1) The document describes the structure and scoring guidelines for a physics exam with two sections: Section 1 on physics concepts and Section 2 on single-digit answers. Section 1 contains 7 multiple choice questions with options to select one or more answers, while Section 2 contains 5 questions each with a single digit answer.
2) The exam also includes a Section 3 on matching questions containing two tables and 3 associated questions to test matching concepts to options.
3) Answers are provided for the sample questions, with the correct options indicated for Section 1 questions and single digit answers for Section 2 questions.
The document provides information about a physics exam, including:
- It has two sections, with Section 1 worth 21 marks and Section 2 worth 28 marks.
- Questions have multiple choice answers labeled A, B, C, or D, with only one correct in Section 1 and one or more correct in Section 2.
- Marks are awarded based on selecting the fully or partially correct answers, with penalties for incorrect selections.
- The questions cover topics of physics including kinematics, electromagnetism, optics, and mechanics.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
Dear Students/Parents
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)
The document contains 17 physics questions in a multiple choice format with single correct answers. Each question is followed by its corresponding solution. The questions cover topics in mechanics, thermodynamics, gravitation, and other core areas of physics.
Dear Students/Parents
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)
Dear Students/Parents
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)
Dear Students/Parents
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 a summary of a physics exam paper containing multiple choice and numerical questions. It tests concepts in circuits, optics, mechanics, and other areas of physics. The summary focuses on highlighting the key topics covered and question formats rather than reproducing content.
The paper contains two sections - the first with multiple choice questions testing circuits, optics, waves, and electrostatics concepts. Answers can have one or more options correct. The second section involves numerical questions where the answer is a single integer between 0-9. Question formats include experimental analysis, mechanics problems, and converting between electrical measuring devices.
The document provides information about a physics exam, including:
- It has two sections, with Section 1 worth 21 marks and Section 2 worth 28 marks.
- Questions have multiple choice answers labeled A, B, C, or D, with only one correct in Section 1 and one or more correct in Section 2.
- Marks are awarded based on selecting the fully or partially correct answers, with penalties for incorrect selections.
- The questions cover topics of physics including kinematics, electromagnetism, optics, and mechanics.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
Dear Students/Parents
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)
The document contains 17 physics questions in a multiple choice format with single correct answers. Each question is followed by its corresponding solution. The questions cover topics in mechanics, thermodynamics, gravitation, and other core areas of physics.
Dear Students/Parents
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)
Dear Students/Parents
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)
Dear Students/Parents
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 a summary of a physics exam paper containing multiple choice and numerical questions. It tests concepts in circuits, optics, mechanics, and other areas of physics. The summary focuses on highlighting the key topics covered and question formats rather than reproducing content.
The paper contains two sections - the first with multiple choice questions testing circuits, optics, waves, and electrostatics concepts. Answers can have one or more options correct. The second section involves numerical questions where the answer is a single integer between 0-9. Question formats include experimental analysis, mechanics problems, and converting between electrical measuring devices.
Full jee mains 2015 online paper 10th april finalPradeep Kumar
The document provides solutions to 13 physics problems from a JEE Mains exam. Some key details:
- Problem 1 asks about the relationship between average force on container walls and temperature in an ideal gas, with the answer being directly proportional.
- Problem 2 asks why electrons diffuse from the n-region to the p-region in an unbiased n-p junction, with the answer being due to a higher electron concentration in the n-region.
- Problem 3 involves calculating the voltage reading of two batteries connected in parallel, with the answer being 13.1V.
- The remaining problems cover topics in physics including de Broglie wavelength, drift velocity, momentum, trajectories, moments of inertia
Dear Students/Parents
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)
The document summarizes the problems from the 7th International Physics Olympiad held in 1974 in Warsaw, Poland. It includes two theoretical problems and their solutions. The first problem involves calculating the minimum velocity for an elastic collision between hydrogen atoms using the Bohr model. The second problem involves calculating refraction indices and trajectory of a light beam passing through a transparent plate with a refractive index that varies linearly with position.
Jee advanced 2015 paper 1 code 1 final Pradeep Kumar
1. The document provides information about JEE Advanced 2015 paper 1, including 8 multiple choice questions in Section 1 and 10 multiple choice questions in Section 2.
2. Section 3 contains 2 matching questions matching concepts in Column I to statements in Column II.
3. The questions cover topics in physics including electromagnetism, quantum mechanics, thermodynamics, and nuclear physics.
This document contains information about JEE Advanced 2015 Paper 2 Code 3 for Physics. It includes 10 multiple choice questions testing concepts in physics. The questions cover topics such as optics, circuits, quantum mechanics, mechanics, thermodynamics and electromagnetism. For each question, students had to select the single correct answer ranging from 0 to 9. The document also provides two additional sections with more complex multi-concept questions, some requiring selecting one or more answers. The questions test a range of fundamental physics principles and problem solving abilities.
The document provides a summary of questions and answers from JEE(ADVANCED) – 2014 PAPER-2 Code-1. It includes 3 sections:
1) Section 1 contains 10 multiple choice questions with one correct answer each about physics concepts like kinetic energy, forces, electric fields, etc.
2) Section 2 contains 3 paragraphs with comprehension questions about thermodynamics, fluid dynamics, and electromagnetism.
3) Section 3 contains 4 matching questions pairing concepts from lists about physics problems involving charges, lenses, and inclined planes.
The summary briefly outlines the 3 main sections and types of questions contained in the document to provide the high-level structure and essential information.
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 contains 9 physics problems involving concepts like dimensional analysis, kinematics, forces, work, energy, and momentum.
Problem 1 asks students to determine the dimensional formula for surface tension using fundamental quantities of energy, velocity, and time. Problem 2 involves calculating the time taken for two ships moving towards each other to reach their shortest distance apart. Problem 3 asks students to determine the acceleration of a particle given its velocity varies with position.
The remaining problems involve calculating forces, work, energy, momentum, and velocities in various mechanical systems involving blocks, springs, and particles. Students must apply physics equations like Newton's laws, work-energy theorem, and conservation of momentum to arrive at the 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.
This document provides instructions for a physics exam. It describes the format and sections of the exam paper. Section 1 contains multiple choice questions with one or more correct answers. Section 2 contains paragraphs followed by related questions, each with a single correct answer. Section 3 has multiple choice questions with matching lists. The marking scheme awards marks for correct answers and deducts marks for incorrect answers. The document then provides sample exam questions in physics.
The document provides instructions for a physics exam. It specifies that the exam booklet contains questions in three parts: Physics, Chemistry, and Mathematics. Each part contains three sections. Section 1 contains multiple choice questions where one or more answers are correct. Section 2 contains paragraphs with two multiple choice questions per paragraph. Section 3 also contains multiple choice questions related to paragraphs. The marking scheme awards points for correctly answering questions and deducts points for incorrect answers. The document also provides an example exam paper following this format and structure.
This document contains a 50 question physics exam with multiple choice answers for each question covering topics like optics, mechanics, electricity and magnetism, heat and thermodynamics, modern physics and more. The questions test understanding of concepts like scattering, pendulums, radioactive decay, impulse, capacitors, semiconductors, diffraction and interference patterns, momentum, torque, center of mass, thermodynamic processes and more.
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.
This document provides instructions for an entrance examination for a five year integrated M.Sc. program in Applied Geology, Chemistry and Physics. It instructs candidates to write their register number, not write their name, shade answer options on the answer sheet using an HB pencil, and not write in the question paper. It notes the exam will have 50 multiple choice questions with four options each, lasting 2 hours with a maximum score of 400 marks. Incorrect answers will receive -1 mark and correct answers will receive 4 marks.
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.
Full jee mains 2015 online paper 10th april finalPradeep Kumar
The document provides solutions to 13 physics problems from a JEE Mains exam. Some key details:
- Problem 1 asks about the relationship between average force on container walls and temperature in an ideal gas, with the answer being directly proportional.
- Problem 2 asks why electrons diffuse from the n-region to the p-region in an unbiased n-p junction, with the answer being due to a higher electron concentration in the n-region.
- Problem 3 involves calculating the voltage reading of two batteries connected in parallel, with the answer being 13.1V.
- The remaining problems cover topics in physics including de Broglie wavelength, drift velocity, momentum, trajectories, moments of inertia
Dear Students/Parents
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)
The document summarizes the problems from the 7th International Physics Olympiad held in 1974 in Warsaw, Poland. It includes two theoretical problems and their solutions. The first problem involves calculating the minimum velocity for an elastic collision between hydrogen atoms using the Bohr model. The second problem involves calculating refraction indices and trajectory of a light beam passing through a transparent plate with a refractive index that varies linearly with position.
Jee advanced 2015 paper 1 code 1 final Pradeep Kumar
1. The document provides information about JEE Advanced 2015 paper 1, including 8 multiple choice questions in Section 1 and 10 multiple choice questions in Section 2.
2. Section 3 contains 2 matching questions matching concepts in Column I to statements in Column II.
3. The questions cover topics in physics including electromagnetism, quantum mechanics, thermodynamics, and nuclear physics.
This document contains information about JEE Advanced 2015 Paper 2 Code 3 for Physics. It includes 10 multiple choice questions testing concepts in physics. The questions cover topics such as optics, circuits, quantum mechanics, mechanics, thermodynamics and electromagnetism. For each question, students had to select the single correct answer ranging from 0 to 9. The document also provides two additional sections with more complex multi-concept questions, some requiring selecting one or more answers. The questions test a range of fundamental physics principles and problem solving abilities.
The document provides a summary of questions and answers from JEE(ADVANCED) – 2014 PAPER-2 Code-1. It includes 3 sections:
1) Section 1 contains 10 multiple choice questions with one correct answer each about physics concepts like kinetic energy, forces, electric fields, etc.
2) Section 2 contains 3 paragraphs with comprehension questions about thermodynamics, fluid dynamics, and electromagnetism.
3) Section 3 contains 4 matching questions pairing concepts from lists about physics problems involving charges, lenses, and inclined planes.
The summary briefly outlines the 3 main sections and types of questions contained in the document to provide the high-level structure and essential information.
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 contains 9 physics problems involving concepts like dimensional analysis, kinematics, forces, work, energy, and momentum.
Problem 1 asks students to determine the dimensional formula for surface tension using fundamental quantities of energy, velocity, and time. Problem 2 involves calculating the time taken for two ships moving towards each other to reach their shortest distance apart. Problem 3 asks students to determine the acceleration of a particle given its velocity varies with position.
The remaining problems involve calculating forces, work, energy, momentum, and velocities in various mechanical systems involving blocks, springs, and particles. Students must apply physics equations like Newton's laws, work-energy theorem, and conservation of momentum to arrive at the 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.
This document provides instructions for a physics exam. It describes the format and sections of the exam paper. Section 1 contains multiple choice questions with one or more correct answers. Section 2 contains paragraphs followed by related questions, each with a single correct answer. Section 3 has multiple choice questions with matching lists. The marking scheme awards marks for correct answers and deducts marks for incorrect answers. The document then provides sample exam questions in physics.
The document provides instructions for a physics exam. It specifies that the exam booklet contains questions in three parts: Physics, Chemistry, and Mathematics. Each part contains three sections. Section 1 contains multiple choice questions where one or more answers are correct. Section 2 contains paragraphs with two multiple choice questions per paragraph. Section 3 also contains multiple choice questions related to paragraphs. The marking scheme awards points for correctly answering questions and deducts points for incorrect answers. The document also provides an example exam paper following this format and structure.
This document contains a 50 question physics exam with multiple choice answers for each question covering topics like optics, mechanics, electricity and magnetism, heat and thermodynamics, modern physics and more. The questions test understanding of concepts like scattering, pendulums, radioactive decay, impulse, capacitors, semiconductors, diffraction and interference patterns, momentum, torque, center of mass, thermodynamic processes and more.
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.
This document provides instructions for an entrance examination for a five year integrated M.Sc. program in Applied Geology, Chemistry and Physics. It instructs candidates to write their register number, not write their name, shade answer options on the answer sheet using an HB pencil, and not write in the question paper. It notes the exam will have 50 multiple choice questions with four options each, lasting 2 hours with a maximum score of 400 marks. Incorrect answers will receive -1 mark and correct answers will receive 4 marks.
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.
Build the Next Generation of Apps with the Einstein 1 Platform.
Rejoignez Philippe Ozil pour une session de workshops qui vous guidera à travers les détails de la plateforme Einstein 1, l'importance des données pour la création d'applications d'intelligence artificielle et les différents outils et technologies que Salesforce propose pour vous apporter tous les bénéfices de l'IA.
Software Engineering and Project Management - Software Testing + Agile Method...Prakhyath Rai
Software Testing: A Strategic Approach to Software Testing, Strategic Issues, Test Strategies for Conventional Software, Test Strategies for Object -Oriented Software, Validation Testing, System Testing, The Art of Debugging.
Agile Methodology: Before Agile – Waterfall, Agile Development.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
VARIABLE FREQUENCY DRIVE. VFDs are widely used in industrial applications for...PIMR BHOPAL
Variable frequency drive .A Variable Frequency Drive (VFD) is an electronic device used to control the speed and torque of an electric motor by varying the frequency and voltage of its power supply. VFDs are widely used in industrial applications for motor control, providing significant energy savings and precise motor operation.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Design and optimization of ion propulsion dronebjmsejournal
Electric propulsion technology is widely used in many kinds of vehicles in recent years, and aircrafts are no exception. Technically, UAVs are electrically propelled but tend to produce a significant amount of noise and vibrations. Ion propulsion technology for drones is a potential solution to this problem. Ion propulsion technology is proven to be feasible in the earth’s atmosphere. The study presented in this article shows the design of EHD thrusters and power supply for ion propulsion drones along with performance optimization of high-voltage power supply for endurance in earth’s atmosphere.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
AI for Legal Research with applications, toolsmahaffeycheryld
AI applications in legal research include rapid document analysis, case law review, and statute interpretation. AI-powered tools can sift through vast legal databases to find relevant precedents and citations, enhancing research accuracy and speed. They assist in legal writing by drafting and proofreading documents. Predictive analytics help foresee case outcomes based on historical data, aiding in strategic decision-making. AI also automates routine tasks like contract review and due diligence, freeing up lawyers to focus on complex legal issues. These applications make legal research more efficient, cost-effective, and accessible.
Discover the latest insights on Data Driven Maintenance with our comprehensive webinar presentation. Learn about traditional maintenance challenges, the right approach to utilizing data, and the benefits of adopting a Data Driven Maintenance strategy. Explore real-world examples, industry best practices, and innovative solutions like FMECA and the D3M model. This presentation, led by expert Jules Oudmans, is essential for asset owners looking to optimize their maintenance processes and leverage digital technologies for improved efficiency and performance. Download now to stay ahead in the evolving maintenance landscape.
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Applications of artificial Intelligence in Mechanical Engineering.pdf
IIT-JEE Advanced 2017 Question Paper 1
1. 3/36 Paper-1 Code 1
PART I : PHYSICS
SECTION 1 (Maximum Marks: 28)
• This section contains SEVEN questions
• Each question has FOUR options [A], [B], [C] and [D]. ONE OR MORE THAN ONE of
these four options is(are) correct
• For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +4 If only the bubble(s) corresponding to all the correct option(s)
is(are) darkened
Partial Marks : +1 For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks : -2 In all other cases
• For example, if [A], [C] and [D] are all the correct options for a question, darkening all these
three will get +4 marks; darkening only [A] and [D] will get +2 marks; and darkening [A]
and [B] will get -2 marks, as a wrong option is also darkened
Q.1 A flat plate is moving normal to its plane through a gas under the action of a constant force
F. The gas is kept at a very low pressure. The speed of the plate v is much less than the
average speed u of the gas molecules. Which of the following options is/are true?
[A] The pressure difference between the leading and trailing faces of the plate is
proportional to uv
[B] The resistive force experienced by the plate is proportional to v
[C] The plate will continue to move with constant non-zero acceleration, at all times
[D] At a later time the external force F balances the resistive force
Space for rough work
Answer for the above question
Ans for Q.1: (A), (B), and (D)
2. 4/36 Paper-1 Code 1
Q.2 A block of mass M has a circular cut with a frictionless surface as shown. The block rests
on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is
at x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest at
the topmost point of the path as shown and it slides down. When the mass loses contact
with the block, its position is x and the velocity is v. At that instant, which of the following
options is/are correct?
[A] The position of the point mass m is: 𝑥 = − 2
!"
!!!
[B] The velocity of the point mass m is: 𝑣 =
!!"
!!
!
!
[C] The x component of displacement of the center of mass of the block M is: −
!"
!!!
[D] The velocity of the block M is: 𝑉 = −
!
!
2𝑔𝑅
Space for rough work
Answer for the above question
Ans for Q.2: (B) and (C)
3. 5/36 Paper-1 Code 1
Q.3 A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit
length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave
pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time
TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2)
without disturbing the position of M it takes time TAO to reach point O. Which of the
following options is/are correct?
M
O
A
Pulse 1
Pulse 2
[A] The time TAO = TOA
[B] The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of
rope
[C] The wavelength of Pulse 1 becomes longer when it reaches point A
[D] The velocity of any pulse along the rope is independent of its frequency and
wavelength
Space for rough work
Answer for the above question
Ans for Q.3: (A) and (D)
4. 6/36 Paper-1 Code 1
Q.4 A human body has a surface area of approximately 1 m!
. The normal body temperature is
10 K above the surrounding room temperature 𝑇!. Take the room temperature to be
𝑇! = 300 K. For 𝑇! = 300 K, the value of 𝜎𝑇!
!
= 460 Wm!!
(where 𝜎 is the Stefan-
Boltzmann constant). Which of the following options is/are correct?
[A] The amount of energy radiated by the body in 1 second is close to 60 Joules
[B] If the surrounding temperature reduces by a small amount ∆𝑇! ≪ 𝑇!, then to
maintain the same body temperature the same (living) human being needs to radiate
∆𝑊 = 4𝜎𝑇!
!
∆𝑇! more energy per unit time
[C] Reducing the exposed surface area of the body (e.g. by curling up) allows humans to
maintain the same body temperature while reducing the energy lost by radiation
[D] If the body temperature rises significantly then the peak in the spectrum of
electromagnetic radiation emitted by the body would shift to longer wavelengths
Space for rough work
Answer for the above question
Ans for Q.4: (C)
5. 7/36 Paper-1 Code 1
Q.5 A circular insulated copper wire loop is twisted to form two loops of area 𝐴 and 2𝐴 as
shown in the figure. At the point of crossing the wires remain electrically insulated from
each other. The entire loop lies in the plane (of the paper). A uniform magnetic field 𝐵
points into the plane of the paper. At 𝑡 = 0, the loop starts rotating about the common
diameter as axis with a constant angular velocity ω in the magnetic field. Which of the
following options is/are correct?
[A] The emf induced in the loop is proportional to the sum of the areas of the two loops
[B] The amplitude of the maximum net emf induced due to both the loops is equal to the
amplitude of maximum emf induced in the smaller loop alone
[C] The net emf induced due to both the loops is proportional to cos ωt
[D] The rate of change of the flux is maximum when the plane of the loops is
perpendicular to plane of the paper
Space for rough work
Answer for the above question
Ans for Q.5: (B) and (D)
6. 8/36 Paper-1 Code 1
Q.6 In the circuit shown, 𝐿 = 1 𝜇H, 𝐶 = 1 𝜇F and 𝑅 = 1 𝑘Ω. They are connected in series with
an a.c. source 𝑉 = 𝑉! sin 𝜔𝑡 as shown. Which of the following options is/are correct?
[A] The current will be in phase with the voltage if 𝜔 = 10!
rad. s!!
[B] The frequency at which the current will be in phase with the voltage is independent
of 𝑅
[C] At 𝜔~0 the current flowing through the circuit becomes nearly zero
[D] At 𝜔 ≫ 10!
rad. s!!
, the circuit behaves like a capacitor
Q.7 For an isosceles prism of angle 𝐴 and refractive index µ, it is found that the angle of
minimum deviation 𝛿! = 𝐴. Which of the following options is/are correct?
[A] For the angle of incidence 𝑖! = 𝐴, the ray inside the prism is parallel to the base of
the prism
[B] For this prism, the refractive index µ and the angle of prism 𝐴 are related as
𝐴 =
!
!
cos!! !
!
[C] At minimum deviation, the incident angle 𝑖! and the refracting angle 𝑟! at the first
refracting surface are related by 𝑟! = (𝑖!/2)
[D] For this prism, the emergent ray at the second surface will be tangential to the
surface when the angle of incidence at the first surface is
𝑖! = sin!!
sin 𝐴 4 cos! !
!
− 1 − cos 𝐴
Space for rough work
Answers for the above questions
V0 sin ω t
L = 1 µH C = 1 µF R = 1 kΩ
Ans for Q.6: (B) and (C) Ans for Q.7: (A), (C) and (D)
7. 9/36 Paper-1 Code 1
SECTION 2 (Maximum Marks: 15)
• This section contains FIVE questions
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive
• For each question, darken the bubble corresponding to the correct integer in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened
Zero Marks : 0 In all other cases
Q.8 A drop of liquid of radius R = 10!!
m having surface tension S =
!.!
!"
Nm!!
divides itself
into 𝐾 identical drops. In this process the total change in the surface energy ∆𝑈 = 10!!
J.
If 𝐾 = 10!
then the value of α is
Q.9 An electron in a hydrogen atom undergoes a transition from an orbit with quantum number
𝑛! to another with quantum number 𝑛!. 𝑉! and 𝑉! are respectively the initial and final
potential energies of the electron. If
!!
!!
= 6.25, then the smallest possible 𝑛! is
Space for rough work
Answers for the above questions
Ans for Q.8: (6) Ans for Q.9: (5)
8. 10/36 Paper-1 Code 1
Q.10 A monochromatic light is travelling in a medium of refractive index 𝑛 = 1.6. It enters a
stack of glass layers from the bottom side at an angle 𝜃 = 30!
. The interfaces of the glass
layers are parallel to each other. The refractive indices of different glass layers are
monotonically decreasing as nm = n – mΔn, where nm is the refractive index of the mth
slab
and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the
(m – 1)th
and mth
slabs from the right side of the stack. What is the value of m?
Space for rough work
Answer for the above question
n
n - Δn
n - 2Δn
n - 3Δn
n – (m-1)Δn
θ
1
2
3
n – mΔn
m-1
m
≈ ≈
Ans for Q.10: (8)
9. 11/36 Paper-1 Code 1
Q.11 A stationary source emits sound of frequency 𝑓! = 492 Hz. The sound is reflected by a
large car approaching the source with a speed of 2 ms!!
. The reflected signal is received
by the source and superposed with the original. What will be the beat frequency of the
resulting signal in Hz? (Given that the speed of sound in air is 330 ms!!
and the car
reflects the sound at the frequency it has received).
Q.12 131
I is an isotope of Iodine that β decays to an isotope of Xenon with a half-life of 8 days.
A small amount of a serum labelled with 131
I is injected into the blood of a person. The
activity of the amount of 131
I injected was 2.4 ×10!
Becquerel (Bq). It is known that the
injected serum will get distributed uniformly in the blood stream in less than half an hour.
After 11.5 hours, 2.5 ml of blood is drawn from the person’s body, and gives an activity of
115 Bq. The total volume of blood in the person’s body, in liters is approximately
(you may use 𝑒!
≈ 1 + 𝑥 for 𝑥 ≪ 1 and ln 2 ≈ 0.7).
Space for rough work
Answers for the above questions
Ans for Q.11: (6) Ans for Q.12: (5)
10. 12/36 Paper-1 Code 1
SECTION 3 (Maximum Marks: 18)
• This section contains SIX questions of matching type
• This section contains TWO tables (each having 3 columns and 4 rows)
• Based on each table, there are THREE questions
• Each question has FOUR options [A], [B], [C], and [D]. ONLY ONE of these four options
is correct
• For each question, darken the bubble corresponding to the correct option in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks: -1 In all other cases
Space for rough work
11. 13/36 Paper-1 Code 1
Answer Q.13, Q.14 and Q.15 by appropriately matching the information given in the three
columns of the following table.
A charged particle (electron or proton) is introduced at the origin (𝑥 = 0, 𝑦 = 0, 𝑧 = 0) with a
given initial velocity 𝑣. A uniform electric field 𝐸 and a uniform magnetic field 𝐵 exist
everywhere. The velocity 𝑣, electric field 𝐸 and magnetic field 𝐵 are given in columns 1, 2 and
3, respectively. The quantities 𝐸! , 𝐵! are positive in magnitude.
Column 1 Column 2 Column 3
(I) Electron with 𝑣 = 2
!!
!!
𝑥 (i) 𝐸 = 𝐸! 𝑧 (P) 𝐵 = −𝐵! 𝑥
(II) Electron with 𝑣 =
!!
!!
𝑦 (ii) 𝐸 = −𝐸! 𝑦 (Q) 𝐵 = 𝐵! 𝑥
(III) Proton with 𝑣 = 0 (iii) 𝐸 = −𝐸! 𝑥 (R) 𝐵 = 𝐵! 𝑦
(IV) Proton with 𝑣 = 2
!!
!!
𝑥 (iv) 𝐸 = 𝐸! 𝑥 (S) 𝐵 = 𝐵! 𝑧
Q.13 In which case will the particle move in a straight line with constant velocity?
[A] (III) (ii) (R) [B] (IV) (i) (S) [C] (III) (iii) (P) [D] (II) (iii) (S)
Q.14 In which case will the particle describe a helical path with axis along the positive 𝑧
direction?
[A] (IV) (i) (S) [B] (II) (ii) (R) [C] (III) (iii) (P) [D] (IV) (ii) (R)
Q.15 In which case would the particle move in a straight line along the negative direction of 𝑦-
axis (i.e., move along – 𝑦)?
[A] (II) (iii) (Q) [B] (III) (ii) (R) [C] (IV) (ii) (S) [D] (III) (ii) (P)
Space for rough work
Answers for the above questions
Ans for Q.13: (D) Ans for Q.14: (A) Ans for Q.15: (B)
12. 14/36 Paper-1 Code 1
Answer Q.16, Q.17 and Q.18 by appropriately matching the information given in the three
columns of the following table.
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the
corresponding 𝑃 − 𝑉 diagrams in column 3 of the table. Consider only the path from state 1 to
state 2. 𝑊 denotes the corresponding work done on the system. The equations and plots in the
table have standard notations as used in thermodynamic processes. Here γ is the ratio of heat
capacities at constant pressure and constant volume. The number of moles in the gas is 𝑛.
Column 1 Column 2 Column 3
(I)
𝑊!→! =
1
𝛾 − 1
(𝑃! 𝑉! − 𝑃! 𝑉!)
(i)
Isothermal
(P)
1 2
P
V
(II)
𝑊!→! = −𝑃 𝑉! + 𝑃 𝑉!
(ii)
Isochoric
(Q)
1
2
P
V
(III)
𝑊!→! = 0
(iii)
Isobaric
(R)
1
2
P
V
(IV)
𝑊!→! = −𝑛𝑅𝑇 ln(
𝑉!
𝑉!
)
(iv)
Adiabatic
(S)
1
2
P
V
Space for rough work
13. 15/36 Paper-1 Code 1
Q.16 Which of the following options is the only correct representation of a process in which
ΔU = ΔQ – PΔV ?
[A] (II) (iv) (R) [B] (III) (iii) (P) [C] (II) (iii) (S) [D] (II) (iii) (P)
Q.17 Which one of the following options is the correct combination?
[A] (IV) (ii) (S) [B] (III) (ii) (S) [C] (II) (iv) (P) [D] (II) (iv) (R)
Q.18 Which one of the following options correctly represents a thermodynamic process that is
used as a correction in the determination of the speed of sound in an ideal gas?
[A] (I) (ii) (Q) [B] (IV) (ii) (R) [C] (III) (iv) (R) [D] (I) (iv) (Q)
END OF PART I : PHYSICS
Space for rough work
Answers for the above questions
Ans for Q.16: (D) Ans for Q.17: (B) Ans for Q.18: (D)
14. 16/36 Paper-1 Code 1
PART II : CHEMISTRY
SECTION 1 (Maximum Marks: 28)
• This section contains SEVEN questions
• Each question has FOUR options [A], [B], [C] and [D]. ONE OR MORE THAN ONE of
these four options is(are) correct
• For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +4 If only the bubble(s) corresponding to all the correct option(s)
is(are) darkened
Partial Marks : +1 For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks : -2 In all other cases
• For example, if [A], [C] and [D] are all the correct options for a question, darkening all these
three will get +4 marks; darkening only [A] and [D] will get +2 marks; and darkening [A]
and [B] will get -2 marks, as a wrong option is also darkened
Q.19 An ideal gas is expanded from (p1, V1, T1) to (p2, V2, T2) under different conditions. The
correct statement(s) among the following is(are)
[A] The work done on the gas is maximum when it is compressed irreversibly from
(p2, V2) to (p1, V1) against constant pressure p1
[B] If the expansion is carried out freely, it is simultaneously both isothermal as well as
adiabatic
[C] The work done by the gas is less when it is expanded reversibly from V1 to V2 under
adiabatic conditions as compared to that when expanded reversibly from V1 to V2
under isothermal conditions
[D] The change in internal energy of the gas is (i) zero, if it is expanded reversibly with
T1 = T2, and (ii) positive, if it is expanded reversibly under adiabatic conditions with
T1 ≠ T2
Space for rough work
Answer for the above question
Ans for Q.19: (A), (B), and (C)
15. 17/36 Paper-1 Code 1
Q.20 For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against
the mole fraction of M in solution is shown in the following figure. Here xL and xM
represent mole fractions of L and M, respectively, in the solution. The correct statement(s)
applicable to this system is(are)
[A] The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed
from xL = 0 to xL = 1
[B] The point Z represents vapour pressure of pure liquid L and Raoult’s law is obeyed
when xL à 1
[C] The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed
when xL à 0
[D] Attractive intermolecular interactions between L-L in pure liquid L and M-M in
pure liquid M are stronger than those between L-M when mixed in solution
Space for rough work
Answer for the above question
Ans for Q.20: (B) and (D)
16. 18/36 Paper-1 Code 1
Q.21 The correct statement(s) about the oxoacids, HClO4 and HClO, is(are)
[A] The central atom in both HClO4 and HClO is sp3
hybridized
[B] HClO4 is more acidic than HClO because of the resonance stabilization of its anion
[C] HClO4 is formed in the reaction between Cl2 and H2O
[D] The conjugate base of HClO4 is weaker base than H2O
Q.22 The colour of the X2 molecules of group 17 elements changes gradually from yellow to
violet down the group. This is due to
[A] the physical state of X2 at room temperature changes from gas to solid down the
group
[B] decrease in ionization energy down the group
[C] decrease in π*-σ* gap down the group
[D] decrease in HOMO-LUMO gap down the group
Space for rough work
Answers for the above questions
Ans for Q.21: (A), (B), and (D) Ans for Q.22: (C) and (D)
17. 19/36 Paper-1 Code 1
Q.23 Addition of excess aqueous ammonia to a pink coloured aqueous solution of MCl2·6H2O
(X) and NH4Cl gives an octahedral complex Y in the presence of air. In aqueous solution,
complex Y behaves as 1:3 electrolyte. The reaction of X with excess HCl at room
temperature results in the formation of a blue coloured complex Z. The calculated spin
only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y.
Among the following options, which statement(s) is(are) correct?
[A] Addition of silver nitrate to Y gives only two equivalents of silver chloride
[B] The hybridization of the central metal ion in Y is d2
sp3
[C] Z is a tetrahedral complex
[D] When X and Z are in equilibrium at 0°C, the colour of the solution is pink
Q.24 The IUPAC name(s) of the following compound is(are)
[A] 1-chloro-4-methylbenzene [B] 4-chlorotoluene
[C] 4-methylchlorobenzene [D] 1-methyl-4-chlorobenzene
Space for rough work
Answers for the above questions
Ans for Q.23: (B), (C), and (D) Ans for Q.24: (A) and (B)
18. 20/36 Paper-1 Code 1
Q.25 The correct statement(s) for the following addition reactions is(are)
[A] O and P are identical molecules
[B] (M and O) and (N and P) are two pairs of diastereomers
[C] (M and O) and (N and P) are two pairs of enantiomers
[D] Bromination proceeds through trans-addition in both the reactions
Space for rough work
Answer for the above question
Ans for Q.25: (B) and (D)
19. 21/36 Paper-1 Code 1
SECTION 2 (Maximum Marks: 15)
• This section contains FIVE questions
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive
• For each question, darken the bubble corresponding to the correct integer in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened
Zero Marks : 0 In all other cases
Q.26 A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of
400 pm. If the density of the substance in the crystal is 8 g cm−3
, then the number of atoms
present in 256 g of the crystal is . The value of is
Q.27 The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was
determined by using a conductivity cell consisting of platinized Pt electrodes. The distance
between the electrodes is 120 cm with an area of cross section of 1 cm2
. The conductance
of this solution was found to be S. The pH of the solution is 4. The value of
limiting molar conductivity of this weak monobasic acid in aqueous solution is
S cm−1
mol−1
. The value of is
Space for rough work
Answers for the above questions
24
10×N N
7
105 −
×
( )o
mΛ
2
10×Z Z
Ans for Q.26: (2) Ans for Q.27: (6)
20. 22/36 Paper-1 Code 1
Q.28 The sum of the number of lone pairs of electrons on each central atom in the following
species is
[TeBr6]2−
, [BrF2]+
, SNF3, and [XeF3]−
(Atomic numbers: N = 7, F = 9, S = 16, Br = 35, Te = 52, Xe = 54)
Q.29 Among H2, He2
+
, Li2, Be2, B2, C2, N2, O2
−
, and F2, the number of diamagnetic species is
(Atomic numbers: H = 1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7, O = 8, F = 9)
Q.30 Among the following, the number of aromatic compound(s) is
Space for rough work
Answers for the above questions
Ans for Q.28: (6) Ans for Q.30: (5)
Due to printing inconsistency in Q.29 in Code1 of Paper1
(and the corresponding question in all other codes), +3
marks will be awarded to all candidates for this question.
21. 23/36 Paper-1 Code 1
SECTION 3 (Maximum Marks: 18)
• This section contains SIX questions of matching type
• This section contains TWO tables (each having 3 columns and 4 rows)
• Based on each table, there are THREE questions
• Each question has FOUR options [A], [B], [C], and [D]. ONLY ONE of these four options
is correct
• For each question, darken the bubble corresponding to the correct option in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks: -1 In all other cases
Space for rough work
22. 24/36 Paper-1 Code 1
Answer Q.31, Q.32 and Q.33 by appropriately matching the information given in the three
columns of the following table.
The wave function, lmln ,,ψ is a mathematical function whose value depends upon spherical
polar coordinates ( φθ,,r ) of the electron and characterized by the quantum numbers ln, and
lm . Here r is distance from nucleus, θ is colatitude and φ is azimuth. In the mathematical
functions given in the Table, Z is atomic number and oa is Bohr radius.
Column 1 Column 2 Column 3
(I) 1s orbital
(i)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∝ o
l
a
Zr
o
mln e
a
Z 2
3
,,ψ
(P)
(II) 2s orbital (ii) One radial node (Q) Probability density at nucleus
∝ 3
1
oa
(III) 2pz orbital
(iii) θψ cos
2
2
5
,,
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∝ o
l
a
Zr
o
mln re
a
Z
(R) Probability density is maximum
at nucleus
(IV) 3dz
2
orbital (iv) xy-plane is a nodal plane (S) Energy needed to excite
electron from n = 2 state to n =
4 state is
32
27
times the energy
needed to excite electron from
n = 2 state to n = 6 state
Q.31 For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like
species is
[A] (I) (ii) (S) [B] (IV) (iv) (R) [C] (II) (ii) (P) [D] (III) (iii) (P)
Q.32 For hydrogen atom, the only CORRECT combination is
[A] (I) (i) (S) [B] (II) (i) (Q) [C] (I) (i) (P) [D] (I) (iv) (R)
Q.33 For He+
ion, the only INCORRECT combination is
[A] (I) (i) (R) [B] (II) (ii) (Q) [C] (I) (iii) (R) [D] (I) (i) (S)
Space for rough work
Answers for the above questions
Ans for Q.31: (C) Ans for Q.32: (A) Ans for Q.33: (C)
23. 25/36 Paper-1 Code 1
Answer Q.34, Q.35 and Q.36 by appropriately matching the information given in the three
columns of the following table.
Columns 1, 2 and 3 contain starting materials, reaction conditions, and type of reactions,
respectively.
Column 1 Column 2 Column 3
(I) Toluene (i) NaOH/ Br2 (P) Condensation
(II) Acetophenone (ii) Br2/ hν (Q) Carboxylation
(III) Benzaldehyde (iii) (CH3CO)2O/ CH3COOK (R) Substitution
(IV) Phenol (iv) NaOH/ CO2 (S) Haloform
Q.34 For the synthesis of benzoic acid, the only CORRECT combination is
[A] (II) (i) (S) [B] (IV) (ii) (P) [C] (I) (iv) (Q) [D] (III) (iv) (R)
Q.35 The only CORRECT combination that gives two different carboxylic acids is
[A] (II) (iv) (R) [B] (IV) (iii) (Q) [C] (III) (iii) (P) [D] (I) (i) (S)
Q.36 The only CORRECT combination in which the reaction proceeds through radical
mechanism is
[A] (III) (ii) (P) [B] (IV) (i) (Q) [C] (II) (iii) (R) [D] (I) (ii) (R)
END OF PART II : CHEMISTRY
Space for rough work
Answers for the above questions
Ans for Q.34: (A) Ans for Q.35: (C) Ans for Q.36: (D)
24. 26/36 Paper-1 Code 1
PART III : MATHEMATICS
SECTION 1 (Maximum Marks: 28)
• This section contains SEVEN questions
• Each question has FOUR options [A], [B], [C] and [D]. ONE OR MORE THAN ONE of
these four options is(are) correct
• For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +4 If only the bubble(s) corresponding to all the correct option(s)
is(are) darkened
Partial Marks : +1 For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks : -2 In all other cases
• For example, if [A], [C] and [D] are all the correct options for a question, darkening all these
three will get +4 marks; darkening only [A] and [D] will get +2 marks; and darkening [A]
and [B] will get -2 marks, as a wrong option is also darkened
Q.37 If 2𝑥 − 𝑦 + 1 = 0 is a tangent to the hyperbola
!!
!!
−
!!
!"
= 1, then which of the following
CANNOT be sides of a right angled triangle?
[A] a, 4, 1 [B] a, 4, 2 [C] 2a, 8, 1 [D] 2a, 4, 1
Q.38 If a chord, which is not a tangent, of the parabola 𝑦!
= 16𝑥 has the equation 2𝑥 + 𝑦 = 𝑝,
and midpoint (ℎ, 𝑘), then which of the following is(are) possible value(s) of 𝑝, ℎ and 𝑘?
[A] 𝑝 = −2, ℎ = 2, 𝑘 = −4 [B] 𝑝 = −1, ℎ = 1, 𝑘 = −3
[C] 𝑝 = 2, ℎ = 3, 𝑘 = −4 [D] 𝑝 = 5, ℎ = 4, 𝑘 = −3
Space for rough work
Answers for the above questions
Ans for Q.37: (A), (B), and (C) Ans for Q.38: (C)
25. 27/36 Paper-1 Code 1
Q.39 Let [𝑥] be the greatest integer less than or equals to 𝑥. Then, at which of the following
point(s) the function 𝑓 𝑥 = 𝑥 cos(𝜋(𝑥 + [𝑥])) is discontinuous?
[A] 𝑥 = −1 [B] 𝑥 = 0 [C] 𝑥 = 1 [D] 𝑥 = 2
Q.40 Let 𝑓: ℝ → (0, 1) be a continuous function. Then, which of the following function(s)
has(have) the value zero at some point in the interval (0, 1)?
[A] 𝑥!
− 𝑓(𝑥) [B] 𝑥 − 𝑓 𝑡 cos 𝑡 𝑑𝑡
!
!
!!
!
[C] 𝑒!
− 𝑓 𝑡 sin 𝑡 𝑑𝑡
!
!
[D] 𝑓 𝑥 + 𝑓 𝑡 sin 𝑡 𝑑𝑡
!
!
!
Q.41 Which of the following is(are) NOT the square of a 3×3 matrix with real entries?
[A]
1 0 0
0 1 0
0 0 1
[B]
1 0 0
0 1 0
0 0 −1
[C]
1 0 0
0 −1 0
0 0 −1
[D]
−1 0 0
0 −1 0
0 0 −1
Space for rough work
Answers for the above questions
Ans for Q.40: (A) and (B) Ans for Q.41: (B) and (D)
Due to printing inconsistency in Q.39 in Code1 of Paper1
(and the corresponding question in all other codes), +4
marks will be awarded to all candidates for this question.
26. 28/36 Paper-1 Code 1
Q.42 Let 𝑎, 𝑏, 𝑥 and 𝑦 be real numbers such that 𝑎 − 𝑏 = 1 and 𝑦 ≠ 0. If the complex number
𝑧 = 𝑥 + 𝑖𝑦 satisfies Im
!"!!
!!!
= y, then which of the following is(are) possible value(s) of
𝑥?
[A] −1 + 1 − 𝑦! [B] −1 − 1 − 𝑦!
[C] 1 + 1 + 𝑦! [D] 1 − 1 + 𝑦!
Q.43 Let 𝑋 and 𝑌 be two events such that 𝑃 𝑋 =
!
!
, 𝑃 𝑋|𝑌 =
!
!
and 𝑃 𝑌|𝑋 =
!
!
. Then
[A] 𝑃 𝑌 =
!
!"
[B] 𝑃 𝑋!
|𝑌 =
!
!
[C] 𝑃 𝑋 ∩ 𝑌 =
!
!
[D] 𝑃 𝑋 ∪ 𝑌 =
!
!
Space for rough work
Answers for the above questions
Ans for Q.42: (A) and (B) Ans for Q.43: (A) and (B)
27. 29/36 Paper-1 Code 1
SECTION 2 (Maximum Marks: 15)
• This section contains FIVE questions
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive
• For each question, darken the bubble corresponding to the correct integer in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct answer is darkened
Zero Marks : 0 In all other cases
Q.44 For how many values of 𝑝, the circle 𝑥!
+ 𝑦!
+ 2𝑥 + 4𝑦 − 𝑝 = 0 and the coordinate axes
have exactly three common points?
Q.45 Let 𝑓: ℝ → ℝ be a differentiable function such that 𝑓 0 = 0, 𝑓
!
!
= 3 and 𝑓!
0 = 1. If
𝑔 𝑥 = [𝑓!
𝑡 cosec 𝑡 − cot 𝑡 cosec 𝑡 𝑓(𝑡)]
!
!
!
𝑑𝑡
for 𝑥 ∈ 0,
!
!
, then lim!→! 𝑔(𝑥) =
Space for rough work
Answers for the above questions
Ans for Q.44: (2) Ans for Q.45: (2)
28. 30/36 Paper-1 Code 1
Q.46 For a real number 𝛼, if the system
1 𝛼 𝛼!
𝛼 1 𝛼
𝛼!
𝛼 1
𝑥
𝑦
𝑧
=
1
−1
1
of linear equations, has infinitely many solutions, then 1 + 𝛼 + 𝛼!
=
Q.47 Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let 𝑥 be the
number of such words where no letter is repeated; and let 𝑦 be the number of such words
where exactly one letter is repeated twice and no other letter is repeated. Then,
!
!!
=
Q.48 The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24,
then what is the length of its smallest side?
Space for rough work
Answers for the above questions
Ans for Q.46: (1) Ans for Q.47: (5) Ans for Q.48: (6)
29. 31/36 Paper-1 Code 1
SECTION 3 (Maximum Marks: 18)
• This section contains SIX questions of matching type
• This section contains TWO tables (each having 3 columns and 4 rows)
• Based on each table, there are THREE questions
• Each question has FOUR options [A], [B], [C], and [D]. ONLY ONE of these four options
is correct
• For each question, darken the bubble corresponding to the correct option in the ORS
• For each question, marks will be awarded in one of the following categories:
Full Marks : +3 If only the bubble corresponding to the correct option is darkened
Zero Marks : 0 If none of the bubbles is darkened
Negative Marks: -1 In all other cases
Space for rough work
30. 32/36 Paper-1 Code 1
Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three
columns of the following table.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact,
respectively.
Column 1 Column 2 Column 3
(I) 𝑥!
+ 𝑦!
= 𝑎!
(i) 𝑚𝑦 = 𝑚!
𝑥 + 𝑎 (P)
!
!!
,
!!
!
(II) 𝑥!
+ 𝑎!
𝑦!
= 𝑎!
(ii) 𝑦 = 𝑚𝑥 + 𝑎 𝑚! + 1 (Q)
!!"
!!!!
,
!
!!!!
(III) 𝑦!
= 4𝑎𝑥 (iii) 𝑦 = 𝑚𝑥 + 𝑎! 𝑚! − 1 (R)
!!!!
!!!!!!
,
!
!!!!!!
(IV) 𝑥!
− 𝑎!
𝑦!
= 𝑎!
(iv) 𝑦 = 𝑚𝑥 + 𝑎! 𝑚! + 1 (S)
!!!!
!!!!!!
,
!!
!!!!!!
Q.49 For 𝑎 = 2, if a tangent is drawn to a suitable conic (Column 1) at the point of contact
(−1, 1), then which of the following options is the only CORRECT combination for
obtaining its equation?
[A] (I) (i) (P) [B] (I) (ii) (Q) [C] (II) (ii) (Q) [D] (III) (i) (P)
Q.50 If a tangent to a suitable conic (Column 1) is found to be 𝑦 = 𝑥 + 8 and its point of contact
is (8, 16), then which of the following options is the only CORRECT combination?
[A] (I) (ii) (Q) [B] (II) (iv) (R) [C] (III) (i) (P) [D] (III) (ii) (Q)
Q.51 The tangent to a suitable conic (Column 1) at ( 3,
!
!
) is found to be 3𝑥 + 2𝑦 = 4, then
which of the following options is the only CORRECT combination?
[A] (IV) (iii) (S) [B] (IV) (iv) (S) [C] (II) (iii) (R) [D] (II) (iv) (R)
Space for rough work
Answers for the above questions
Ans for Q.49: (B) Ans for Q.50: (C) Ans for Q.51: (D)
31. 33/36 Paper-1 Code 1
Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three
columns of the following table.
Let 𝑓 𝑥 = 𝑥 + log! 𝑥 − 𝑥 log! 𝑥, 𝑥 ∈ (0, ∞).
• Column 1 contains information about zeros of 𝑓 𝑥 , 𝑓!
𝑥 and 𝑓!!
(𝑥).
• Column 2 contains information about the limiting behavior of 𝑓 𝑥 , 𝑓!
𝑥 and 𝑓!!
(𝑥) at infinity.
• Column 3 contains information about increasing/decreasing nature of 𝑓 𝑥 and 𝑓!
𝑥 .
Column 1 Column 2 Column 3
(I) 𝑓 𝑥 = 0 for some 𝑥 ∈ (1, 𝑒!
) (i) lim!→! 𝑓 𝑥 = 0 (P) 𝑓 is increasing in (0, 1)
(II) 𝑓!
𝑥 = 0 for some 𝑥 ∈ (1, 𝑒) (ii) lim!→! 𝑓 𝑥 = −∞ (Q) 𝑓 is decreasing in (𝑒, 𝑒!
)
(III) 𝑓!
𝑥 = 0 for some 𝑥 ∈ (0, 1) (iii) lim!→! 𝑓!
𝑥 = −∞ (R) 𝑓!
is increasing in (0, 1)
(IV) 𝑓!!
𝑥 = 0 for some 𝑥 ∈ (1, 𝑒) (iv) lim!→! 𝑓!!
𝑥 = 0 (S) 𝑓!
is decreasing in (𝑒, 𝑒!
)
Q.52 Which of the following options is the only CORRECT combination?
[A] (I) (i) (P) [B] (II) (ii) (Q) [C] (III) (iii) (R) [D] (IV) (iv) (S)
Q.53 Which of the following options is the only CORRECT combination?
[A] (I) (ii) (R) [B] (II) (iii) (S) [C] (III) (iv) (P) [D] (IV) (i) (S)
Q.54 Which of the following options is the only INCORRECT combination?
[A] (I) (iii) (P) [B] (II) (iv) (Q) [C] (III) (i) (R) [D] (II) (iii) (P)
END OF THE QUESTION PAPER
Space for rough work
Answers for the above questions
Ans for Q.52: (B) Ans for Q.53: (B) Ans for Q.54: (C)