This document provides instructions for a test being administered by Sri Chaitanya IIT Academy in India. The test is 3 hours long and contains 90 questions in Mathematics, Physics, and Chemistry worth a total of 360 marks. Candidates will receive 4 marks for each correct answer and lose 1/4 marks for incorrect answers, with no penalty for unanswered questions. Only one answer per question is allowed. Calculators and other materials are prohibited during the test.
The document contains 14 math word problems involving fractions, percentages, ratios, time/work problems, and other quantitative reasoning questions. It provides the questions, possible multiple choice answers, and in some cases hints or step-by-step solutions to arrive at the answers. The problems cover a range of basic math skills and concepts commonly assessed on standardized tests.
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
−3
3
−2
3
3
+ + ( −3) 2 ⋅ − + ( −3) −3
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1) The document contains 8 math expressions to solve. It provides the solutions and steps to solving each one. 2) The expressions involve fractions, exponents, addition, subtraction, multiplication, and division. 3) The solutions simplify the expressions and calculate the final numeric value or fraction.
1. The document contains 17 multiple choice questions related to numbers and arithmetic concepts.
2. It tests skills such as comparing and ordering fractions, solving word problems involving ratios and remainders, and performing arithmetic operations.
3. The questions have answer options ranging from simple calculations to multi-step word problems requiring setup and solution of equations.
This document contains step-by-step workings and solutions to various problems involving surds and indices. It shows calculations to simplify surd expressions, rationalize denominators, determine which of two expressions is greater, and other algebraic manipulations with surds and rational numbers. The document serves as an example of how to work through different types of surd and index problems systematically.
The document contains solutions to permutation and combination problems. It lists the number of total outcomes for rolling a dice n times as 6n, and the number of total outcomes for tossing a coin (n-1) times as 2n-1. It then works through additional problems calculating permutations, combinations, and compound probabilities.
This document provides the key and solutions to questions from the AIEEE 2012 B.Tech exam for the mathematics section. It contains 19 multiple choice questions related to topics in mathematics like trigonometry, calculus, sequences and series, probability, and functions. Each question is followed by the answer and a brief explanation of the solution steps. The document is intended to help students understand the concepts tested in the exam and check their work.
This document contains 10 multiple choice questions covering various math and statistics topics, including functions, geometry, probability, percentages, sequences, trigonometry, ellipses, and bank interest. It also contains 5 more difficult problems involving arithmetic sequences, trigonometric equations, modeling bacterial growth, finding distances on an ellipse, and comparing interest earned at different banks over 10 years. The questions range from easy to more challenging high school level math.
The document contains 14 math word problems involving fractions, percentages, ratios, time/work problems, and other quantitative reasoning questions. It provides the questions, possible multiple choice answers, and in some cases hints or step-by-step solutions to arrive at the answers. The problems cover a range of basic math skills and concepts commonly assessed on standardized tests.
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
−3
3
−2
3
3
+ + ( −3) 2 ⋅ − + ( −3) −3
3 6
2
Se
1) The document contains 8 math expressions to solve. It provides the solutions and steps to solving each one. 2) The expressions involve fractions, exponents, addition, subtraction, multiplication, and division. 3) The solutions simplify the expressions and calculate the final numeric value or fraction.
1. The document contains 17 multiple choice questions related to numbers and arithmetic concepts.
2. It tests skills such as comparing and ordering fractions, solving word problems involving ratios and remainders, and performing arithmetic operations.
3. The questions have answer options ranging from simple calculations to multi-step word problems requiring setup and solution of equations.
This document contains step-by-step workings and solutions to various problems involving surds and indices. It shows calculations to simplify surd expressions, rationalize denominators, determine which of two expressions is greater, and other algebraic manipulations with surds and rational numbers. The document serves as an example of how to work through different types of surd and index problems systematically.
The document contains solutions to permutation and combination problems. It lists the number of total outcomes for rolling a dice n times as 6n, and the number of total outcomes for tossing a coin (n-1) times as 2n-1. It then works through additional problems calculating permutations, combinations, and compound probabilities.
This document provides the key and solutions to questions from the AIEEE 2012 B.Tech exam for the mathematics section. It contains 19 multiple choice questions related to topics in mathematics like trigonometry, calculus, sequences and series, probability, and functions. Each question is followed by the answer and a brief explanation of the solution steps. The document is intended to help students understand the concepts tested in the exam and check their work.
This document contains 10 multiple choice questions covering various math and statistics topics, including functions, geometry, probability, percentages, sequences, trigonometry, ellipses, and bank interest. It also contains 5 more difficult problems involving arithmetic sequences, trigonometric equations, modeling bacterial growth, finding distances on an ellipse, and comparing interest earned at different banks over 10 years. The questions range from easy to more challenging high school level math.
This document contains a series of math butterfly worksheets. Students are presented with numbers on the left side of the page and instructed to perform the mathematical operation indicated in each square using that number and the number in the square, writing the answer on the right side. The operations included are addition, subtraction, multiplication, division, and more complex operations combining multiple steps. This continues for 10 pages with increasing levels of difficulty.
This document provides classroom materials on exponents including guide cards, activity cards, assessment cards, enrichment cards, and a reference card. The cards introduce exponents, ask students to identify bases and exponents, rewrite expressions without zero or negative exponents, simplify expressions using laws of exponents, and evaluate exponential expressions. The reference card reviews the general form of exponential expressions and laws for multiplying, dividing, and taking powers of exponential expressions.
This document contains 15 problems related to logarithms and their properties. It includes the name of the author, their contact information, and the date. For each problem, the author has written the problem statement and solution. The problems cover topics like simplifying logarithmic expressions, determining unknown variables from logarithmic equations, and finding integral parts of logarithms.
The document provides examples for solving systems of linear equations using the reduced row echelon form matrix method and Gauss-Jordan elimination method. It gives step-by-step solutions for solving sample systems of equations using both methods. It also provides practice problems for students to solve systems of equations using the reduced row echelon form and Gauss elimination methods.
This document discusses finding the sum and product of the roots of quadratic equations. It provides the formulas for calculating the sum and product of roots without explicitly solving for the individual roots. The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0. Several examples are worked out applying these formulas. The document also contains exercises asking the reader to find the sum and product of roots for additional quadratic equations using the given coefficients a, b, and c.
The document provides definitions and examples for key terms related to order of operations, including numerical expression, evaluate, sum, difference, product, factor, and quotient. It gives the order of operations as parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right. An example problem is worked through step-by-step to demonstrate applying the order of operations. Additional practice problems are provided for students to evaluate.
The document discusses the mathematical operation of multiplication. Multiplication is defined as the operation where a number indicates how many times another number is added to itself. The document then provides tables showing the multiplication facts for multiplying any single digit number from 0 to 12 by any other single digit number from 0 to 12.
This document contains a math practice worksheet for a 3rd period exam at Colegio San Patricio. The worksheet includes problems on the binary system, number lines, equations, word problems, simplifying expressions, and writing algebraic expressions. It provides practice with various math concepts to help students prepare for their upcoming exam.
This document discusses solving systems of equations by elimination. It provides examples of eliminating a variable by adding or subtracting equations. The key steps are: 1) write the equations in standard form; 2) add or subtract the equations to eliminate one variable; 3) substitute the eliminated variable back into one equation to solve for the other variable. Checking the solution in both original equations verifies the correct solution was found.
Speed mathematics provides techniques to solve problems faster without extensive calculation. Some key methods described in the document include:
- Squaring numbers ending in 5 by multiplying the previous digit by one more than itself and adding the product of the last digits.
- Multiplying numbers by 9s or 1s by subtracting or adding to the digits from 9 or 1 respectively and placing the answer left to right.
- Mental calculation techniques like breaking numbers into place values to add, subtract or multiply mentally.
- The criss-cross system to multiply multi-digit numbers by working through place values vertically and cross-wise in steps.
This document discusses exponent rules and formulas involving positive, negative, fractional and zero exponents. It provides examples of simplifying expressions using these rules. Key points covered include:
- Formula I: am×an = am+n
- Formulas II-V cover properties for negative exponents and fractional exponents
- Examples are worked through applying the exponent rules and formulas
This document provides problems in four areas: number theory, algebra, geometry, and probability. It includes:
1) Five number theory exercises involving divisibility, remainders, and properties of numbers.
2) Five algebra exercises involving solving equations, finding roots, and relationships between coefficients and roots.
3) Five geometry exercises involving properties of shapes like triangles, cylinders, and trapezoids.
4) Five probability exercises calculating chances of outcomes and applying distributions to real-world scenarios.
The document provides the problems in each area along with the full worked out solutions and explanations. It covers a range of fundamental mathematical concepts across multiple domains.
This document provides a lesson on finding missing numbers in mathematical equations. It discusses different properties of operations like the commutative, associative, distributive, and identity properties. Examples of equations are provided and students are asked to determine the missing numbers by identifying which property is being used. Practice problems are included for students to solve. The goal is for students to understand how to use properties of operations to determine missing numbers in equations.
The document provides information about inequalities:
1. It discusses the meaning of inequalities and how they differ from equations by having a range of possible solutions rather than a single solution.
2. Examples of common signs involving inequalities are presented, such as signs for minimum heights or drinking ages, and how they should be written using inequality symbols.
3. The basic rules for solving and graphing inequalities on a number line are introduced, such as using open or closed circles to represent < or ≤, and how the inequality sign must be flipped when multiplying or dividing by a negative number to maintain the relationship.
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
The document provides solutions to 10 multiple choice questions related to aptitude. It also provides detailed working for questions 2, 5, and 7. Some key details:
- Question 2 asks about the area enclosed between two straight lines passing through the origin and calculates it to be 0.5.
- Question 5 involves calculating the relation between the areas of three squares based on a diagram with lines tangential to a circle. The relation is that the area of one square is the sum of the other two.
- Question 7 calculates what value of x makes the ratio of investments equal to the ratio of profits received, finding x to be 3000.
The document contains a solution to an aptitude test with 14 multiple choice questions covering topics like ratios, probability, geometry, linear equations, and mechanics. For each question, the correct answer is provided along with a brief explanation of the solution. The questions assess logical reasoning and problem-solving abilities.
The document provides instructions on using the order of operations PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to evaluate numerical expressions. It gives examples of solving expressions step-by-step using PEMDAS. Students are then given 10 practice problems and instructed to use PEMDAS and a calculator, if available, to find the value of each expression.
Prepare for the IITJEE with past papers solved by the coaching experts at Sri Chaitanya Junior College. Set your sights on the IITJEE 2014 Entrance examinations. To know more - visit www.srichaitanya.net or call 040 66060606. You can also stay in touch with us at www.facebook.com/SriChaitanyaEducationalInstitutes
This document contains a series of math butterfly worksheets. Students are presented with numbers on the left side of the page and instructed to perform the mathematical operation indicated in each square using that number and the number in the square, writing the answer on the right side. The operations included are addition, subtraction, multiplication, division, and more complex operations combining multiple steps. This continues for 10 pages with increasing levels of difficulty.
This document provides classroom materials on exponents including guide cards, activity cards, assessment cards, enrichment cards, and a reference card. The cards introduce exponents, ask students to identify bases and exponents, rewrite expressions without zero or negative exponents, simplify expressions using laws of exponents, and evaluate exponential expressions. The reference card reviews the general form of exponential expressions and laws for multiplying, dividing, and taking powers of exponential expressions.
This document contains 15 problems related to logarithms and their properties. It includes the name of the author, their contact information, and the date. For each problem, the author has written the problem statement and solution. The problems cover topics like simplifying logarithmic expressions, determining unknown variables from logarithmic equations, and finding integral parts of logarithms.
The document provides examples for solving systems of linear equations using the reduced row echelon form matrix method and Gauss-Jordan elimination method. It gives step-by-step solutions for solving sample systems of equations using both methods. It also provides practice problems for students to solve systems of equations using the reduced row echelon form and Gauss elimination methods.
This document discusses finding the sum and product of the roots of quadratic equations. It provides the formulas for calculating the sum and product of roots without explicitly solving for the individual roots. The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0. Several examples are worked out applying these formulas. The document also contains exercises asking the reader to find the sum and product of roots for additional quadratic equations using the given coefficients a, b, and c.
The document provides definitions and examples for key terms related to order of operations, including numerical expression, evaluate, sum, difference, product, factor, and quotient. It gives the order of operations as parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right. An example problem is worked through step-by-step to demonstrate applying the order of operations. Additional practice problems are provided for students to evaluate.
The document discusses the mathematical operation of multiplication. Multiplication is defined as the operation where a number indicates how many times another number is added to itself. The document then provides tables showing the multiplication facts for multiplying any single digit number from 0 to 12 by any other single digit number from 0 to 12.
This document contains a math practice worksheet for a 3rd period exam at Colegio San Patricio. The worksheet includes problems on the binary system, number lines, equations, word problems, simplifying expressions, and writing algebraic expressions. It provides practice with various math concepts to help students prepare for their upcoming exam.
This document discusses solving systems of equations by elimination. It provides examples of eliminating a variable by adding or subtracting equations. The key steps are: 1) write the equations in standard form; 2) add or subtract the equations to eliminate one variable; 3) substitute the eliminated variable back into one equation to solve for the other variable. Checking the solution in both original equations verifies the correct solution was found.
Speed mathematics provides techniques to solve problems faster without extensive calculation. Some key methods described in the document include:
- Squaring numbers ending in 5 by multiplying the previous digit by one more than itself and adding the product of the last digits.
- Multiplying numbers by 9s or 1s by subtracting or adding to the digits from 9 or 1 respectively and placing the answer left to right.
- Mental calculation techniques like breaking numbers into place values to add, subtract or multiply mentally.
- The criss-cross system to multiply multi-digit numbers by working through place values vertically and cross-wise in steps.
This document discusses exponent rules and formulas involving positive, negative, fractional and zero exponents. It provides examples of simplifying expressions using these rules. Key points covered include:
- Formula I: am×an = am+n
- Formulas II-V cover properties for negative exponents and fractional exponents
- Examples are worked through applying the exponent rules and formulas
This document provides problems in four areas: number theory, algebra, geometry, and probability. It includes:
1) Five number theory exercises involving divisibility, remainders, and properties of numbers.
2) Five algebra exercises involving solving equations, finding roots, and relationships between coefficients and roots.
3) Five geometry exercises involving properties of shapes like triangles, cylinders, and trapezoids.
4) Five probability exercises calculating chances of outcomes and applying distributions to real-world scenarios.
The document provides the problems in each area along with the full worked out solutions and explanations. It covers a range of fundamental mathematical concepts across multiple domains.
This document provides a lesson on finding missing numbers in mathematical equations. It discusses different properties of operations like the commutative, associative, distributive, and identity properties. Examples of equations are provided and students are asked to determine the missing numbers by identifying which property is being used. Practice problems are included for students to solve. The goal is for students to understand how to use properties of operations to determine missing numbers in equations.
The document provides information about inequalities:
1. It discusses the meaning of inequalities and how they differ from equations by having a range of possible solutions rather than a single solution.
2. Examples of common signs involving inequalities are presented, such as signs for minimum heights or drinking ages, and how they should be written using inequality symbols.
3. The basic rules for solving and graphing inequalities on a number line are introduced, such as using open or closed circles to represent < or ≤, and how the inequality sign must be flipped when multiplying or dividing by a negative number to maintain the relationship.
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
The document provides solutions to 10 multiple choice questions related to aptitude. It also provides detailed working for questions 2, 5, and 7. Some key details:
- Question 2 asks about the area enclosed between two straight lines passing through the origin and calculates it to be 0.5.
- Question 5 involves calculating the relation between the areas of three squares based on a diagram with lines tangential to a circle. The relation is that the area of one square is the sum of the other two.
- Question 7 calculates what value of x makes the ratio of investments equal to the ratio of profits received, finding x to be 3000.
The document contains a solution to an aptitude test with 14 multiple choice questions covering topics like ratios, probability, geometry, linear equations, and mechanics. For each question, the correct answer is provided along with a brief explanation of the solution. The questions assess logical reasoning and problem-solving abilities.
The document provides instructions on using the order of operations PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to evaluate numerical expressions. It gives examples of solving expressions step-by-step using PEMDAS. Students are then given 10 practice problems and instructed to use PEMDAS and a calculator, if available, to find the value of each expression.
Prepare for the IITJEE with past papers solved by the coaching experts at Sri Chaitanya Junior College. Set your sights on the IITJEE 2014 Entrance examinations. To know more - visit www.srichaitanya.net or call 040 66060606. You can also stay in touch with us at www.facebook.com/SriChaitanyaEducationalInstitutes
This document contains a math test with 4 problems for 6th grade students. Problem 1 involves calculating fractions, percentages, and operations with fractions. Problem 2 involves solving equations for unknown variables. Problem 3 involves calculating the area of a rectangular plot of land and determining how it is divided for different crops. Problem 4 involves drawing angles and rays on a coordinate plane and determining if a ray is a bisector. The test assesses students' skills in performing fraction and percentage calculations, solving equations, using geometry concepts, and applying math to real-world situations.
The document contains a 14 question mathematics assessment for Form 4 students. It covers topics including functions, graphs of quadratic functions, solving quadratic equations and simultaneous equations. Students are instructed to answer all questions within the time limit of 1 hour and 30 minutes. The questions range from 3 to 5 marks each and cover skills such as finding function values, determining function types, solving quadratic equations, sketching graphs and solving simultaneous equations.
Dear Students/Parents
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
This document provides instructions for a 50 question multiple choice exam on Computer Science and Applications. It states that the exam will be 1 hour and 15 minutes long. It provides detailed instructions on filling out the scantron answer sheet correctly, including bubbling in the test booklet number and other identifying information. It also warns candidates that any attempts to cheat, such as changing answers after or using prohibited materials, will result in disqualification.
The document contains 10 multiple choice questions about quadratic equations. It assesses the test taker's understanding of key concepts like identifying quadratic equations, graphing quadratic functions, writing quadratic equations in standard form, and solving quadratic equations by extracting square roots. The questions range from easy to difficult levels of difficulty.
The document provides instructions for a test. It describes how to fill out identifying information on the answer sheet, how the test is structured with different sections and time limits, how to arrive at answers and mark them on the answer sheet, and what to do after completing the test. It warns that candidates who seek or receive assistance will forfeit admission rights. The test booklet serial number and form number should be filled out on the answer sheet. Rough work should be done in the test booklet, not on the answer sheet.
This document is an examination for Integrated Algebra given on January 22, 2013. It contains 4 parts with a total of 39 multiple-choice and short answer questions. The first part has 30 multiple-choice questions worth 2 credits each. The next 3 parts have short answer questions worth 2, 3, and 3 credits respectively. Students must show their work, except for multiple-choice questions. Formulas are provided at the end. Graphing is permitted but not required.
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
This document contains a collection of presentations on algebra for grade 10 compiled by Beatrice S Zwane at the University of Johannesburg on March 6, 2014. It includes definitions of key algebra terms like algebraic expressions, variables, and evaluating expressions. It provides examples and discusses simplifying expressions by combining like terms. It also covers writing equations in slope-intercept form, finding the slope and y-intercept of lines, and operations with algebraic fractions. References are listed at the end from various sources accessed between 2007-2013.
The document provides instructions for holiday homework assignments for various subjects for children over summer vacations. It includes assignments for subjects like English, Hindi, Science, Maths, Social Science, Computer and Art & Craft. Some of the assignments involve creating projects, writing assignments, solving questions, making charts and maps. The purpose is to keep children engaged in constructive learning activities during holidays through creative and innovative assignments related to their subjects.
This quiz is open book and open notes/tutorialoutletBeardmore
FOR MORE CLASSES VISIT
tutorialoutletdotcom
Math 107 Quiz 2 Spring 2017 OL4
Professor: Dr. Katiraie Name________________________________ Instructions: The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
will be posted in your Portfolio with comments.
Class 10 Cbse Maths 2010 Sample Paper Model 3 Sunaina Rawat
The document provides information on the design of a mathematics question paper for Class X. It specifies:
1) The weightage and distribution of marks for different content units and forms of questions. Number systems, algebra and geometry make up the bulk of the content with the highest marks.
2) The paper will contain very short answer questions worth 1 mark each, short answer questions worth 2-3 marks each, and long answer questions worth 6 marks.
3) Some questions will provide internal choices while maintaining the overall scheme.
4) Questions will be evenly distributed between easy, average, and difficult levels in terms of marks.
5) Sample papers and blueprints are included based on this design to
Contoh cover, rumus, maklumat kepada calon matematik tambahan kertas 2 (1)Pauling Chia
The document is a practice SPM 2016 Additional Mathematics paper consisting of 3 sections - Section A, Section B and Section C. It provides information for candidates taking the exam such as answering all questions in Section A, 4 questions from Section B and 2 questions from Section C. Formulae that may be helpful in answering questions are listed on pages 2-4 covering Algebra, Calculus, Statistics, Geometry and Trigonometry. Graph paper and mathematical tables are provided to candidates taking the exam.
Raj and Ajay traveled by car to Ranikhet. Raj's car traveled at speed x km/hr while Ajay's was 5 km/hr faster. Raj took 4 hours more than Ajay to complete the 400 km journey.
A motor boat traveled upstream at a speed of 20 km/hr. To cover 15 km it took 1 hour more than traveling downstream.
A seminar had participants in Hindi (60), English (84) and Math (108). The maximum in each room was 12. The minimum rooms needed was 21.
Real numbers, polynomials, linear equations and quadratic equations word problems were presented as case studies with multiple choice questions to test understanding of concepts. Concise
The document contains a math worksheet with multiple-choice and word problems involving integers, addition, subtraction, multiplication, division, and other basic math operations. Some example problems include representing situations with integers, comparing and ordering integers, and solving word problems about money, temperatures, distances, and rates. The document provides the steps to solve each problem.
Prepare for the IITJEE with past papers solved by the coaching experts at Sri Chaitanya Junior College. Set your sights on the IITJEE 2014 Entrance examinations. To know more - visit www.srichaitanya.net or call 040 66060606. You can also stay in touch with us at www.facebook.com/SriChaitanyaEducationalInstitutes
This document contains a lesson plan for teaching factoring non-perfect trinomials in Math 8. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences through various activities, an evaluation, and assignment. Students will learn to define trinomials, factor non-perfect square trinomials, and apply factoring trinomials to geometric figures through guided practice with algebra tiles and examples.
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These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
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1. Sri Chaitanya IIT Academy., India
Corporate Office: Plot No:304,Kasetty Heights, Ayyappa Society, Madhapur - Hyd
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JEE-MAIN
2. 2014 JEE-MAIN Q. PAPER WITH SOLUTIONS
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EMAIL: ICONCOHYD@SRICHAITANYACOLLEGE.NET, WEB: WWW.SRICHAITANYA.NET
2
IMPORTANT INSTRUCTIONS:
1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of
pencil is strictly prohibited.
2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out
the Answer Sheet and fill in the particulars carefully.
3. The test is of 3 hours duration.
4. The test Booklet consists of 90 questions. The maximum marks are 360.
5. There are three parts in the question paper A, B, C consisting of Mathematics, Physics and Chemistry having
30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct
response.
6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question
1/4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from
the total score will be made if no response is indicated for an item in the answer sheet.
7. There is only one correct response for each question. Filling up more than one response in each question will
be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6
above.
8. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and Side 2 of the
Answer Sheet. Use of pencil is strictly prohibited.
9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,
any electronic device, etc., except the Admit Card inside the examination hall/room.
10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given
at the bottom of each page and in 3 pages (Pages 21 – 23) at the end of the booklet.
11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the
Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.
12. The CODE for this Booklet is G. Make sure that the CODE printed on Side-2 of the Answer Sheet is the same
as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the
Invigilator for replacement of both the Test Booklet and the Answer Sheet.
13. Do not fold or make any stray mark on the Answer Sheet.
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3
MATHEMATICS
1. The image of the line
x 1 y 3 z 4
3 1 5
in the plane 2x – y + z + 3 = 0 is the line:
1)
x 3 y 5 z 2
3 1 5
2)
x 3 y 5 z 2
3 1 5
3)
x 3 y 5 z 2
3 1 5
4)
x 3 y 5 z 2
3 1 5
Key: 1
Sol :
x 1 y 3 z 4
is parallel to 2x y z 3 0
3 1 5
Image
h 1 k 3 l 4
2
2 1 1
h, k, l 3, 5, 2
Required equation
x 3 y 5 z 2
3 1 5
2. If the coefficients of 3 4
x and x in the expansion of
182
1 ax bx 1 2x in powers
of ‘x’ are both zero, then (a, b) is equal to:
1)
251
16,
3
2)
251
14,
3
3)
272
14,
3
4)
272
16,
3
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Key : 4
Sol : Equating coefficients of 3 4
x and x is zero
32 17
17a b 0
3
1615 – 32 a + 3b = 0
Solving (a, b) =
272
16,
3
3. If a R and the equation
2 2
3 x x 2 x x a 0 (where [x] denotes the
greatest integer x ) has no integral solution, then all possible values of a lie in
the interval :
1) 1, 0 0, 1
2) (1, 2)
3) (-2, -1)
4) , 2 2,
Key : 1
Sol : 2 2
3f 2f a 0 where x x
2
1 1 3a
f 1
3
1 a 1; a 0
a 1, 0 0, 1
4. If
2
a b b c c a a b c
then is equal to:
1) 2
2) 3
3) 0
4) 1
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Key : 4
Sol :
2
a b b c c a a b c
5. The variance of first 50 even natural numbers is :
1)
833
4
2) 833
3) 437
4)
437
4
Key : 2
Sol : Variance of first ‘n’ even natural numbers is equal to
2
n 1
3
2
50 1
833
3
6. A bird is sitting on the top of a vertical pole 20 m high and its elevation from a
point ‘O’ on the ground is 0
45 . It flies off horizontally straight away from the
point ‘O’. After one second, the elevation of the bird from ‘O’ is reduced to 0
30 .
Then the speed (in m/s) of the bird is:
1) 40 2 1
2) 40 3 2
3) 20 2
4) 20 3 1
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Key : 4
Sol :
P Q
A B C
450
300
0
A 45 AB PB 20 mts and CQ 20
0 20
Tan30 BC 20 3 1 PQ
20 BC
distance
speed 20 3 1 mts
time
7. The integral 2
0
x x
1 4sin 4sin dx
2 2
equals:
1) 4
2)
2
4 4 3
3
3) 4 3 4
4) 4 3 4
3
Key : 4
Sol :
3
0 0
3
x x x
1 2sin dx 1 2sin dx 2sin 1 dx
2 2 2
3
0
3
x x
x 4cos 4cos x
2 2
4 3 4
3
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8. The statement ~ p ~ q is :
1) equivalent to p q
2) equivalent to ~ p q
3) a tautology
4) a fallacy
Key : 1
Sol : The statement ~ p ~ q is
P q ~q p ~ q ~ p ~ q p q
T T F F T T
T F T T F F
F T F T F F
F F T F T T
~ p ~ q is equivalent to p q
9. If A is an 3 3 non-singular matrix such that 1
AA' A'A and B A A', then BB'
equals :
1) I + B
2) I
3) 1
B
4) 1
B
Key : 2
Sol :
11 1 1 1
BB' A A A A
11 1 1
A AA A I. I I
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10. The integral
1
x
x
1
1 x e dx
x
is equal to :
1)
1
x
x
x 1 e c
2)
1
x
x
xe c
3)
1
x
x
x 1 e c
4)
1
x
x
xe c
Key : 2
Sol :
1
x
x
1
1 x e dx
x
1
x
x
2
1
1 x 1 e dx
x
1 1
x x
x x
2
1
e dx x 1 e dx
x
By parts =
1
x
x
xe c
11. If ‘z’ is a complex number such that | z | 2, then the minimum value of
1
z
2
:
1) is equal to
5
2
2) lies in the interval (1, 2)
3) is strictly greater than
5
3
4) is strictly greater than
3
2
but less than
5
2
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Key: 2
Sol : z rcis then | z | r 2
2 2
2 21 1
z rcos r sin
2 2
2 1
r rcos
4
17 9 25
2cos which lies in ,
4 4 4
1 3 5
z ,
2 2 2
Minimum value
3
2
lies in (1, 2)
12. If ‘g’ is the inverse of a function ‘f’ and 5
1
f ' x , then g' x
1 x
is equal to:
1) 5
1 x
2) 4
5x
3)
5
1
1 g x
4)
5
1 g x
Key : 4
Sol : If ‘g’ is the inverse of a function ‘f’, then x f g x f ' g x g' x 1
51
g' x 1 g x
f ' g x
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13. If
n n
3 1 f 1 1 f 2
, 0, and f n and 1 f 1 1 f 2 1 f 3
1 f 2 1 f 3 1 f 4
=
2 2 2
K 1 1 , then K is equal to :
1)
2)
1
3) 1
4) -1
Key : 3
Sol : Given determinant = 2
2 2 2
1 1 1 1 1 1
1 . 1
1 1
K 1
14. Let k k
k
1
f x sin x cos x
k
where x R and k 1 . Then 4 6f x f x equals:
1)
1
6
2)
1
3
3)
1
4
4)
1
12
Key : 4
Sol : 4 6f x f x = 2 2 2 21 1
[1 2sin xcos x] 1 3sin xcos x
4 6
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15. Let and be the roots of equation 2
px qx r 0, p 0 . If p, q, r are in A.P
and
1 1
4,
then the value of | | is :
1)
61
9
2)
2 17
9
3)
34
9
4)
2 13
9
Key : 4
Sol :
q
p
r
.
p
2q p q
By given condition
1 1
4
q
4
r
2
4
16. Let A and B be two events such that
1 1 1
P A B , P A B and P A , where A
6 4 4
stands for the complement of the
event A. Then the events A and B are :
1) mutually exclusive and independent
2) equally likely but not independent
3) independent but not equally likely
4) independent and equally likely
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Key : 3
Sol :
1 5
P A B 1
6 6
1 5
P A P B
4 6
3 1 5
P B
4 4 6
5 1 5 3 1
P B
6 2 6 3
3 1 1
P A .P B P A B
4 3 4
A, B are independent but not equally likely P A P B
17. If ‘f’ and ‘g’ are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0
and f(1) = 6, then for some c ]0, 1[ :
1) 2f ' c g' c
2) 2f ' c 3g' c
3) f ' c g' c
4) f ' c 2g' c
Key : 4
Sol :
f ' c f 1 f 0
for c 0, 1
g' c g 1 g 0
18. Let the population of rabbits surviving at a time ‘t’ be governed by the
differentiable equation
dp t 1
p t 200
dt 2
. If p(0) = 100, then p(t) equals :
1) t/2
400 300 e
2) t/2
300 200 e
3) t/2
600 500 e
4) t/2
400 300 e
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Key : 1
Sol :
dp 1
p t 200
dt 2
This is linear d.e in ‘p’
1 1
t t
2 2
p.e 400e c
By given condition p(0) = 100, c = -300
1
t
2
p 400 300e
19. Let ‘C’ be the circle with centre at (1, 1) and radius = 1. If ‘T’ is the circle
centred at (0, y), passing through origin and touching the circle ‘C’ externally,
then the radius of ‘T’ is equal to :
1)
3
2
2)
3
2
3)
1
2
4)
1
4
Key : 4
Sol :
1 2c 1, 1 c 0, y
1 2r 1, r y
1 2 1 2c c r r
2 2
1 y 1 1 y
1= 4y
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20. The area of the region described by 2 2 2
A x, y :x y 1 and y 1 x is
1)
4
2 3
2)
4
2 3
3)
2
2 3
4)
2
2 3
Key : 1
Sol.
Required area =
1
0
4
2 1 x dx
2 2 3
21. Let a, b, c and d be non-zero numbers. If the point of intersection of the line
4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is
equidistant from the two axes then :
1) 2bc – 3ad = 0
2) 2bc + 3ad = 0
3) 3bc – 2ad = 0
4) 3bc + 2ad = 0
Key : 3
Sol. Point of intersection
2ad 2bc 5bc 4ad
,
2ab 2ab
Equidistance from the both axis in
fourth quadrant 3bc 2ad 0
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22. Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3).
The equation of the line passing through (1, -1) and parallel to PS is
1) 4x 7y 11 0
2) 2x 9y 7 0
3) 4x 7y 3 0
4) 2x 9y 11 0
Key : 2
Sol : Mid point
13
,1
2
Slope PS
2
9
23.
2
2x 0
sin cos x
lim
x
is equal to :
1)
2
2) 1
3)
4)
Key : 4
Sol :
2
2x 0
sin sin x
lim
x
2 2
2 2x 0
sin sin x sin x
lim 1 1
sin x x
24. If n
X 4 3n 1: n N and Y 9 n 1 :n N , where N is the set of natural
numbers, then X Y is equal to:
1) N
2) Y – X
3) X
4) Y
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Key : 4
Sol : X and Y are multiplies of 9 and X Y
X Y Y
25. The locus of the foot of perpendicular drawn from the centre of the ellipse
2 2
x 3y 6 on any tangent to it is :
1)
22 2 2 2
x y 6x 2y
2)
22 2 2 2
x y 6x 2y
3)
22 2 2 2
x y 6x 2y
4)
22 2 2 2
x y 6x 2y
Key : 3
Sol. Given that ellipse
2 2
x y
1
6 2
C
P
A
B
Slope CP = 1
1
y
x
Slope of AB = 1
1
x
y
= m
Equation of the tangent is 2
y mx 6m 2
By above equations we get
22 2 2 2
x y 6x 2y
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26. Three positive numbers from an increasing G.P. If the middle term in this G.P is
doubled, the new numbers are in A.P. Then the common ratio of the G.P is :
1) 2 3
2) 3 2
3) 2 3
4) 2 3
Key : 4
Sol : 2
a,ar,ar G.P .
2
a ar
2ar
2
2
4ar a ar
2
r 4r 1 0
4 16 4
r
2
r 2 3
r 2 3
27. If
9 1 8 2 7 9 9
10 2 11 10 3 11 10 ..... 10 11 k 10 , then ‘k’ is equal to
1)
121
10
2)
441
100
3) 100
4) 110
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Key : 3
Sol :
9 1 8 2 7 9
S 10 2 11 10 3 11 10 .....10 11 ……… (1)
2 3 6 108 711
S 11.10 2 11 10 3 11 10 .....9 11 11
10
……… (2)
(2) ... (1)
29 8 7 9 101
S 10 11.10 11 10 .... 11 11
10
9
S 100 10
K 100
28. The angle between the lines whose direction cosines satisfy the equations
2 2 2
m n 0 and m nl l is :
1)
3
2)
4
3)
6
4)
2
Key : 1
Sol :
2 2 2
l m n 0
l m n
2 2 2
m n m n 0
2mn = 0
m = 0 (or) n = 0
If m = 0
l = -(0 + n)
l = -n
l : m : n = -n : 0 : n = -1 : 0 : 1
similarly if n = 0 then
l : m : n = -1, : 1 : 0
1 0 0
cos
2 2
3
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29. The slope of the line touching both the parabolas 2 2
y 4x and x 32y is :
1)
1
2
2)
3
2
3)
1
8
4)
2
3
Key : 1
Sol : Common tangent of
2/32 2 1/3 1/3
y 4ax and x 4by is a x b y ab 0
Here 4a = 4 and 4b = -32
Slope of the common tangent = 1/2
30. If x = -1 and x = 2 are extreme points of 2
f x log | x | x x then:
1)
1
6,
2
2)
1
6,
2
3)
1
2,
2
4)
1
2,
2
Key : 3
Sol : f ' 1 0 and f ' 2 0
Solving above equations we get
1
2,
2
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PHYSICS
31. When a rubber-band is stretched by a distance x , it exerts a restoring force of
magnitude 2
F ax bx where a and b are constants. The work done in stretching
the unstretched rubber-band by L is:
1)
2 3
1
2 2 3
aL bL
2) 2 3
aL bL
3) 2 31
2
aL bL
4)
2 3
2 3
aL bL
Key: 4
Sol:
2 3
2
0
2 3
L
aL bL
w Fdx ax bx dx
32. The coercivity of a small magnet where the ferromagnet gets demagnetized is
3 1
3 10 Am
. The current required to be passed in a solenoid of length 10 cm and
number of turns 100, so that the magnet gets demagnetized when inside the
solenoid, is:
1) 6A
2) 30 mA
3) 60 mA
4) 3 A
Key: 4
Sol: 3100
I=3 10
0.1
nI H
3I A
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33. In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80
Wand 1heater of 1 kW. The voltage of the electric mains is 220 V. The minimum
capacity of the main fuse of the building will be:
1) 14A
2) 8A
3) 10A
4) 12A
Key: 4
Sol:
1
40 15 100 5 80 5 1000
220
P IV I
2500
11.4 12A
220
A
34. An open glass tube is immersed in mercury in such a way that a length of 8 cm
extends above the mercury level. The open end of the tube is then closed and
sealed and the tube is raised vertically up by additional 46cm. What will be
length of the air column above mercury in the tube now?
(Atmospheric pressure = 76 cm of Hg)
1) 6 cm
2) 16 cm
3) 22 cm
4) 38 cm
Key: 2
Sol: 76 8 22x x
By trail and error method 16x
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35. A bob of mass m attached to an inextensible string of length l is suspended from
a vertical support. The bob rotates in a horizontal circle with an angular speed
rad/s about the vertical. About the point of suspension:
1) angular momentum changes both in direction and magnitude
2) angular momentum is conversed
3) angular momentum changes in magnitude but not in direction
4) angular momentum changes in direction but not in magnitude
Key: 4
Sol: Angular Momentum Changes in directions
36. The current voltage relation of diode is given by 1000 /
1 ,V T
I e mA where the
applied voltage V is in volts and the temperature T is in degree Kelvin. If a
student makes an error measuring 0.01V while measuring the current of 5mA at
300 K, what will be the error in the value of current in mA?
1) 0.05 Ma
2) 0.2 mA
3) 0.02 mA
4) 0.5 mA
Key: 2
Sol: I+1 = 1000 /V T
e
1000V
ln I 1
T
1000
V
I+1 T
I
31000
I= 6 10 0.01
3
= 0.2 mA
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37. From a tower of height H, a particle is thrown vertically upwards with a speed u.
The time taken by the particle to hit the ground, is n times that taken by it to
reach the highest point of its path. The relation between H, u and n is:
1) 2
2gH n u
2) 2 2
2gH n u
3)
2 2
2gH n u
4) 2
2 2gH nu n
Key: 4
Sol:
H
u
Let 1t is the time taken to reach max height 1
u
t
g
Let 2t is the time taken to reach ground from tower equation
2
2 2
1
2
H ut gt
2
2
2 4 8
2
u u gH
t
g
2
2
2u u gH
g g
Given that
2 1t nt
2
2
2u u gH nu
g g g
,
2 2
2 2
2
1
u gH u
n
g g
22
2 1 1gH u n
2 2
2 2gH u n n
2
2 2gH u n n
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38. A thin convex lens made from crown glass
3
2
has focal length f . When it is
measured in two different liquids having refractive indices
4
3
and
5
3
, it has the
focal lengths 1f and 2f respectively. The correct relation between the focal lengths
is:
1) 1f and 2f both become negative
2) 1 2f f f
3) 1f f and 2f becomes negative
4) 2f f and 1f becomes negative
Key: 3
Sol: From
1 2
1
f R
1 1
f R
3 2/
f R
For medium 4 3/
3
1 2 12 1
4 3 4f / R R
1 4f R
for medium
2
1 3 2 2
5 3 1
5 3
/
M /
f / R
1
5R
2 5f R
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39. A parallel plate capacitor is made of two circular plates separated by a distance
of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the
electric field in the dielectric is 4
3 10 /V m , the charge density of the positive plate
will be close to:
1) 4 2
6 10 /C m
2) 7 2
6 10 /C m
3) 7 2
3 10 /C m
4) 4 2
3 10 /C m
Key: 2
Sol: 4
0
3 10
K
12 4
2.2 8.8 10 3 10
7
6 10
40. In the circuit shown here, the point ‘C’ is kept connected to point ‘A’ till the
current flowing through the circuit becomes constant. Afterward, suddenly, point
‘C’ is disconnected from point ‘A’ and connected to point ‘B’at time t=0. Ratio of
the voltage across resistance and the inductor at t = L/R will be equal to:
L
R
B
A C
1)
1 e
e
2)
1
e
e
3) 1
4) 1
Key: 4
Sol: 0R LV V always for 0t
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41. Two beams, A and B, of plane polarized light with mutually perpendicular planes
of polarization are seen through a polaroid. From the position when the beam A
has maximum intensity (and beam B has zero intensity), a rotation of polaroid
through 30makes the two beams appear equally bright. If the initial intensities
of two beams are AI and BI respectively, then A
B
I
I
equals:
1)
1
3
2) 3
3)
3
2
4) 1
Key: 1
Sol: 1 1 2 2
30 60A B A BI I I cos I cos
2
2
cos 60 1
cos 30 3
A
B
I
I
42. There is a circular tube in a vertical plane. Two liquids which do not mix and of
densities 1d and 2d are filled in the tube. Each liquid subtends 90 angle at centre.
Radius joining their interface makes an angle with vertical. Ratio 1
2
d
d
is:
1d
2d
1)
1 sin
1 cos
2)
1 sin
1 sin
3)
1 cos
1 cos
4)
1 tan
1 tan
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Key: 4
Sol: A BP P
1 1 2 2h d g h d g
1 2cos sin cos sinR d R d
1
2
cos sin 1 tan
cos sin 1 tan
d
d
A
B
R
2h
2d
1d
1h
R
43. The pressure that has to be applied to the ends of a steel wire of length 10 cm to
keep its length constant when its temperature is raised by 100 C is: (For steel
Young’s modulus is 11 2
2 10 N m
and coefficient of thermal expansion is 5 1
1.1 10 K
)
1) 6
2.2 10 Pa
2) 8
2.2 10 Pa
3) 9
2.2 10 Pa
4) 7
2.2 10 Pa
Key: 2
Sol: Pressure 11 5 8
α 2 10 1.1 10 100 2.2 10y
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44. A block of mass m is placed on a surface with a vertical cross section given by
3
6
x
y . If the coefficient of friction is 0.5, the maximum height above the ground
at which the block can be placed without slipping is:
1)
1
2
m
2)
1
6
m
3)
2
3
m
4)
1
3
m
Key: 2
Sol: At the instant of just sliding
H=?
tan
0.5
dy
dx
2
1
2
x
x
1
' ' 1
6
H y at x m
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45. Three rods of Copper, Brass and Steel are welded together to form a Y – shaped
structure. Area of cross – section of each rod 2
4cm . End of copper rod is
maintained at 100 C where as ends of brass and steel are kept at 0 C . Lengths of
the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are
thermally insulated from surroundings except at ends. Thermal conductivites of
copper, brass and steel are 0.92,0.26 and 0.12 CGS units respectively. Rate of heat
flow through copper rod is:
1) 6.0 cal/s
2) 1.2 cal/s
3) 2.4 cal/s
4) 4.8 cal/s
Key: 4
Sol: Let T is the junction temperature then
cu Brass steelH H H
100cu B S
cu B S
K A T K A T K AT
l l l
,
0 96 0 26 0 12
100
46 13 12
. . .
T T T
200 5T
40T C
Heat flow per sec through copper
100KA T
l
0 96 4 60
46
.
4 8. cal/sec
0 C0 C
100 C
Brass
Copper
Steell=13 cm
k=0.26
l=12 cm
k=0.12
l=46
k=0.96
T
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46. A mass ‘m’ is supported by a massless string wound around a uniform hollow
cylinder of mass m and radius R. If the string does not slip on the cylinder, with
what acceleration will the mass fall on release?
m
R
m
1) g
2)
2
3
g
3)
2
g
4)
5
6
g
Key: 3
Sol: mg T ma
2 2
.
a
TR mR mR T ma
R
2ma mg or / 2a g
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47. Match List-I (Electromagnetic wave type) with List – II (Its
association/application) and select the correct option from the choices given
below the lists:
List-I List-II
(a) Infrared waves (i) To treat muscular strain
(b) Radio waves (ii) For broadcasting
(c) X-rays (iii) To detect fracture of bones
(d) Ultra violet rays (iv) Absorbed by the ozone layer
of the atmosphere
(a) (b) (c) (d)
1) (i) (ii) (iii) (iv)
2) (iv) (iii) (ii) (i)
3) (i) (ii) (iv) (iii)
4) (iii) (ii) (i) (iv)
Key: 1
Sol: Conceptual
48. The radiation corresponding to 3 2 transition of hydrogen atom falls on a
metal surface to produce photoelectrons. These electrons are made to enter a
magnetic field of 4
3 10 T
. If the radius of largest circular path followed by these
electrons is 10.0 mm, the work function of the metal is close to:
1) 1.6 eV
2) 1.8 eV
3) 1.1 eV
4) 0.8 eV
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Key: 3
Sol: In magnetic field ,
2 KE m
r
Bq
28 19 42 2 2
31 19
9 10 1.6 10 10 1
2 2 9 10 1.6 10
B q r
KE
m
0.8ev
1 1
13.6 1.89
4 9
E eV
0 1.89 0.8 1.1W E KE eV
49. During the propagation of electromagnetic waves in a medium:
1) Both electric and magnetic energy densities are zero
2) Electric energy density is double of the magnetic energy density
3) Electric energy density is half of the magnetic energy density
4) Electric energy density is equal to the magnetic energy density
Key: 4
Sol: Conceptual
50. A green light is incident from the water the air – water interface at the critical
angle . Select the correct statement.
1) The entire spectrum of visible light will come out of the water at various angles
to the normal
2) The entire spectrum of visible light will come out of the water at an angle of
90 to the normal
3) The spectrum of visible light whose frequency is less than that of green light
will come out to the air medium
4) The spectrum of visible light whose frequency is more than that of green light
will come out to the air medium
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Key: 3
Sol: With increase in frequency, critical angle c decreases i.e., present angle of
incidence in water will be more than respective critical angles of high frequencies
radiation. Hence high frequency radiations will get TIR and low frequencies
radiations will come out in to air
51. Four particles, each of mass M and equidistant from each other, move along a
circle of radius R under the action of their mutual gravitational attraction. The
speed of each particle is:
1) 1
1 2 2
2
GM
R
2)
GM
R
3) 2 2
GM
R
4) 1 2 2
GM
R
Key: 1
Sol:
V
R
R 2
2
2
2 2
mv 1 1 1
2
2 42
Gm
R R R
2 1
v 2 2 1
4
Gm
R
1
v 2 2 1
2
Gm
R
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52. A particle moves with simple harmonic motion in a straight line. In first s ,
after starting from rest it travels a distance a, and in next s it travels 2a, in
same direction, then:
1) time period of oscillations is 6
2) amplitude of motion is 3a
3) time period of oscillations is 8
4) amplitude of motion is 4a
Key: 1
Sol:
a a a
0 2
6
T
53. A conductor lies along the z – axis at 1.5 1.5z m and carries a fixed current of
10.0 A in ˆza direction (see figure). For a field 4 0.2
ˆ3.0 10 x
yB e a T
, find the power
required to move the conductor at constant speed to 2.0x m , 0y m in 3
5 10 s
.
Assume parallel motion along the x axis.
x
yB
I
2.0
1.5
1.5
1) 29.7 W
2) 1.57 W
3) 2.97 W
4) 14.85 W
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Key: 3
Sol: 4 0.2
Instant 3
2
3 10 3
5 10
x
P B V e
1 0.212
10
5
x
P e
2.97range
pdx
P W
dx
54. The forward biased diode connection is:
1)
2V 2V
2)
2V2V
3)
3V3V
4)
2V 4V
Key: 2
Sol: Conceptual
55. Hydrogen 1
1 H , Deuterium 2
1 H , singly ionized Helium 4
2 He
and doubly
ionized lithium 6
3 Li
all have one electron around the nucleus. Consider an
electron transition from 2n to 1n . If the wavelengths of emitted radiation are
1 2 3, , and 4 respectively then approximately which one of the following is
correct?
1) 1 2 3 42 3 4
2) 1 2 3 44 2 2
3) 1 2 3 42 2
4) 1 2 3 44 9
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Key: 4
Sol: 2
2
1 1 1
1
4
Rz
z
1 2 as 1z for both 1
1H and 2
1 H
2
31
1 32
3 1
4 4
z
z
2
1 4
1 42
4 1
9 9
z
z
1 2 3 44 9
56. On heating water, bubbles being formed at the bottom of the vessel detach and
rise. Take the bubbles to be spheres of radius R and making a circular contact of
radius r with the bottom of the vessel. If ,r R and the surface tension of water
is T, value of r just before bubbles detach is: (density of water is w )
R
2r
1) 2 3 wg
R
T
2) 2
3
wg
R
T
3) 2
6
wg
R
T
4) 2 wg
R
T
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Key: 3(This is an ambigious Question, so expected key is 3)
Sol: sinTdl buoyancy force on bubble
R
r r
2
r
T r
R
34
3
wR g
4
2 2
3
wR g
r
T
2 2
3
wg
r R
T
57. A pipe of length 85 cm is closed from one end. Find the number of possible
natural oscillations of air column in the pipe whose frequencies lie below 1250
Hz. The velocity of sound in air is 340 m/s.
1) 4
2) 12
3) 8
4) 6
Key: 4
Sol: From 2
340
100
4 4 85 10
V
n HZ
l
Possible frequencies in closed pipe is odd harmonics only So
100 300 500 700 900HZ, HZ, HZ, HZ, HZ and 1100 1300 1500HZ, HZ, HZ..... etc below
1250HZ , 6 natural oscillations are possible
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58. Assume that an electric field
2ˆ30E x i
exists in space. Then the potential
difference A OV V
, where OV
is the potential at the origin and AV
the potential at
2x m is:
1) 80 J
2) 120 J
3) – 120 J
4)– 80 J
Key: 4
Sol:
0
2
2
0
0 0
30 80
AV A
A
V
dv Edx V V x dx J
59. A student measured the length of a rod and wrote it as 3.50 cm. Which
instrument did he use to measure it?
1) A screw guage having 50 divisions in the circular scale and pitch as 1mm
2) A meter scale
3) A vernier calipers where the 10 divisions in vernier scale matches with 9
division in main scale has 10 divisions in 1cm
4) A screw guage having 100 divisions in the circular scale and pitch as 1mm
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Key: 3
Sol: Least count of vernier
1
10
mm
60. One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in
figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K,
800 K and 600 K respectively. Choose the correct statement:
P
V
A
400K
C
B 800 K
600 K
1) The change in internal energy in the process BC is 500R
2) The change in internal energy in whole cyclic process is 250 R
3) The change in internal energy in the process CA is 700 R
4) The change in internal energy in the process AB is 350R
Key: 1
Sol: 1) du for isochoric process VnC dT
3
1 400 600
2
R
R
2) for Process BC
1 2 200
500
1 1 7 / 5
nR T T R
du R
r
3) for whole process 0du
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CHEMSITRY
61. Which one is classified as a condensation polymer?
1) Acrylonitrile
2) Dacron
3) Neoprene
4) Teflon
Key: 2
Sol: Dacron is the condensation polymer
n
Neoprene
Add polymers
Teflon
62. Which one of the following properties is not shown by NO?
1) It’s bond order is 2.5
2) It is diamagnetic in gaseous state
3) It is a neutral oxide
4) It combines with oxygen to form nitrogen dioxide
Key: 2
Sol: NO is paramagnetic
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63. Sodium phenoxide when heated with 2CO under pressure at 0
125 C yields a product
which on acetylation produces C.
2CO
0
125
5Atm
2
H
AC O
B C
ONa
The major product C would be:
1) 3OCOCH
COOH
2) 3OCOCH
COOH
3) OH
3COCH
3COCH
4) OH
3COOCH
Key: 2
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Sol:
ONa
0125 C
5atm2
CO
OH
COOH H
AC O2
COOH
3
OCOCH
(B) (C)
Aspirin
64. Given below are the half-cell reactions:
2 0
2 ; 1.18Mn e Mn E V
3 2 0
2 ; 1.51Mn e Mn E V
The 0
E for 2 3
3 2Mn Mn Mn
will be:
1) - 0.33 V; the reaction will occur
2) – 2.69 V; the reaction will not occur
3) – 2.69 V; the reaction will occur
4) – 0.33 V; the reaction will not occur
Key: 2
Sol: 0
1.18 1.51E
= –2.69 V
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65. For complete combustion of ethanol. 2 5 2 2 23 2 3C H OH l O g CO g H O l , the
amount of heat produced as measured in bomb calorimeter, is 1364.47 1
kJmol
at
0
25 C . Assuming ideally the Enthalpy of combustion, cH , for the reaction will be:
1
8.314R kJmol
1) 1
1350.50kJmol
2) 1
1366.95kJmol
3) 1
1361.95kJmol
4) 1
1460.50kJmol
Key: 2
Sol: H U nRT
3
1364 1 8.314 298 10
66. For the estimation of nitrogen, 1.4 g of an organic compound was digested by
Kjeldahl method and the evolved ammonia was absorbed in 60 mL of
10
M
sulphuric acid. The unreacted acid required 20 mL of
10
M
sodium hydroxide for
complete neutralization. The percentage of nitrogen in the compound is:
1) 5%
2) 6%
3) 10%
4) 3%
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Key: 3
Sol: Meq of 2 4
1
H SO 60 2 12
10
Meq of base used for back titration
1
20 2
10
= Meq of acid left
Meq of acid reacted with liberated
Ammonia = 12-2 = 10 meq
= meq of 3
NH
Millimoles of 3
NH liberated = 10 [ n-factor = 1]
Moles of 3
3
NH 10 10
Moles “N” 3
10 10
Wt of “N” 3
10 10 14
% of “N” in the organic compound
3
10 10 14
100 10%
1.4
67. The major organic compound formed by the reaction of 1, 1, 1 – trichloroethane
with silver powder is:
1) 2 – Butene
2) Acetylene
3) Ethene
4) 2 – Butyne
Key: 4
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Sol:
3
2CH C Cl
Cl
Cl
3 3
6Ag CH C C CH
2-Butyne
+ 6 AgCl
68. The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 :
4. The ratio of number of their molecule is:
1) 3 : 16
2) 1 : 4
3) 7 : 32
4) 1 : 8
Key: 3
Sol: Ratio of the molecules =
1 4
:
32 28
= 7: 32
69. The metal that cannot be obtained by electrolysis of an aqueous solution of its salt
is:
1) Cr
2) Ag
3) Ca
4) Cu
Key: 3
Sol: Ca cannot be obtained by the electrolysis of aqueous solution of its salt.
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70. The equivalent conductance of NaCl at concentration C and at infinite dilution
are C and , respectively. The correct relationship between C and is given as
(where the constant B is positive)
1) C B C
2) C B C
3) C B C
4) C B C
Key: 4
Sol: C B C
71. The correct set of four quantum numbers for the valence electrons of rubidium
atom (Z=37) is:
1)
1
5,0,1,
2
2)
1
5,0,0,
2
3)
1
5,1,0,
2
4)
1
5,1,1,
2
Key: 2
Sol: 1
5s
72. Consider separate solutions of 0.500 M 2 5 ,C H OH aq 3 4 2
0.100 ,M Mg PO aq
0.250M KBr aq and 3 40.125M Na PO aq at 0
25 C . Which statement is true about these
solutions, assuming all salts to be strong electrolytes?
1) 2 50.500M C H OH aq has the highest osmotic pressure
2) They all have the same osmotic pressure
3) 3 4 2
0.100M Mg PO aq has the highest osmotic pressure
4) 3 40.125M Na PO aq has the highest osmotic pressure
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Key: 2
Sol: iCST
73. The most suitable reagent for the conversion of 2R CH OH R CHO is:
1) PCC (Pyridinium Chlorochromate)
2) 4KMnO
3) 2 2 7K Cr O
4) 3CrO
Key: 1
Sol: Most suitable reagent for the conversion of 0
1 alcohol to aldehyde is “PCC”
74. CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which
of the following expressions is correct?
1) 3Cs Cl
r r a
2) 3Cs Cl
r r a
3)
3
2Cs Cl
a
r r
4)
3
2Cs Cl
r r a
Key: 4
Sol: c a3a 2(r r )
c a
3a
r r
2
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75. In which of the following reactions 2 2H O acts as reducing agent?
(a) 2 2 22 2 2H O H e H O
(b) 2 2 22 2H O e O H
(c) 2 2 2 2H O e OH
(d) 2 2 2 22 2 2H O OH e O H O
1) (b), (d)
2) (a), (b)
3) (c), (d)
4) (a), (c)
Key: 1
Sol: While acting as reducing agent it gives up electrons and release oxygen gas.
76. For which of the following molecule significant 0 ?
a)
Cl
Cl b)
CN
CN c)
OH
OH d)
SH
SH
1) (c) and (d)
2) Only (a)
3) (a) and (b)
4) Only (c)
Key: 1
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Sol:
Cl
Cl
0
CN
CN
0 ;
0 0 ;
O H
O
H
S H
S
H
But dipole moment of
"SH"
SH is less than dipolemoment of
OH
OH , but is significant
77. On heating an aliphatic primary amine with chloroform and ethanolic potassium
hydroxide, the organic compound formed is:
1) an alkyl isocyanide
2) an alkanol
3) an alkanediol
4) an alkyl cyanide
Key: 1
Sol: 2 3
R NH CHCl KOH R NC alkylisocyanide
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78. In 2NS reactions, the correct order of reactivity for the following compounds:
3 3 2 3 2
, ,CH Cl CH CH Cl CH CHCl and 3 3
CH CCl is
1) 3 3 2 3 32 3
CH CHCl CH CH Cl CH Cl CH CCl
2) 3 3 3 2 32 3
CH Cl CH CHCl CH CH Cl CH CCl
3) 3 3 2 3 32 3
CH Cl CH CH Cl CH CHCl CH CCl
4) 3 2 3 3 32 3
CH CH Cl CH Cl CH CHCl CH CCl
Key: 3
Sol: 3 3 2 3 32 3
CH Cl CH CH Cl CH CHCl CH CCl
79. The octahedral complex of a metal ion 3
M
with four monodentate ligands
1 2 3, ,L L L and 4L absorb wavelengths in the region of red, green, yellow and blue,
respectively. The increasing order of ligand strength of the four ligands is:
1) 1 2 4 3L L L L
2) 4 3 2 1L L L L
3) 1 3 2 4L L L L
4) 3 2 4 1L L L L
Key: 3
Sol: Order of wavelength of colours
Red >Yellow > Green > Blue
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80. The equation which is balanced and represents the correct product(s) is:
1) 4 2 2 44
4CuSO KCN K Cu CN K SO
2) 2 22 2Li O KCl LiCl K O
3) 2
3 45
5 5CoCl NH H Co NH Cl
4)
2 24
2 26
6excess NaOH
Mg H O EDTA Mg EDTA H O
Key: 3
Sol: 2
3 45
CoCl NH 5H Co 5NH Cl
81. In the reaction, 54 .
3 ,PClLiAlH Alc KOH
CH COOH A B C the product C is:
1) Acetyl chloride
2) Acetaldehyde
3) Acetylene
4) Ethylene
Key: 4
Sol:
54
3 3 2 3 2 2 2
PClLiAlH Alc.KOH
CH C OH CH CH OH CH CH Cl CH CH
O
82. The correct statement for the molecule, 3CsI , is:
1) it contains ,Cs I
and lattice 2I molecule
2) it is a covalent molecule
3) it contains Cs
and 3I
ions
4) it contains 3
Cs
and I
ions
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Key: 3
Sol: 3
CsI contains Cs
and 3
I
ions
83. For the reaction 2 2 3
1
2g g g
SO O SO , if
x
p cK K RT where the symbols have
usual meaning then the value of x is: (assuming ideality)
1) 1
2) 1
3)
1
2
4)
1
2
Key: 3
Sol: n
P CK K (RT)
3 1
n 1
2 2
84. For the non-stoichiometre reaction 2 ,A B C D the following kinetic data
were obtained in three separate experiments, all at 298 K.
Initial
Concentration
(A)
Initial Concentration
(B)
Initial rate of formation
of C mol L S
0.1M
0.1 M
0.2 M
0.1 M
0.2 M
0.1 M
3
1.2 10
3
1.2 10
3
2.4 10
The rate law for the formation of ‘C’ is?
1)
dc
k A
dt
2)
dc
k A B
dt
3)
2dc
k A B
dt
4)
2dc
k A B
dt
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Key: 1
Sol: m m
r K(A) (B)
85. Resistance of 0.2 M solution of an electrolyte is 50. The specific conductance of
the solution is 1
1.4 S m
. The resistance of 0.5 M solution of the same electrolyte is
280. The molar conductivity of 0.5 M solution of the electrolyte in 2 1
S m mol
is:
1) 2
5 10
2) 4
5 10
3) 3
5 10
4) 3
5 10
Key: 2
Sol:
l
R
a
1 l
50
1.4 a
70
a
l
280 (70) 4
K = 0.25
3
410 0.25
5 10
0.5
86. Among the following oxoacids, the correct decreasing order of acid strength is:
1) 2 4 3HClO HClO HClO HOCl
2) 2 3 4HOCl HClO HClO HClO
3) 4 2 3HClO HOCl HClO HClO
4) 4 3 2HClO HClO HClO HOCl
Key: 4
Sol: With increase in unprotonated oxygen atoms acidic strength increases
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87. Which one of the following bases is not present in DNA?
1) Thymine
2) Quinoline
3) Adenine
4) Cytosine
Key: 2
Sol: Qunoline is the base which is not present in DNA
88. Considering the basic strength of amines in aqueous solution, which one has the
smallest bpK value?
1) 6 5 2C H NH
2) 3 2
CH NH
3) 3 2CH NH
4) 3 3
CH N
Key: 2
Sol: 3 2
CH NH Stronger base in aqueous medium than 3
Me N . So its pKb value is
smallest
89. If Z is a compressibility factor, vander Waals equation at low pressure can be
written as:
1) 1
Pb
Z
RT
2) 1
RT
Z
Pb
3) 1
a
Z
VRT
4) 1
Pb
Z
RT
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Key: 3
Sol: 2
a
P V RT
V
a
PV RT
V
a
Z 1
RTV
90. Which series of reactions correctly represents chemical relations related to iron
and its compound?
1)
0 0
2 , ,600 ,700
3 4
O heat CO C CO C
Fe Fe O FeO Fe
2) 2 4 2 4 2dil ,
4 2 4 3
H SO H SO O heat
Fe FeSO Fe SO Fe
3) 2 2 4, dil
4
O heat H SO heat
Fe FeO FeSO Fe
4) 2 , ,
3 2
Cl heat heat air Zn
Fe FeCl FeCl Fe
Key: 1
Sol: O heat CO CO2
600 7003 4
Fe Fe O FeO Fe