Page 1 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. 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 â€˜*â€™, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics and Physics are 22 minutes, 21 minutes and 25 minutes respectively. FIITJEE SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 2 Time: 3 Hours Maximum Marks: 180ase 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 6. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct 7. Section 2 contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE correct answer among the four choices (A), (B), (C) and (D). 8. Section 3 contains 4 multiple choice questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE CORRECT ANSWER among the four choices (A), (B), (C) and (D). C. Marking Scheme 9. For each question in Section 1, you will be awarded 3 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 (â€“1) mark will be awarded. 10. For each question Section 2 and 3, you will be awarded 3 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 (â€“1) mark will be awarded. 3 Page 2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. 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 â€˜*â€™, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics and Physics are 22 minutes, 21 minutes and 25 minutes respectively. FIITJEE SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 2 Time: 3 Hours Maximum Marks: 180ase 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 6. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct 7. Section 2 contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE correct answer among the four choices (A), (B), (C) and (D). 8. Section 3 contains 4 multiple choice questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE CORRECT ANSWER among the four choices (A), (B), (C) and (D). C. Marking Scheme 9. For each question in Section 1, you will be awarded 3 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 (â€“1) mark will be awarded. 10. For each question Section 2 and 3, you will be awarded 3 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 (â€“1) mark will be awarded. 3 JEE(ADVANCED)2013-Paper 2-PCM-2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. SECTION â€“ 1 (One or more options correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. *1. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are) (A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 4 L (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 2 L . (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GM L (D) The energy of the mass m remains constant. Sol. (B) 2 2GMm 1 mv 0 L 2 ? ? ? ? GM v 2 L ? Note: The energy of mass â€˜mâ€™ means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) â€“ which is the potential energy of the system. *2. A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u 0 . When the speed of the particle is 0.5 u 0 . It collides elastically with a rigid wall. After this collision, (A) the speed of the particle when it returns to its equilibrium position is u 0 . (B) the time at which the particle passes through the equilibrium position for the first time is m t . k ? ? (C) the time at which the maximum compression of the spring occurs is 4 m t 3 k ? ? . (D) the time at which the particle passes through the equilibrium position for the second time is 5 m t . 3 k ? ? Sol. (A, D) 0 v u sin t ? ? (suppose t 1 is the time of collision) 0 0 1 u u cos t 2 ? ? ? 1 t 3 ? ? ? Now the particle returns to equilibrium position at time t 2 = 2t 1 i.e. 2 3 ? ? with the same mechanical energy i.e. its speed will u 0 . Let t 3 is the time at which the particle passes through the equilibrium position for the second time. PART - I: PHYSICS Page 3 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. 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 â€˜*â€™, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics and Physics are 22 minutes, 21 minutes and 25 minutes respectively. FIITJEE SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 2 Time: 3 Hours Maximum Marks: 180ase 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 6. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct 7. Section 2 contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE correct answer among the four choices (A), (B), (C) and (D). 8. Section 3 contains 4 multiple choice questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE CORRECT ANSWER among the four choices (A), (B), (C) and (D). C. Marking Scheme 9. For each question in Section 1, you will be awarded 3 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 (â€“1) mark will be awarded. 10. For each question Section 2 and 3, you will be awarded 3 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 (â€“1) mark will be awarded. 3 JEE(ADVANCED)2013-Paper 2-PCM-2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. SECTION â€“ 1 (One or more options correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. *1. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are) (A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 4 L (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 2 L . (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GM L (D) The energy of the mass m remains constant. Sol. (B) 2 2GMm 1 mv 0 L 2 ? ? ? ? GM v 2 L ? Note: The energy of mass â€˜mâ€™ means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) â€“ which is the potential energy of the system. *2. A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u 0 . When the speed of the particle is 0.5 u 0 . It collides elastically with a rigid wall. After this collision, (A) the speed of the particle when it returns to its equilibrium position is u 0 . (B) the time at which the particle passes through the equilibrium position for the first time is m t . k ? ? (C) the time at which the maximum compression of the spring occurs is 4 m t 3 k ? ? . (D) the time at which the particle passes through the equilibrium position for the second time is 5 m t . 3 k ? ? Sol. (A, D) 0 v u sin t ? ? (suppose t 1 is the time of collision) 0 0 1 u u cos t 2 ? ? ? 1 t 3 ? ? ? Now the particle returns to equilibrium position at time t 2 = 2t 1 i.e. 2 3 ? ? with the same mechanical energy i.e. its speed will u 0 . Let t 3 is the time at which the particle passes through the equilibrium position for the second time. PART - I: PHYSICS JEE(ADVANCED)2013-Paper 2-PCM-3 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. ? 3 1 T t 2t 2 ? ? 2 5 3 3 ? ? ? ? ? ? ? ? ? 5 m 3 k ? ? Energy of particle and spring remains conserved. 3. A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are) (A) In the region 0 < r < R, the magnetic field is non-zero (B) In the region R < r < 2R, the magnetic field is along the common axis. (C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis. (D) In the region r > 2R, the magnetic field is non-zero. Sol. (A, D) Due to field of solenoid is non zero in region 0 < r < R and non zero in region r>2R due to conductor. *4. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency 1 f . An observer in the other vehicle hears the frequency of the whistle to be 2 f . The speed of sound in still air is V. The correct statement(s) is (are) (A) If the wind blows from the observer to the source, 2 1 f f ? . (B) If the wind blows from the source to the observer, 2 1 f f ? . (C) If the wind blows from observer to the source, 2 1 f f ? . (D) If the wind blows from the source to the observer 2 1 f f ? . Sol. (A, B) If wind blows from source to observer 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? When wind blows from observer towards source 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? In both cases, 2 1 f f ? . *5. Using the expression 2d sin ? = ?, one calculates the values of d by measuring the corresponding angles ? in the range ? to 90°. The wavelength ? is exactly known and the error in ? is constant for all values of ?. As ? increases from 0°, (A) the absolute error in d remains constant. (B) the absolute error in d increases (C) the fractional error in d remains constant. (D) the fractional error in d decreases. Sol. (D) d 2sin ? ? ? ln d ln ln sin 2 ? ? ? ? ? ? ? ? ? ? Page 4 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. 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 â€˜*â€™, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics and Physics are 22 minutes, 21 minutes and 25 minutes respectively. FIITJEE SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 2 Time: 3 Hours Maximum Marks: 180ase 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 6. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct 7. Section 2 contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE correct answer among the four choices (A), (B), (C) and (D). 8. Section 3 contains 4 multiple choice questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE CORRECT ANSWER among the four choices (A), (B), (C) and (D). C. Marking Scheme 9. For each question in Section 1, you will be awarded 3 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 (â€“1) mark will be awarded. 10. For each question Section 2 and 3, you will be awarded 3 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 (â€“1) mark will be awarded. 3 JEE(ADVANCED)2013-Paper 2-PCM-2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. SECTION â€“ 1 (One or more options correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. *1. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are) (A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 4 L (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 2 L . (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GM L (D) The energy of the mass m remains constant. Sol. (B) 2 2GMm 1 mv 0 L 2 ? ? ? ? GM v 2 L ? Note: The energy of mass â€˜mâ€™ means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) â€“ which is the potential energy of the system. *2. A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u 0 . When the speed of the particle is 0.5 u 0 . It collides elastically with a rigid wall. After this collision, (A) the speed of the particle when it returns to its equilibrium position is u 0 . (B) the time at which the particle passes through the equilibrium position for the first time is m t . k ? ? (C) the time at which the maximum compression of the spring occurs is 4 m t 3 k ? ? . (D) the time at which the particle passes through the equilibrium position for the second time is 5 m t . 3 k ? ? Sol. (A, D) 0 v u sin t ? ? (suppose t 1 is the time of collision) 0 0 1 u u cos t 2 ? ? ? 1 t 3 ? ? ? Now the particle returns to equilibrium position at time t 2 = 2t 1 i.e. 2 3 ? ? with the same mechanical energy i.e. its speed will u 0 . Let t 3 is the time at which the particle passes through the equilibrium position for the second time. PART - I: PHYSICS JEE(ADVANCED)2013-Paper 2-PCM-3 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. ? 3 1 T t 2t 2 ? ? 2 5 3 3 ? ? ? ? ? ? ? ? ? 5 m 3 k ? ? Energy of particle and spring remains conserved. 3. A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are) (A) In the region 0 < r < R, the magnetic field is non-zero (B) In the region R < r < 2R, the magnetic field is along the common axis. (C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis. (D) In the region r > 2R, the magnetic field is non-zero. Sol. (A, D) Due to field of solenoid is non zero in region 0 < r < R and non zero in region r>2R due to conductor. *4. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency 1 f . An observer in the other vehicle hears the frequency of the whistle to be 2 f . The speed of sound in still air is V. The correct statement(s) is (are) (A) If the wind blows from the observer to the source, 2 1 f f ? . (B) If the wind blows from the source to the observer, 2 1 f f ? . (C) If the wind blows from observer to the source, 2 1 f f ? . (D) If the wind blows from the source to the observer 2 1 f f ? . Sol. (A, B) If wind blows from source to observer 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? When wind blows from observer towards source 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? In both cases, 2 1 f f ? . *5. Using the expression 2d sin ? = ?, one calculates the values of d by measuring the corresponding angles ? in the range ? to 90°. The wavelength ? is exactly known and the error in ? is constant for all values of ?. As ? increases from 0°, (A) the absolute error in d remains constant. (B) the absolute error in d increases (C) the fractional error in d remains constant. (D) the fractional error in d decreases. Sol. (D) d 2sin ? ? ? ln d ln ln sin 2 ? ? ? ? ? ? ? ? ? ? JEE(ADVANCED)2013-Paper 2-PCM-4 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. d cos d 0 d sin ? ? ? ? ? ? max d d ? ? ? ? ? ? ? = cot ? ? ? ? Also max ( d) dcot ? ? ? ? ? cot 2sin ? ? ? ? ? 2 cos 2 sin ? ? ? ? ? ? As ? increases cot ? decreases and 2 cos sin ? ? also decreases. 6. Two non-conducting spheres of radii R 1 and R 2 and carrying uniform volume charge densities + ? and â€“ ?, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region, (A) the electrostatic field is zero (B) the electrostatic potential is constant (C) the electrostatic field is constant in magnitude (D) the electrostatic field has same direction â€“ ? ? R 1 R 2 Sol. (C, D) In triangle PC 1 C 2 2 1 r d r ? ? ? ? ? The electrostatic field at point P is ? ? 3 3 1 2 2 1 3 3 1 2 4 4 K R r K R r 3 3 E R R ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 1 4 E K (r r ) 3 ? ? ? ? ? ? ? 0 E d 3 ? ? ? ? ? â€“ ? ? C 1 R 2 1 r ? 2 r ? R 1 d P C 2 *7. The figure shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation. (A) the rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T. (B) heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400 â€“ 500 K. (C) there is no change in the rate of heat absorption in range 400 â€“ 500 K. (D) the rate of heat absorption increases in the range 200 â€“ 300 K. C ? 100 ? 200 ? 300 ? 400 ? 500 ? T (K) ? Page 5 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. 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 â€˜*â€™, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics and Physics are 22 minutes, 21 minutes and 25 minutes respectively. FIITJEE SOLUTIONS TO JEE(ADVANCED)-2013 CODE PAPER 2 Time: 3 Hours Maximum Marks: 180ase 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 6. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections. Section 1 contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct 7. Section 2 contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE correct answer among the four choices (A), (B), (C) and (D). 8. Section 3 contains 4 multiple choice questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has ONLY ONE CORRECT ANSWER among the four choices (A), (B), (C) and (D). C. Marking Scheme 9. For each question in Section 1, you will be awarded 3 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 (â€“1) mark will be awarded. 10. For each question Section 2 and 3, you will be awarded 3 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 (â€“1) mark will be awarded. 3 JEE(ADVANCED)2013-Paper 2-PCM-2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. SECTION â€“ 1 (One or more options correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. *1. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are) (A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 4 L (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is GM 2 L . (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2GM L (D) The energy of the mass m remains constant. Sol. (B) 2 2GMm 1 mv 0 L 2 ? ? ? ? GM v 2 L ? Note: The energy of mass â€˜mâ€™ means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) â€“ which is the potential energy of the system. *2. A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u 0 . When the speed of the particle is 0.5 u 0 . It collides elastically with a rigid wall. After this collision, (A) the speed of the particle when it returns to its equilibrium position is u 0 . (B) the time at which the particle passes through the equilibrium position for the first time is m t . k ? ? (C) the time at which the maximum compression of the spring occurs is 4 m t 3 k ? ? . (D) the time at which the particle passes through the equilibrium position for the second time is 5 m t . 3 k ? ? Sol. (A, D) 0 v u sin t ? ? (suppose t 1 is the time of collision) 0 0 1 u u cos t 2 ? ? ? 1 t 3 ? ? ? Now the particle returns to equilibrium position at time t 2 = 2t 1 i.e. 2 3 ? ? with the same mechanical energy i.e. its speed will u 0 . Let t 3 is the time at which the particle passes through the equilibrium position for the second time. PART - I: PHYSICS JEE(ADVANCED)2013-Paper 2-PCM-3 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. ? 3 1 T t 2t 2 ? ? 2 5 3 3 ? ? ? ? ? ? ? ? ? 5 m 3 k ? ? Energy of particle and spring remains conserved. 3. A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are) (A) In the region 0 < r < R, the magnetic field is non-zero (B) In the region R < r < 2R, the magnetic field is along the common axis. (C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis. (D) In the region r > 2R, the magnetic field is non-zero. Sol. (A, D) Due to field of solenoid is non zero in region 0 < r < R and non zero in region r>2R due to conductor. *4. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency 1 f . An observer in the other vehicle hears the frequency of the whistle to be 2 f . The speed of sound in still air is V. The correct statement(s) is (are) (A) If the wind blows from the observer to the source, 2 1 f f ? . (B) If the wind blows from the source to the observer, 2 1 f f ? . (C) If the wind blows from observer to the source, 2 1 f f ? . (D) If the wind blows from the source to the observer 2 1 f f ? . Sol. (A, B) If wind blows from source to observer 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? When wind blows from observer towards source 2 1 V w u f f V w u ? ? ? ? ? ? ? ? ? ? ? In both cases, 2 1 f f ? . *5. Using the expression 2d sin ? = ?, one calculates the values of d by measuring the corresponding angles ? in the range ? to 90°. The wavelength ? is exactly known and the error in ? is constant for all values of ?. As ? increases from 0°, (A) the absolute error in d remains constant. (B) the absolute error in d increases (C) the fractional error in d remains constant. (D) the fractional error in d decreases. Sol. (D) d 2sin ? ? ? ln d ln ln sin 2 ? ? ? ? ? ? ? ? ? ? JEE(ADVANCED)2013-Paper 2-PCM-4 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. d cos d 0 d sin ? ? ? ? ? ? max d d ? ? ? ? ? ? ? = cot ? ? ? ? Also max ( d) dcot ? ? ? ? ? cot 2sin ? ? ? ? ? 2 cos 2 sin ? ? ? ? ? ? As ? increases cot ? decreases and 2 cos sin ? ? also decreases. 6. Two non-conducting spheres of radii R 1 and R 2 and carrying uniform volume charge densities + ? and â€“ ?, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region, (A) the electrostatic field is zero (B) the electrostatic potential is constant (C) the electrostatic field is constant in magnitude (D) the electrostatic field has same direction â€“ ? ? R 1 R 2 Sol. (C, D) In triangle PC 1 C 2 2 1 r d r ? ? ? ? ? The electrostatic field at point P is ? ? 3 3 1 2 2 1 3 3 1 2 4 4 K R r K R r 3 3 E R R ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 1 4 E K (r r ) 3 ? ? ? ? ? ? ? 0 E d 3 ? ? ? ? ? â€“ ? ? C 1 R 2 1 r ? 2 r ? R 1 d P C 2 *7. The figure shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation. (A) the rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T. (B) heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400 â€“ 500 K. (C) there is no change in the rate of heat absorption in range 400 â€“ 500 K. (D) the rate of heat absorption increases in the range 200 â€“ 300 K. C ? 100 ? 200 ? 300 ? 400 ? 500 ? T (K) ? JEE(ADVANCED)2013-Paper 2-PCM-5 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. Sol. (A, B, C, D) Option (A) is correct because the graph between (0 â€“ 100 K) appears to be a straight line upto a reasonable approximation. Option (B) is correct because area under the curve in the temperature range (0 ? 100 K) is less than in range (400 ? 500 K.) Option (C) is correct because the graph of C versus T is constant in the temperature range (400 ? 500 K) Option (D) is correct because in the temperature range (200 â€“ 300 K) specific heat capacity increases with temperature. 8. The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a 0 where a 0 is the Bohr radius. Its orbital angular momentum is 3h 2 ? . It is given that h is Planckâ€™s constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are) (A) 9 32R (B) 9 16R (C) 9 5R (D) 4 3R Sol. (A, C) Given data 2 0 0 n 4.5a a Z ? â€¦(i) nh 3h 2 2 ? ? ? â€¦(ii) So n = 3 and z = 2 So possible wavelength are 2 2 2 1 1 1 1 RZ 1 3 ? ? ? ? ? ? ? ? ? ? 1 9 32R ? ? 2 2 2 2 1 1 1 RZ 1 2 ? ? ? ? ? ? ? ? ? ? 2 1 3R ? ? 2 2 2 3 1 1 1 RZ 2 3 ? ? ? ? ? ? ? ? ? ? 3 9 5R ? ? SECTION â€“ 2 : (Paragraph Type) This section contains 4 paragraphs each describing theory, experiment, date etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of paragraph has only one correct answer along the four choice (A), (B), (C) and (D). Paragraph for Questions 9 to 10 A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s ?2 ). R ? R ? P ? Q ? 30 ? ?Read More

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