(D)
π
4
4.5 If sin α sin 2α sin 3α sin 4α is written as a polynomial in sin2
α, the sum of the coefficients
of the polynomial is
(A) 0 (B) 1 (C) −1 (D) 4
4.6 If X and Y are two singular matrices such that XY = Y and Y X = X, then X2
+ Y 2
equals
(A) X + Y (B) XY (C) Y X (D) 2(X + Y )
Page 21
22. 4.7 Let ABCD be a rectangle and a semicircle be drawn with AB as the diameter, externally
to the rectangle. If the perimeter of the figure so obtained is a constant p and the figure
has the maximum possible area, then the ratio of the area of the rectangular portion to
the area of the rest of the figure is
(A) 2 : π (B) π : 2 (C) π : 4 (D) 4 : π
4.8 Let a, b be positive real numbers such that 10 < a < b. Then the number of positive
integers b such that (i) 10, a, b are in geometric progression, and (ii) 10, a, b form the
sides of a triangle is
(A) 15 (B) 16 (C) 17 (D) 26
4.9 The set {z ∈ C : |z + 1| = |z − 1|} is
(A) a circle.
(B) an ellipse.
(C) the imaginary axis.
(D) the empty set.
4.10 Let A, B be points of intersection of the ellipse
x2
36
+
y2
25
= 1 and the parabola y2
= 20x.
The area bounded by the parabola and the line AB lies in the interval
(A) (6, 7) (B) (7, 8) (C) (8, 9) (D) (9, ∞)
4.11 Let f(x), g(x), h(x) be real non-constant polynomials such that
f g(x) = g(x)h(x),
g h(x) = h(x)f(x),
h f(x) = f(x)g(x).
The sum of the degrees of the polynomials f(x), g(x), h(x) is
(A) 6 (B) 9 (C) 12 (D) not determinable.
4.12 lim
x→0
1
x2
x
0
tdt
t4 + 1
is equal to
(A) 0
(B) 1
(C) 1
2
(D) does not exist.
Page 22
23. 4.13 If ω is an imaginary cube root of unity then the system of linear equations
2x + 2ωy − ω2
z = 0
x + y + z = 0
x − y = 0
(A) has only the trivial solution: (x, y, z) = (0, 0, 0).
(B) has only one non-trivial solution.
(C) has infinitely many non-trivial solutions.
(D) has no solution at all.
4.14 The coefficient of x100
in
(1 + x)100
(1 − x101
)
(1 − x)
is
(A) 1
(B) 200
(C) 100
C2
(D) 2100
4.15 The image of the function tan−1
(2x2
) is
(A) [0,
π
2
)
(B) (−
π
2
,
π
2
)
(C) [0,
π
2
]
(D) (0,
π
2
)
For questions 4.16 to 4.20 one or more than one of the 4 options may be correct. Your
answer is regarded correct only if you choose all the correct option(s) and no incor-
rect option(s). A correct answer will earn 5 marks, a wrong answer or an unattempted
question will earn 0 mark.
4.16 Let f(x) = min{x, x2
}, where x belongs to R. The function f(x) is
(A) continuous everywhere.
(B) continuous except 0 and 1.
(C) differentiable everywhere.
(D) differentiable everywhere except 0 and 1.
Page 23
24. 4.17 Let f(x, y) = x2
− axy + y2
be a quadratic polynomial in real variables x, y, a being a
real constant. Then
(A) f(x, y) is nonnegative for all real values of x and y, if −1 ≤ a ≤ 1.
(B) there are real values of a outside the interval [−1, 1] for which f(x, y) is again
nonnegative for all real values of x and y.
(C) the graph of f(x, y) = 0 is a single point in the xy-plane, when a = 1.
(D) the graph of f(x, y) = c is a circle, ellipse or a hyperbola but never a pair of
lines for any given real numbers a and c, where c is positive.
4.18 Let ABC be an acute-angled triangle; L, M, N be the feet of perpendiculars respec-
tively from A, B, C to the opposite sides; D, E, F be the midpoints of the sides BC,
CA, AB respectively; and I1, I2 I3 be the ex-centres of triangle ABC. Then
(A) the ortho-centre of triangle ABC is the in-centre of triangle LMN.
(B) The circum-centre of triangle ABC is the ortho-centre of triangle DEF.
(C) The in-centre of triangle ABC is the ortho-centre of triangle I1I2I3.
(D) the centroid of triangle ABC is the centroid of triangle DEF.
4.19 Consider the second order ordinary differential equation: y − y = 0. Then
(A) there is a non-zero solution of the equation which is bounded on R.
(B) any solution of this equation may be represented by y = aex
+ be−x
, where a
and b are two suitable constants.
(C) any solution of this equation may also be represented by y = a cosh x + be−x
,
where a and b are two suitable constants.
(D) there are infinitely many solution curves y = aex
+be−x
, passing through (0,0)
in the xy-plane.
4.20 If v1, v2, v3 are unit vectors given by
v1 = ai + bj + ck
v2 = bi + cj + ak
v3 = ci + aj + bk,
where a, b, c are nonnegative real numbers, and vα · vβ = 0, for α = β, then
(A) |[v1, v2, v3]| = 1
(B) a + b + c = 1
(C) v1 + v2 + v3 = 0
(D) v1, v2, v3 are coplanar.
Page 24
25. Section 5: PHYSICS
Marks for Section 5: 70
This section contains 20 questions.
For questions 5.1 to 5.15 only one of the 4 options is correct. A correct answer will
earn 3 marks, a wrong answer will earn (−1) mark, and an unattempted question will earn
0 mark.
5.1 A car of mass m, moving to the right, collides elastically with a truck of mass 3m moving
to the left with equal speed. The collision is head-on. After the collision
(A) the car comes to a stop and the truck moves to the right.
(B) both the car and the truck move to the left.
(C) both the car and the truck come to a stop.
(D) the truck comes to a stop and the car moves to the left.
5.2 A non-conducting sphere of radius R has a positive charge Q uniformly distributed over
its entire volume. A smaller, concentric, spherical volume of radius r (r < R) is scooped
out of the sphere. The magnitude of the electric field E at a point inside the body at a
distance x from the centre (r < x < R) is (K = 1/(4π 0) = constant):
(A)
KQ
x2
(B)
KQ
x2
r3
R3
(C)
KQ
x2
x3
− r3
R3
(D) 0
5.3 Unpolarised light of intensity I falls on a polaroid. The emerging light is passed through
another polaroid whose axis makes an angle of 30◦
with respect to the first one. The
final emergent light has an intensity of
(A) 3I/4 (B) 3I/8 (C) I/8 (D) I/2
5.4 A parallel-plate capacitor is formed with plates of area A, and separation between the
plates d. A second parallel-plate capacitor has plates of area A and separation d/2. The
two capacitors are connected in series. The resultant capacitance is:
(A)
0A
d
(B) 2
0A
d
(C)
3
2
0A
d
(D)
2
3
0A
d
Page 25
26. 5.5 We want to determine the value of Planck’s constant, h, by doing an experiment using
the photoelectric effect. This experiment is performed by varying both the frequency
of the incident light as well as its intensity, and measuring both the voltage and the
current. In order to calculate h, it would be best to plot
(A) current as a function of frequency.
(B) current as a function of intensity.
(C) stopping potential as a function of intensity.
(D) stopping potential as a function of frequency.
5.6 A block is placed on a rough inclined plane. The angle of the incline, θ, is slowly
increased, starting from the horizontal position. At a certain angle, the block starts to
slide along the plane. The angle of the incline is increased further.
θ
Consider the following graphs:
(I) (II)
(III) (IV)
Which of the above graphs correctly depicts the variation of the frictional force, f,
exerted by the plane on the block, as a function of θ? (Assume that the block does not
topple.)
(A) (I) (B) (II) (C) (III) (D) (IV)
5.7 In a repeat of one of Michael Faraday’s classic experiments, a solenoid of length 10 cm
with 200 turns and radius 1 cm is surrounded by another solenoid of the same length,
but with 400 turns and radius 2 cm. The two solenoids are not in contact. A current
is switched on through the inner solenoid. Suppose that the current increases at the
rate of 100 A s−1
during the switch-on. What is the emf induced in the outer solenoid?
(Assume that a current carrying solenoid has no magnetic field outside it.)
(A) Zero (B) 31.6 mV (C) 126.4 mV (D) 316 mV
Page 26
27. 5.8 A shaft is rotating at a speed of 4000 revolutions per minute. If the power expended in
driving the shaft is 12 kW, the magnitude of the driving torque is:
(A) 90/π N m (B) 90 N m (C) 180 N m (D) 36/π N m
5.9 An ideal gas undergoes a cyclic process 1 → 2 → 3 → 4 depicted on the P–V diagram,
where the processes 1 → 2 and 3 → 4 are isobaric, and 2 → 3 and 4 → 1 are adiabatic.
(0,0)
2
V
4 3
1
P
Consider the following diagrams on the V –T plane.
(I)
2
4
3
1
(0,0) T
V
(II)
1
4
3
2
(0,0) T
V
(III)
1
3
2
4
(0,0) T
V
(IV)
1
3
2
4
(0,0) T
V
The correct representation of the cycle is given by the graph
(A) (I) (B) (II) (C) (III) (D) (IV)
5.10 An astronomical telescope has an objective of focal length 100 cm and a diameter D.
The eyepiece has a focal length of 2.5 cm and the eye is held close to the eyepiece for
viewing. Let M1 be the magnifying power when the telescope is in normal adjustment
(i.e., final image is at infinity), and M2 be the magnifying power when the final image
is at the least distance of distinct vision (25 cm). Then
(A) M1 = M2.
(B) M1 is slightly greater than M2.
(C) M1 is slightly less than M2.
(D) The ratio M1/M2 depends on D.
Page 27
28. 5.11 The wall of a concert hall consists of a uniform brick wall of thickness 25 cm on the
outside. On the inside, it is completely covered with a uniform wooden layer of thickness
5 cm. The thermal conductivities of brick and wood are, respectively, 0.60 Wm−1
K−1
and
0.06 Wm−1
K−1
. The thermal conductivity of the composite wall of the hall is
(A) 0.51 Wm−1
K−1
(B) 0.24 Wm−1
K−1
(C) 0.33 Wm−1
K−1
(D) 0.15 Wm−1
K−1
5.12 Assume that the battery in your mobile phone can be treated as a simple capacitor
that stores charge, and discharges when you use the phone. Suppose you start to charge
a completely discharged phone and it takes 100 minutes to charge it to half its full
capacity. How long more will you have to charge it to reach 3/4th its full capacity?
(A) 25 minutes (B) 50 minutes (C) 100 minutes (D) 200 minutes
5.13 In the tube shown below, the wider part has cross-sectional area A, and the narrower
part has cross-sectional area A/3. When water inside the tube is at rest, the vertical
manometers show the same height of water, as shown.
0000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
0000000000000000
1111111111111111
11111111111111111111111111111111
11111111111111111111111111111111
11111111111111111111111111111111
11111111111111111111111111111111
11111111111111111111111111111111
1111111111111111
When water is made to flow steadily through the tube, the difference in heights of water
in the two manometers is 40 cm. Neglecting viscosity effects, the speed of water flow in
the narrower part of the tube is (taking g = 10 m s−2
)
(A) 1 m s−1
(B) 0.5 m s−1
(C) 2 m s−1
(D) 3 m s−1
5.14 Electrons accelerated in an X-ray tube strike a nickel target (ZNi = 28) and come
to rest. The resulting continuous X-ray spectrum has a minimum wavelength given by
λmin = 3.0×10−11
m. If the nickel target is replaced by a molybdenum target (ZMo = 42),
the minimum wavelength will be
(A) 3.0 × 10−11
m.
(B) 2.0 × 10−11
m.
(C) 4.5 × 10−11
m.
(D) 6.8 × 10−11
m.
Page 28
29. 5.15 An excited state of doubly ionised Lithium (Li2+
) has an orbital radius that is about
1.33 times that of the ground state of hydrogen (H) (in Bohr’s theory). The ratio of
energy of the two states, E(Li2+
)/E(H), is
(A) 2.25 (B) 4.5 (C) 1 (D) 9
For questions 5.16 to 5.20 one or more than one of the 4 options may be correct. Your
answer is regarded correct only if you choose all the correct option(s) and no incor-
rect option(s). A correct answer will earn 5 marks, a wrong answer or an unattempted
question will earn 0 mark.
5.16 A machine gun mounted on a stationary vehicle fires bullets at a fixed target at the
speed of 100 m s−1
. The sound waves produced by the firing travel at the speed of
330 m s−1
. The vehicle now moves toward the target with a speed of 20 m s−1
. Which of
the following statements is/are true?
(A) The fractional change in frequency (δν/ν) of the sound of firing coming from
the moving vehicle, as measured by a stationary ground observer, is approxi-
mately 2/33.
(B) For a stationary ground observer, the speed of sound from the moving vehicle
is 350 m s−1
and that of the bullets is 120 m s−1
.
(C) An echo is heard when the sound waves are reflected by the target. For a
ground observer stationed close to the target, the intensity of echo is more
than the intensity of sound received directly from the machine gun.
(D) Suppose the vehicle now stops and the observer moves towards the vehicle at
the speed of 20 m s−1
. In this case the moving observer will find the wavelength
of the sound of firing to be the same as when both he and the vehicle were at
rest.
5.17 A solid sphere and a solid cylinder, both of mass M and radius R, are released from
rest at the same height on an inclined plane. Both roll down the plane without slipping.
Which of the following statements is/are true?
(A) The moment of inertia of the rolling sphere is greater than the moment of
inertia of the rolling cylinder.
(B) The frictional force on the cylinder is greater than that on the sphere.
(C) The sphere will reach the bottom before the cylinder.
(D) When the two objects reach the bottom, the speed of the cylinder will be
greater than that of the sphere.
Page 29
30. 5.18 An electron moving in the positive x-direction, enters a region that has a constant
electric field pointing in the positive y-direction, and a constant magnetic field pointing
in the positive z-direction. Then, which of the following statements is/are true?
(A) The electron will be undeflected and travel in a straight line.
(B) The net work done on the electron is zero.
(C) The velocity component of the electron in the negative y-direction will increase
continuously.
(D) The electron will be confined in the xy-plane.
5.19 Consider positron (e+
) emission from a nucleus at rest:
A
ZX → A
Z−1Y + e+
+ ν
Which of the following statements is/are correct?
(A) The emitted e+
has a continuous energy spectrum since the energy released in
the decay is shared by e+
and ν.
(B) If there there was no additional particle ν emitted in the decay, the energy of
the emitted e+
would be always equal to (MX −MY)c2
, if the recoil energy of Y
is neglected. (MX and MY are rest masses of the nuclei X and Y, respectively,
and c is the speed of light in vacuum.)
(C) The emitted neutrino (ν) always has non-relativistic speed (i.e., speed much
less than c) due to its very small rest mass.
(D) Consider the competing process to the positron emission, in which an electron
(e−
) from an inner orbit of the atom (K shell) is captured by the nucleus and
a neutrino is emitted.
e−
+A
Z X → A
Z−1Y + ν
This process is energetically allowed if e+
emission process is energetically
allowed. (“Energetically allowed” means “allowed by the principle of conser-
vation of energy and linear momentum”.)
5.20 One mole of Helium gas (assumed ideal) is subjected to a process such that PT−2
remains constant in the process, where P and T represent its pressure and volume,
respectively. Which of the following statements is/are true?
(A) The heat capacity of the gas in this process is R/2.
(B) If the temperature of the gas is doubled in the process, the entropy of the gas
changes by 0.5R ln 2.
(C) In this process, work of an amount R∆T is done on the gas, where ∆T =
Tfinal − Tinitial.
(D) This process is represented by a straight line in the V –T diagram.
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