SOLUTIONS TO JEE(ADVANCED)-2013, Paper -1, IIT-JEE Exam Preparation

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Page 1 Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2013 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 30 minutes, 20 minutes and 30 minutes respectively. SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 1 Time: 3 Hours Maximum Marks: 180 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General: 1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators. 2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadgets are NOT allowed inside the examination hall. 3. Write your name and roll number in the space provided on the back cover of this booklet. 4. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided separately. These parts should only be separated at the end of the examination when instructed by the invigilator. The upper sheet is a machine-gradable Objective Response Sheet (ORS) which will be retained by the invigilator. You will be allowed to take away the bottom sheet at the end of the examination. 5. Using a black ball point pen darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom duplicate sheet. B. Question Paper Format : The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 constrains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Section 2 contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. Section 3 contains 5 questions. The answer to each question is a single–digit integer, ranging from 0 to 9 (both inclusive) C. Marking Scheme: For each question in Section 1, you will be awarded 2 marks if your darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 5 Page 2 Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2013 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 30 minutes, 20 minutes and 30 minutes respectively. SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 1 Time: 3 Hours Maximum Marks: 180 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General: 1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators. 2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadgets are NOT allowed inside the examination hall. 3. Write your name and roll number in the space provided on the back cover of this booklet. 4. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided separately. These parts should only be separated at the end of the examination when instructed by the invigilator. The upper sheet is a machine-gradable Objective Response Sheet (ORS) which will be retained by the invigilator. You will be allowed to take away the bottom sheet at the end of the examination. 5. Using a black ball point pen darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom duplicate sheet. B. Question Paper Format : The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 constrains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Section 2 contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. Section 3 contains 5 questions. The answer to each question is a single–digit integer, ranging from 0 to 9 (both inclusive) C. Marking Scheme: For each question in Section 1, you will be awarded 2 marks if your darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 5 JEE(ADVANCED)2013-Paper 1-PCM-2 PAPER-1 [Code – 5] JEE(ADVANCED) 2013 SECTION – 1: (Only one option correct Type) This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct. * 1. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00 Sol. (C) F ? F ? 2L, 2R ? L, R ? 2 2 1 2 4R x R y k , k 2L L ? ? ? ? 1 2 F k x k y ? ? ? 1 2 k y x k ? = 2 * 2. The work done on a particle of mass m by a force 2 2 3/2 2 2 3/2 x y ˆ ˆ K i j (x y ) (x y ) ? ? ? ? ? ? ? ? ? (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is (A) 2K a ? (B) K a ? (C) K 2a ? (D) 0 Sol. (D) ˆ ˆ dw F dr F (dxi dyj) ? ? ? ? ? ? ? ? 2 2 3/2 2 2 3/2 xdx ydy K (x y ) (x y ) ? ? ? ? ? 2 2 2 x y a ? ? w 0 a 3 a 0 K xdx ydy a ? ? ? ? 2 2 3 K a a 2 2 a ? ? ? ? ? ? ? ? ? ? ? = 0. * 3. Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity ? and the other 2 ? . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is 2 ? ? ? ? 2 ? ? ? ? Configuration I Configuration II ? x ? (A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s PART - I: PHYSICS Page 3 Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2013 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 30 minutes, 20 minutes and 30 minutes respectively. SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 1 Time: 3 Hours Maximum Marks: 180 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General: 1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators. 2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadgets are NOT allowed inside the examination hall. 3. Write your name and roll number in the space provided on the back cover of this booklet. 4. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided separately. These parts should only be separated at the end of the examination when instructed by the invigilator. The upper sheet is a machine-gradable Objective Response Sheet (ORS) which will be retained by the invigilator. You will be allowed to take away the bottom sheet at the end of the examination. 5. Using a black ball point pen darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom duplicate sheet. B. Question Paper Format : The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 constrains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Section 2 contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. Section 3 contains 5 questions. The answer to each question is a single–digit integer, ranging from 0 to 9 (both inclusive) C. Marking Scheme: For each question in Section 1, you will be awarded 2 marks if your darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 5 JEE(ADVANCED)2013-Paper 1-PCM-2 PAPER-1 [Code – 5] JEE(ADVANCED) 2013 SECTION – 1: (Only one option correct Type) This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct. * 1. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00 Sol. (C) F ? F ? 2L, 2R ? L, R ? 2 2 1 2 4R x R y k , k 2L L ? ? ? ? 1 2 F k x k y ? ? ? 1 2 k y x k ? = 2 * 2. The work done on a particle of mass m by a force 2 2 3/2 2 2 3/2 x y ˆ ˆ K i j (x y ) (x y ) ? ? ? ? ? ? ? ? ? (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is (A) 2K a ? (B) K a ? (C) K 2a ? (D) 0 Sol. (D) ˆ ˆ dw F dr F (dxi dyj) ? ? ? ? ? ? ? ? 2 2 3/2 2 2 3/2 xdx ydy K (x y ) (x y ) ? ? ? ? ? 2 2 2 x y a ? ? w 0 a 3 a 0 K xdx ydy a ? ? ? ? 2 2 3 K a a 2 2 a ? ? ? ? ? ? ? ? ? ? ? = 0. * 3. Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity ? and the other 2 ? . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is 2 ? ? ? ? 2 ? ? ? ? Configuration I Configuration II ? x ? (A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s PART - I: PHYSICS JEE(ADVANCED)2013-Paper 1-PCM-3 Sol. (A) 1 L L 3L R A 2 A 2 A ? ? ? ? ? ? 2 1 1 1 3 A L L R L A 2 A ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 L R 3 A ? ? 1 2 Q Q ? ? ? 1 2 1 2 T T t t R R ? ? ? ? 2 2 1 1 R t t R ? = 2 sec. 4. A ray of light travelling in the direction 1 ˆ ˆ (i 3j) 2 ? is incident on a plane mirror. After reflection, it travels along the direction 1 ˆ ˆ (i 3j). 2 ? The angle of incidence is (A) 30° (B) 45° (C) 60° (D) 75° Sol. (A) Let angle between the directions of incident ray and reflected ray be ? 1 1 ˆ ˆ ˆ ˆ cos (i 3j) (i 3j) 2 2 ? ? ? ? ? 1 cos 2 ? ? ? 120 ? ? ? ? * 5. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is (A) 5.112 cm (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm Sol. (B) Main scale division (s) = .05 cm Vernier scale division (v) = 49 100 = .049 Least count = .05 – .049 = .001 cm Diameter: 5.10 + 24 × .001 = 5.124 cm Page 4 Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2013 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 30 minutes, 20 minutes and 30 minutes respectively. SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 1 Time: 3 Hours Maximum Marks: 180 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General: 1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators. 2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadgets are NOT allowed inside the examination hall. 3. Write your name and roll number in the space provided on the back cover of this booklet. 4. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided separately. These parts should only be separated at the end of the examination when instructed by the invigilator. The upper sheet is a machine-gradable Objective Response Sheet (ORS) which will be retained by the invigilator. You will be allowed to take away the bottom sheet at the end of the examination. 5. Using a black ball point pen darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom duplicate sheet. B. Question Paper Format : The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 constrains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Section 2 contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. Section 3 contains 5 questions. The answer to each question is a single–digit integer, ranging from 0 to 9 (both inclusive) C. Marking Scheme: For each question in Section 1, you will be awarded 2 marks if your darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 5 JEE(ADVANCED)2013-Paper 1-PCM-2 PAPER-1 [Code – 5] JEE(ADVANCED) 2013 SECTION – 1: (Only one option correct Type) This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct. * 1. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00 Sol. (C) F ? F ? 2L, 2R ? L, R ? 2 2 1 2 4R x R y k , k 2L L ? ? ? ? 1 2 F k x k y ? ? ? 1 2 k y x k ? = 2 * 2. The work done on a particle of mass m by a force 2 2 3/2 2 2 3/2 x y ˆ ˆ K i j (x y ) (x y ) ? ? ? ? ? ? ? ? ? (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is (A) 2K a ? (B) K a ? (C) K 2a ? (D) 0 Sol. (D) ˆ ˆ dw F dr F (dxi dyj) ? ? ? ? ? ? ? ? 2 2 3/2 2 2 3/2 xdx ydy K (x y ) (x y ) ? ? ? ? ? 2 2 2 x y a ? ? w 0 a 3 a 0 K xdx ydy a ? ? ? ? 2 2 3 K a a 2 2 a ? ? ? ? ? ? ? ? ? ? ? = 0. * 3. Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity ? and the other 2 ? . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is 2 ? ? ? ? 2 ? ? ? ? Configuration I Configuration II ? x ? (A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s PART - I: PHYSICS JEE(ADVANCED)2013-Paper 1-PCM-3 Sol. (A) 1 L L 3L R A 2 A 2 A ? ? ? ? ? ? 2 1 1 1 3 A L L R L A 2 A ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 L R 3 A ? ? 1 2 Q Q ? ? ? 1 2 1 2 T T t t R R ? ? ? ? 2 2 1 1 R t t R ? = 2 sec. 4. A ray of light travelling in the direction 1 ˆ ˆ (i 3j) 2 ? is incident on a plane mirror. After reflection, it travels along the direction 1 ˆ ˆ (i 3j). 2 ? The angle of incidence is (A) 30° (B) 45° (C) 60° (D) 75° Sol. (A) Let angle between the directions of incident ray and reflected ray be ? 1 1 ˆ ˆ ˆ ˆ cos (i 3j) (i 3j) 2 2 ? ? ? ? ? 1 cos 2 ? ? ? 120 ? ? ? ? * 5. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is (A) 5.112 cm (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm Sol. (B) Main scale division (s) = .05 cm Vernier scale division (v) = 49 100 = .049 Least count = .05 – .049 = .001 cm Diameter: 5.10 + 24 × .001 = 5.124 cm JEE(ADVANCED)2013-Paper 1-PCM-4 * 6. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9 Sol. (D) PV = nRT = m RT M ? PM = ?RT 1 1 1 1 1 2 2 2 2 2 P M P M 4 2 8 P M P M 3 3 9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Here ? 1 and ? 2 are the densities of gases in the vessel containing the mixture. 7. In the Young’s double slit experiment using a monochromatic light of wavelength ?, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is (A) ? ? 2n 1 2 ? ? (B) ? ? 2n 1 4 ? ? (C) ? ? 2n 1 8 ? ? (D) ? ? 2n 1 16 ? ? Sol. (B) 2 max m I I cos 2 2 ? ? ? ? ? ? ? ? ? 1 cos 2 2 ? ? ? ? ? ? ? ? ? 2 4 ? ? ? ? ? ? 2n 1 2 ? ? ? ? ? x 2 ? ? ? ? ? = (2n 1) (2n 1) 2 2 4 ? ? ? ? ? ? ? ? 8. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2 3 times the wavelength in free space. The radius of the curved surface of the lens is (A) 1 m (B) 2 m (C) 3 m (D) 4 m Sol. (C) 8. a m 3 2 ? ? ? ? ? ? 1 1 1 f R 2R ? ? ? ? ? 1 1 1 f v u ? ? 24 m ? 8 m ? ? 1 1 1 8 24 2R ? ? ? ? 3 1 1 24 2R ? ? ? R = 3 m Page 5 Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2013 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 30 minutes, 20 minutes and 30 minutes respectively. SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 1 Time: 3 Hours Maximum Marks: 180 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General: 1. This booklet is your Question Paper. Do not break the seals of this booklet before being instructed to do so by the invigilators. 2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadgets are NOT allowed inside the examination hall. 3. Write your name and roll number in the space provided on the back cover of this booklet. 4. Answers to the questions and personal details are to be filled on a two-part carbon-less paper, which is provided separately. These parts should only be separated at the end of the examination when instructed by the invigilator. The upper sheet is a machine-gradable Objective Response Sheet (ORS) which will be retained by the invigilator. You will be allowed to take away the bottom sheet at the end of the examination. 5. Using a black ball point pen darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is created on the bottom duplicate sheet. B. Question Paper Format : The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 constrains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Section 2 contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. Section 3 contains 5 questions. The answer to each question is a single–digit integer, ranging from 0 to 9 (both inclusive) C. Marking Scheme: For each question in Section 1, you will be awarded 2 marks if your darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 5 JEE(ADVANCED)2013-Paper 1-PCM-2 PAPER-1 [Code – 5] JEE(ADVANCED) 2013 SECTION – 1: (Only one option correct Type) This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct. * 1. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00 Sol. (C) F ? F ? 2L, 2R ? L, R ? 2 2 1 2 4R x R y k , k 2L L ? ? ? ? 1 2 F k x k y ? ? ? 1 2 k y x k ? = 2 * 2. The work done on a particle of mass m by a force 2 2 3/2 2 2 3/2 x y ˆ ˆ K i j (x y ) (x y ) ? ? ? ? ? ? ? ? ? (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is (A) 2K a ? (B) K a ? (C) K 2a ? (D) 0 Sol. (D) ˆ ˆ dw F dr F (dxi dyj) ? ? ? ? ? ? ? ? 2 2 3/2 2 2 3/2 xdx ydy K (x y ) (x y ) ? ? ? ? ? 2 2 2 x y a ? ? w 0 a 3 a 0 K xdx ydy a ? ? ? ? 2 2 3 K a a 2 2 a ? ? ? ? ? ? ? ? ? ? ? = 0. * 3. Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity ? and the other 2 ? . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is 2 ? ? ? ? 2 ? ? ? ? Configuration I Configuration II ? x ? (A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s PART - I: PHYSICS JEE(ADVANCED)2013-Paper 1-PCM-3 Sol. (A) 1 L L 3L R A 2 A 2 A ? ? ? ? ? ? 2 1 1 1 3 A L L R L A 2 A ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 L R 3 A ? ? 1 2 Q Q ? ? ? 1 2 1 2 T T t t R R ? ? ? ? 2 2 1 1 R t t R ? = 2 sec. 4. A ray of light travelling in the direction 1 ˆ ˆ (i 3j) 2 ? is incident on a plane mirror. After reflection, it travels along the direction 1 ˆ ˆ (i 3j). 2 ? The angle of incidence is (A) 30° (B) 45° (C) 60° (D) 75° Sol. (A) Let angle between the directions of incident ray and reflected ray be ? 1 1 ˆ ˆ ˆ ˆ cos (i 3j) (i 3j) 2 2 ? ? ? ? ? 1 cos 2 ? ? ? 120 ? ? ? ? * 5. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is (A) 5.112 cm (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm Sol. (B) Main scale division (s) = .05 cm Vernier scale division (v) = 49 100 = .049 Least count = .05 – .049 = .001 cm Diameter: 5.10 + 24 × .001 = 5.124 cm JEE(ADVANCED)2013-Paper 1-PCM-4 * 6. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9 Sol. (D) PV = nRT = m RT M ? PM = ?RT 1 1 1 1 1 2 2 2 2 2 P M P M 4 2 8 P M P M 3 3 9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Here ? 1 and ? 2 are the densities of gases in the vessel containing the mixture. 7. In the Young’s double slit experiment using a monochromatic light of wavelength ?, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is (A) ? ? 2n 1 2 ? ? (B) ? ? 2n 1 4 ? ? (C) ? ? 2n 1 8 ? ? (D) ? ? 2n 1 16 ? ? Sol. (B) 2 max m I I cos 2 2 ? ? ? ? ? ? ? ? ? 1 cos 2 2 ? ? ? ? ? ? ? ? ? 2 4 ? ? ? ? ? ? 2n 1 2 ? ? ? ? ? x 2 ? ? ? ? ? = (2n 1) (2n 1) 2 2 4 ? ? ? ? ? ? ? ? 8. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2 3 times the wavelength in free space. The radius of the curved surface of the lens is (A) 1 m (B) 2 m (C) 3 m (D) 4 m Sol. (C) 8. a m 3 2 ? ? ? ? ? ? 1 1 1 f R 2R ? ? ? ? ? 1 1 1 f v u ? ? 24 m ? 8 m ? ? 1 1 1 8 24 2R ? ? ? ? 3 1 1 24 2R ? ? ? R = 3 m JEE(ADVANCED)2013-Paper 1-PCM-5 * 9. A particle of mass m is projected from the ground with an initial speed u 0 at an angle ? with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u 0 . The angle that the composite system makes with the horizontal immediately after the collision is (A) 4 ? (B) 4 ? ? ? (C) 4 ? ? ? (D) 2 ? Sol. (A) Velocity of particle performing projectile motion at highest point = v 1 = v 0 cos ? Velocity of particle thrown vertically upwards at the position of collision = 2 2 2 2 2 0 u sin v u 2g 2g ? ? ? = 0 v cos ? So, from conservation of momentum mv 0 ? mu 0 cos ? ? ? ? 0 0 mv cos tan 1 mu cos ? ? ? ? ? ? ? = ?/4 10. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 ? 10 8 m/s. The final momentum of the object is (A) 0.3 ? 10 ?17 kg ms ?1 (B) 1.0 ? 10 ?17 kg ms ?1 (C) 3.0 ? 10 ?17 kg ms ?1 (B) 9.0 ? 10 ?17 kg ms ?1 Sol. (B) t = 9 100 10 ? ? sec, 3 P 30 10 ? ? ? Watt, 8 C C 10 ? ? m/s Momentum = 3 9 8 Pt 30 10 100 10 C 3 10 ? ? ? ? ? ? ? = 1.0 ? 10 ?17 kg ms ?1 SECTION – 2 : (One or more options correct Type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 11. In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S 1 is pressed first to fully charge the capacitor C 1 and then released. The switch S 2 is then pressed to charge the capacitor C 2 . After some time, S 2 is released and then S 3 is pressed. After some time, (A) the charge on the upper plate of C 1 is 2CV 0 . (B) the charge on the upper plate of C 1 is CV 0 . (C) the charge on the upper plate of C 1 is 0. (D) The charge on the upper plate of C 2 is ?CV 0 . S 1 ? S 2 ? S 3 ? 2V 0 ? V 0 ? C 1 ? C 2 ? Sol. (B, D) After switch S 1 is closed, C 1 is charged by 2CV 0 , when switch S 2 is closed, C 1 and C 2 both have upper plate charge CV 0 . When S 3 is closed, then upper plate of C 2 becomes charged by ?CV 0 and lower plate by +CV 0 .Read More