Class 11th & 12th Physics, Chemistry & Mathematics exam paper to practice for preparation of JEE Advanced 2019 exam by expert faculty. This is previous year paper on JEE Advanced exam. You can download free from https://bit.ly/2UsDFQK
An exact solution of einstein equations for interior field of an anisotropic ...eSAT Journals
Abstract
In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at
the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an
anisotropic fluid.
The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space
constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The
material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is
shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial
pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically.
Key Words: Cosmology, Anisotropic fluid sphere, Radial pressure, Radial density, Relativistic model.
This document provides solutions to the JEE Advanced 2013 paper 2 exam with code 0. It includes the answer key and detailed solutions for physics, chemistry, and math questions. The document is divided into multiple sections. Section 1 contains multiple choice questions where one or more options may be correct. Section 2 contains paragraphs describing experiments or concepts followed by related multiple choice questions with a single correct answer for each question. The document provides the questions, answers, and explanations for each question to help students understand the solutions.
In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit. We use negativity as a measure of entanglement in our study. We apply magnetic field, uniform and nonuniform field, on it. The results show that the entanglement decreases with increase in temperature. Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases. We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles. Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.
applications of second order differential equationsly infinitryx
1) Second-order differential equations are used to model vibrating springs and electric circuits. They describe oscillations, vibrations, and resonance.
2) Springs obey Hooke's law, resulting in a second-order differential equation relating position to time. The solutions describe simple harmonic motion.
3) Damping forces can be added, resulting in overdamped, critically damped, or underdamped systems with different behavior.
Using resonant ultrasound spectroscopy (RUS), the author will determine the complete elastic constant matrices of two thermoelectric single crystal samples, Ce.75Fe3CoSb12 and CeFe4Sb12. RUS involves measuring the resonant frequencies of a sample's vibrations, which depend on the sample's elastic constants, shape, orientation, and density. The author aims to obtain the elastic moduli from a single RUS spectrum for each sample. Understanding the elastic properties may help identify better thermoelectric materials by correlating low elastic stiffness with low thermal conductivity and higher thermoelectric efficiency. The author will compute the resonant frequencies using the samples' properties and compare to measurements.
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
This document contains an unsolved physics paper from 2009 for the IIT JEE exam. It has 4 sections - multiple choice, multiple answer, paragraph and matrix match questions. The multiple choice section has 8 questions on topics like simple harmonic motion, electric fields and magnetic fields. The multiple answer section has 5 questions involving circuits and gas properties. The paragraph section has 2 passages with 5 total questions on quantum confinement and nuclear fusion. The matrix match section has 2 questions matching physical statements and systems. The document provides a physics practice test to help students prepare for the IIT JEE exam.
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.
An exact solution of einstein equations for interior field of an anisotropic ...eSAT Journals
Abstract
In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at
the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an
anisotropic fluid.
The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space
constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The
material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is
shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial
pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically.
Key Words: Cosmology, Anisotropic fluid sphere, Radial pressure, Radial density, Relativistic model.
This document provides solutions to the JEE Advanced 2013 paper 2 exam with code 0. It includes the answer key and detailed solutions for physics, chemistry, and math questions. The document is divided into multiple sections. Section 1 contains multiple choice questions where one or more options may be correct. Section 2 contains paragraphs describing experiments or concepts followed by related multiple choice questions with a single correct answer for each question. The document provides the questions, answers, and explanations for each question to help students understand the solutions.
In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit. We use negativity as a measure of entanglement in our study. We apply magnetic field, uniform and nonuniform field, on it. The results show that the entanglement decreases with increase in temperature. Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases. We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles. Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.
applications of second order differential equationsly infinitryx
1) Second-order differential equations are used to model vibrating springs and electric circuits. They describe oscillations, vibrations, and resonance.
2) Springs obey Hooke's law, resulting in a second-order differential equation relating position to time. The solutions describe simple harmonic motion.
3) Damping forces can be added, resulting in overdamped, critically damped, or underdamped systems with different behavior.
Using resonant ultrasound spectroscopy (RUS), the author will determine the complete elastic constant matrices of two thermoelectric single crystal samples, Ce.75Fe3CoSb12 and CeFe4Sb12. RUS involves measuring the resonant frequencies of a sample's vibrations, which depend on the sample's elastic constants, shape, orientation, and density. The author aims to obtain the elastic moduli from a single RUS spectrum for each sample. Understanding the elastic properties may help identify better thermoelectric materials by correlating low elastic stiffness with low thermal conductivity and higher thermoelectric efficiency. The author will compute the resonant frequencies using the samples' properties and compare to measurements.
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
This document contains an unsolved physics paper from 2009 for the IIT JEE exam. It has 4 sections - multiple choice, multiple answer, paragraph and matrix match questions. The multiple choice section has 8 questions on topics like simple harmonic motion, electric fields and magnetic fields. The multiple answer section has 5 questions involving circuits and gas properties. The paragraph section has 2 passages with 5 total questions on quantum confinement and nuclear fusion. The matrix match section has 2 questions matching physical statements and systems. The document provides a physics practice test to help students prepare for the IIT JEE exam.
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.
Effect of an Inclined Magnetic Field on Peristaltic Flow of Williamson Fluid ...QUESTJOURNAL
ABSTRACT: This paper deals with the influence ofinclined magnetic field on peristaltic flow of an incompressible Williamson fluid in an inclined channel with heat and mass transfer. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
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.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Influence of MHD on Unsteady Helical Flows of Generalized Oldoyd-B Fluid betw...IJERA Editor
Considering a fractional derivative model for unsteady magetohydrodynamic (MHD)helical flows of an
Oldoyd-B fluid in concentric cylinders and circular cylinder are studied by using finite Hankel and Laplace
transforms .The solution of velocity fields and the shear stresses of unsteady magetohydrodynamic
(MHD)helical flows of an Oldoyd-B fluid in an annular pipe are obtained under series form in terms of
Mittag –leffler function,satisfy all imposed initial and boundary condition , Finally the influence of model
parameters on the velocity and shear stress are analyzed by graphical illustrations.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
The document contains 14 chemistry questions and their solutions. The questions cover topics like organic reactions, estimation of nitrogen content, precipitation of salts, uses of additives in soaps, properties of metal nitrates, bond orders, atomic radii trends, activation energy determination, isoelectronic and isostructural species, organic compound identification based on tests, and magnetic moments. The solutions provided explain the reasoning for the answers in 2-3 sentences each.
Lesson 15: Exponential Growth and Decay (Section 041 handout)Matthew Leingang
Many problems in nature are expressible in terms of a certain differential equation that has a solution in terms of exponential functions. We look at the equation in general and some fun applications, including radioactivity, cooling, and interest.
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
Outgoing ingoingkleingordon spvmforminit_proceedfromfoxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfrom12dec18foxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
This document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. The document lists properties of parallelograms, including: opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; if one angle is a right angle, all angles are right angles. It also states that the diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Examples demonstrate using these properties to find missing measures and intersection points of diagonals.
Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyr...IOSR Journals
In this paper we have obtained axially symmetric Bianchi type-I cosmological models for perfect
fluid distribution in the context of Lyra’s manifold. Exact solutions of the field equations are obtained by
assuming the expansion in the model is proportional to the shear . This leads to the condition
A Bn
where A and B are scale factors and n( 0) is a constant. Some kinematical and physical parameters of the
model have been discussed. The solutions are compatible with recent observations.
This document discusses solutions to the Klein-Gordon equation in Schwarzschild spacetime near a black hole's event horizon. Very near the horizon, the radial Klein-Gordon equation can be approximated as an oscillatory solution in Regge-Wheeler coordinates. The time and radial solutions are then expressed in terms of outgoing and ingoing coordinates, which leads to outgoing and ingoing waves with different analytic properties on either side of the event horizon.
This document discusses solutions to the Klein-Gordon equation in Schwarzschild spacetime near a black hole's event horizon. Very near the horizon, the radial Klein-Gordon equation can be approximated as an oscillatory solution in Regge-Wheeler coordinates. These solutions are then expressed in terms of outgoing and ingoing coordinates, which have distinct analytic properties inside and outside the event horizon.
Toeplitz Hermitian Positive Definite (THPD) matrices play an important role in signal processing and computer graphics and circular models, related to angular / periodic data, have vide applications in various walks of life. Visualizing a circular model through THPD matrix the required computations on THPD matrices using single bordering and double bordering are discussed. It can be seen that every tridiagonal THPD leads to Cardioid model.
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.
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 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 instructions for a JEE Advanced exam paper. It details the format and structure of the exam, including three sections in physics, chemistry, and math. Section 1 has 8 single-digit answer questions worth +4 points for correct answers. Section 2 has 8 multiple choice questions worth +4 for fully correct, 0 for unattempted, and -2 for incorrect answers. Section 3 has 2 paragraph-style questions each with multiple choice answers graded the same as Section 2.
Jee mains 2015 11th april answer key without solution (2)100marks
This document contains a 27 question multiple choice test on physics concepts. The questions cover topics like gravitation potential, circular motion in a magnetic field, simple harmonic motion, center of mass calculations, buoyancy, oscillations, electrical circuits, electromagnetic waves, radioactivity, polarization, capacitors, and more. For each question there are 4 possible answers labeled 1-4 and only one correct answer is provided.
Aieee 2011 Solved Paper by Prabhat GauravSahil Gaurav
1. The document provides instructions for a test being administered. It details that the test is 3 hours, consists of 90 questions worth a total of 360 marks, and covers physics, mathematics, and chemistry. It provides instructions on marking answers, time limits, and materials allowed during the test.
2. Candidates will have their answers scored with plus and minus marks depending on correct and incorrect responses. They must fill in their details on the answer sheet carefully and hand it in after completing the test while keeping the question booklet.
3. The code for this test booklet is Q and candidates should check it matches their answer sheet, reporting any discrepancies to the invigilator.
Effect of an Inclined Magnetic Field on Peristaltic Flow of Williamson Fluid ...QUESTJOURNAL
ABSTRACT: This paper deals with the influence ofinclined magnetic field on peristaltic flow of an incompressible Williamson fluid in an inclined channel with heat and mass transfer. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
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.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Influence of MHD on Unsteady Helical Flows of Generalized Oldoyd-B Fluid betw...IJERA Editor
Considering a fractional derivative model for unsteady magetohydrodynamic (MHD)helical flows of an
Oldoyd-B fluid in concentric cylinders and circular cylinder are studied by using finite Hankel and Laplace
transforms .The solution of velocity fields and the shear stresses of unsteady magetohydrodynamic
(MHD)helical flows of an Oldoyd-B fluid in an annular pipe are obtained under series form in terms of
Mittag –leffler function,satisfy all imposed initial and boundary condition , Finally the influence of model
parameters on the velocity and shear stress are analyzed by graphical illustrations.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
The document contains 14 chemistry questions and their solutions. The questions cover topics like organic reactions, estimation of nitrogen content, precipitation of salts, uses of additives in soaps, properties of metal nitrates, bond orders, atomic radii trends, activation energy determination, isoelectronic and isostructural species, organic compound identification based on tests, and magnetic moments. The solutions provided explain the reasoning for the answers in 2-3 sentences each.
Lesson 15: Exponential Growth and Decay (Section 041 handout)Matthew Leingang
Many problems in nature are expressible in terms of a certain differential equation that has a solution in terms of exponential functions. We look at the equation in general and some fun applications, including radioactivity, cooling, and interest.
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
Outgoing ingoingkleingordon spvmforminit_proceedfromfoxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfrom12dec18foxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
This document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. The document lists properties of parallelograms, including: opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; if one angle is a right angle, all angles are right angles. It also states that the diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Examples demonstrate using these properties to find missing measures and intersection points of diagonals.
Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyr...IOSR Journals
In this paper we have obtained axially symmetric Bianchi type-I cosmological models for perfect
fluid distribution in the context of Lyra’s manifold. Exact solutions of the field equations are obtained by
assuming the expansion in the model is proportional to the shear . This leads to the condition
A Bn
where A and B are scale factors and n( 0) is a constant. Some kinematical and physical parameters of the
model have been discussed. The solutions are compatible with recent observations.
This document discusses solutions to the Klein-Gordon equation in Schwarzschild spacetime near a black hole's event horizon. Very near the horizon, the radial Klein-Gordon equation can be approximated as an oscillatory solution in Regge-Wheeler coordinates. The time and radial solutions are then expressed in terms of outgoing and ingoing coordinates, which leads to outgoing and ingoing waves with different analytic properties on either side of the event horizon.
This document discusses solutions to the Klein-Gordon equation in Schwarzschild spacetime near a black hole's event horizon. Very near the horizon, the radial Klein-Gordon equation can be approximated as an oscillatory solution in Regge-Wheeler coordinates. These solutions are then expressed in terms of outgoing and ingoing coordinates, which have distinct analytic properties inside and outside the event horizon.
Toeplitz Hermitian Positive Definite (THPD) matrices play an important role in signal processing and computer graphics and circular models, related to angular / periodic data, have vide applications in various walks of life. Visualizing a circular model through THPD matrix the required computations on THPD matrices using single bordering and double bordering are discussed. It can be seen that every tridiagonal THPD leads to Cardioid model.
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.
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 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 instructions for a JEE Advanced exam paper. It details the format and structure of the exam, including three sections in physics, chemistry, and math. Section 1 has 8 single-digit answer questions worth +4 points for correct answers. Section 2 has 8 multiple choice questions worth +4 for fully correct, 0 for unattempted, and -2 for incorrect answers. Section 3 has 2 paragraph-style questions each with multiple choice answers graded the same as Section 2.
Jee mains 2015 11th april answer key without solution (2)100marks
This document contains a 27 question multiple choice test on physics concepts. The questions cover topics like gravitation potential, circular motion in a magnetic field, simple harmonic motion, center of mass calculations, buoyancy, oscillations, electrical circuits, electromagnetic waves, radioactivity, polarization, capacitors, and more. For each question there are 4 possible answers labeled 1-4 and only one correct answer is provided.
Aieee 2011 Solved Paper by Prabhat GauravSahil Gaurav
1. The document provides instructions for a test being administered. It details that the test is 3 hours, consists of 90 questions worth a total of 360 marks, and covers physics, mathematics, and chemistry. It provides instructions on marking answers, time limits, and materials allowed during the test.
2. Candidates will have their answers scored with plus and minus marks depending on correct and incorrect responses. They must fill in their details on the answer sheet carefully and hand it in after completing the test while keeping the question booklet.
3. The code for this test booklet is Q and candidates should check it matches their answer sheet, reporting any discrepancies to the invigilator.
The document provides information about Section 1 of the JEE (Advanced) 2018 Paper 2 exam for physics. It includes:
- Section 1 contains 6 multiple choice questions with one or more correct options.
- The marking scheme awards full marks for selecting only the correct options, partial marks for selecting some but not all correct options, and negative marks for incorrect selections.
- An example is given to illustrate the marking scheme.
So in summary, the document outlines the format and scoring details for the multiple choice section of the JEE (Advanced) physics exam. It provides guidance on selecting answer options and how points will be awarded.
Class 11th & 12th Physics, Chemistry & Mathematics exam paper to practice for preparation of JEE Advanced 2019 exam by expert faculty. This is previous year paper on JEE Advanced exam. You can download free from https://bit.ly/2Peumhs
The document summarizes the problems presented at the 6th International Physics Olympiad held in Bucharest, Romania in 1972. It includes 4 theoretical problems and 1 experimental problem.
The first problem involves three cylinders rolling down an inclined plane with different densities and configurations, and calculates their accelerations and conditions for non-sliding. The second problem analyzes the adiabatic expansion of argon gas and isothermal compression of oxygen between two cylinders, and calculates the final pressure when mixed. The third problem determines the height a dielectric liquid rises between the plates of a vertical capacitor based on the electric field strength and liquid properties.
The document describes a study that investigated the effect of using computer simulations in teaching physics concepts related to oscillations at the undergraduate level. The study aimed to identify difficulties students face in learning oscillations, develop a computer simulation package and assessment tool, and measure the impact of the simulations compared to traditional teaching methods. Results showed that students who used the simulations had significantly higher normalized learning gains compared to the control group on a post-test of oscillations concepts.
In this paper we consider the initial-boundary value problem for a nonlinear equation induced with respect to the mathematical models in mass production process with the one sided spring boundary condition by boundary feedback control. We establish the asymptotic behavior of solutions to this problem in time, and give an example and simulation to illustrate our results. Results of this paper are able to apply industrial parts such as a typical model widely used to represent threads, wires, magnetic tapes, belts, band saws, and so on.
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.
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.
1) The document discusses solving diffusion problems using Fourier transforms. It provides the solution for the temperature distribution over time resulting from an initial localized injection of heat into an infinite domain.
2) The solution is a Gaussian distribution that broadens over time according to the square root of time. This analysis is extended to model the diffusion of ionization from a meteorite shooting through the earth's atmosphere, treating it as a cylindrical diffusion problem.
3) The solution for electron density as a function of distance from the meteor trail and time since passage has the form of a Gaussian distribution, indicating the ionization diffuses away from the meteor trail over time.
Methods to determine pressure drop in an evaporator or a condenserTony Yen
This articles aims to explain how one can relatively easily calculate the pressure drop within a condenser or an evaporator, where two-phase flow occurs and the Navier-Stokes equation becomes very tedious.
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2018 JEE Advanced Paper 1 Question Papers
1. JEE (Advanced) 2018 Paper 1
1/12
JEE (ADVANCED) 2018 PAPER 1
PART-I PHYSICS
SECTION 1 (Maximum Marks: 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +𝟒 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +𝟑 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +𝟐 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +𝟏 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −𝟐 In all other cases.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option) ,without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in -2 marks.
Q.1 The potential energy of a particle of mass 𝑚 at a distance 𝑟 from a fixed point 𝑂 is given by
𝑉(𝑟) = 𝑘𝑟2
/2, where 𝑘 is a positive constant of appropriate dimensions. This particle is
moving in a circular orbit of radius 𝑅 about the point 𝑂. If 𝑣 is the speed of the particle and
𝐿 is the magnitude of its angular momentum about 𝑂, which of the following statements is
(are) true?
(A) 𝑣 = √
𝑘
2𝑚
𝑅
(B) 𝑣 = √
𝑘
𝑚
𝑅
(C) 𝐿 = √𝑚𝑘 𝑅2
(D) 𝐿 = √
𝑚𝑘
2
𝑅2
2. JEE (Advanced) 2018 Paper 1
2/12
Q.2 Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time 𝑡 = 0. A force 𝐹⃗ = (𝛼𝑡 𝑖̂ + 𝛽 𝑗̂)
is applied on the body, where 𝛼 = 1.0 𝑁𝑠−1
and 𝛽 = 1.0 𝑁. The torque acting on the body
about the origin at time 𝑡 = 1.0 𝑠 is 𝜏⃗. Which of the following statements is (are) true?
(A) |𝜏⃗| =
1
3
𝑁 𝑚
(B) The torque 𝜏⃗ is in the direction of the unit vector + 𝑘̂
(C) The velocity of the body at 𝑡 = 1 𝑠 is v⃗⃗ =
1
2
(𝑖̂ + 2𝑗̂) 𝑚 𝑠−1
(D) The magnitude of displacement of the body at 𝑡 = 1 𝑠 is
1
6
𝑚
Q.3 A uniform capillary tube of inner radius 𝑟 is dipped vertically into a beaker filled with water.
The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The
surface tension of water is 𝜎. The angle of contact between water and the wall of the capillary
tube is 𝜃. Ignore the mass of water in the meniscus. Which of the following statements is
(are) true?
(A) For a given material of the capillary tube, ℎ decreases with increase in 𝑟
(B) For a given material of the capillary tube, ℎ is independent of 𝜎
(C) If this experiment is performed in a lift going up with a constant acceleration, then ℎ
decreases
(D) ℎ is proportional to contact angle 𝜃
3. JEE (Advanced) 2018 Paper 1
3/12
Q.4 In the figure below, the switches 𝑆1 and 𝑆2 are closed simultaneously at 𝑡 = 0 and a current
starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive
force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between
the inductors. The current 𝐼 in the middle wire reaches its maximum magnitude 𝐼 𝑚𝑎𝑥 at time
𝑡 = 𝜏. Which of the following statements is (are) true?
(A) 𝐼 𝑚𝑎𝑥 =
𝑉
2𝑅
(B) 𝐼 𝑚𝑎𝑥 =
𝑉
4𝑅
(C) 𝜏 =
𝐿
𝑅
ln 2 (D) 𝜏 =
2𝐿
𝑅
ln 2
Q.5 Two infinitely long straight wires lie in the 𝑥𝑦-plane along the lines 𝑥 = ±𝑅. The wire
located at 𝑥 = +𝑅 carries a constant current 𝐼1 and the wire located at 𝑥 = −𝑅 carries a
constant current 𝐼2. A circular loop of radius 𝑅 is suspended with its centre at (0, 0, √3𝑅)
and in a plane parallel to the 𝑥𝑦-plane. This loop carries a constant current 𝐼 in the clockwise
direction as seen from above the loop. The current in the wire is taken to be positive if it is
in the +𝑗̂ direction. Which of the following statements regarding the magnetic field 𝐵⃗⃗ is (are)
true?
(A) If 𝐼1 = 𝐼2, then 𝐵⃗⃗ cannot be equal to zero at the origin (0, 0, 0)
(B) If 𝐼1 > 0 and 𝐼2 < 0, then 𝐵⃗⃗ can be equal to zero at the origin (0, 0, 0)
(C) If 𝐼1 < 0 and 𝐼2 > 0, then 𝐵⃗⃗ can be equal to zero at the origin (0, 0, 0)
(D) If 𝐼1 = 𝐼2, then the 𝑧-component of the magnetic field at the centre of the loop is (−
𝜇0 𝐼
2𝑅
)
4. JEE (Advanced) 2018 Paper 1
4/12
Q.6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure
(where V is the volume and T is the temperature). Which of the statements below is (are)
true?
(A) Process I is an isochoric process
(B) In process II, gas absorbs heat
(C) In process IV, gas releases heat
(D) Processes I and III are not isobaric
5. JEE (Advanced) 2018 Paper 1
5/12
SECTION 2 (Maximum Marks: 24)
This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE.
For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to
the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-
screen virtual numeric keypad in the place designated to enter the answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct numerical value is entered as answer.
Zero Marks : 0In all other cases.
Q.7 Two vectors 𝐴⃗ and 𝐵⃗⃗ are defined as 𝐴⃗ = 𝑎 𝑖̂ and 𝐵⃗⃗ = 𝑎 (cos 𝜔𝑡 𝑖̂ + sin 𝜔𝑡 𝑗̂), where 𝑎 is a
constant and 𝜔 = 𝜋/6 𝑟𝑎𝑑 𝑠−1
. If |𝐴⃗ + 𝐵⃗⃗| = √3|𝐴⃗ − 𝐵⃗⃗ | at time 𝑡 = 𝜏 for the first time,
the value of 𝜏, in 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, is __________.
Q.8 Two men are walking along a horizontal straight line in the same direction. The man in front
walks at a speed 1.0 𝑚 𝑠−1
and the man behind walks at a speed 2.0 𝑚 𝑠−1
. A third man is
standing at a height 12 𝑚 above the same horizontal line such that all three men are in a
vertical plane. The two walking men are blowing identical whistles which emit a sound of
frequency 1430 𝐻𝑧. The speed of sound in air is 330 𝑚 𝑠−1
. At the instant, when the moving
men are 10 𝑚 apart, the stationary man is equidistant from them. The frequency of beats in
𝐻𝑧, heard by the stationary man at this instant, is __________.
Q.9 A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes
an angle 60° with the horizontal. They start to roll without slipping at the same instant of
time along the shortest path. If the time difference between their reaching the ground is
(2 − √3) /√10 𝑠, then the height of the top of the inclined plane, in 𝑚𝑒𝑡𝑟𝑒𝑠, is __________.
Take 𝑔 = 10 𝑚 𝑠−2
.
6. JEE (Advanced) 2018 Paper 1
6/12
Q.10 A spring-block system is resting on a frictionless floor as shown in the figure. The spring
constant is 2.0 𝑁 𝑚−1
and the mass of the block is 2.0 𝑘𝑔. Ignore the mass of the spring.
Initially the spring is in an unstretched condition. Another block of mass 1.0 𝑘𝑔 moving with
a speed of 2.0 𝑚 𝑠−1
collides elastically with the first block. The collision is such that the
2.0 𝑘𝑔 block does not hit the wall. The distance, in 𝑚𝑒𝑡𝑟𝑒𝑠, between the two blocks when
the spring returns to its unstretched position for the first time after the collision is _________.
Q.11 Three identical capacitors 𝐶1, 𝐶2 and 𝐶3 have a capacitance of 1.0 𝜇𝐹 each and they are
uncharged initially. They are connected in a circuit as shown in the figure and 𝐶1 is then
filled completely with a dielectric material of relative permittivity 𝜖 𝑟. The cell electromotive
force (emf) 𝑉0 = 8 𝑉. First the switch 𝑆1 is closed while the switch 𝑆2 is kept open. When
the capacitor 𝐶3 is fully charged, 𝑆1 is opened and 𝑆2 is closed simultaneously. When all the
capacitors reach equilibrium, the charge on 𝐶3 is found to be 5 𝜇𝐶. The value of
𝜖 𝑟 =____________.
7. JEE (Advanced) 2018 Paper 1
7/12
Q.12 In the 𝑥𝑦-plane, the region 𝑦 > 0 has a uniform magnetic field 𝐵1 𝑘̂ and the region 𝑦 < 0 has
another uniform magnetic field 𝐵2 𝑘̂. A positively charged particle is projected from the
origin along the positive 𝑦-axis with speed 𝑣0 = 𝜋 𝑚 𝑠−1
at 𝑡 = 0, as shown in the figure.
Neglect gravity in this problem. Let 𝑡 = 𝑇 be the time when the particle crosses the 𝑥-axis
from below for the first time. If 𝐵2 = 4𝐵1, the average speed of the particle, in 𝑚 𝑠−1
, along
the 𝑥-axis in the time interval 𝑇 is __________.
Q.13 Sunlight of intensity 1.3 𝑘𝑊 𝑚−2
is incident normally on a thin convex lens of focal length
20 𝑐𝑚. Ignore the energy loss of light due to the lens and assume that the lens aperture size
is much smaller than its focal length. The average intensity of light, in 𝑘𝑊 𝑚−2
, at a distance
22 𝑐𝑚 from the lens on the other side is __________.
8. JEE (Advanced) 2018 Paper 1
8/12
Q.14 Two conducting cylinders of equal length but different radii are connected in series between
two heat baths kept at temperatures 𝑇1 = 300 𝐾 and 𝑇2 = 100 𝐾, as shown in the figure.
The radius of the bigger cylinder is twice that of the smaller one and the thermal
conductivities of the materials of the smaller and the larger cylinders are 𝐾1 and 𝐾2
respectively. If the temperature at the junction of the two cylinders in the steady state is
200 𝐾, then 𝐾1/𝐾2 =__________.
9. JEE (Advanced) 2018 Paper 1
9/12
SECTION 3 (Maximum Marks: 12)
This section contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions.
Each question has FOUR options. ONLY ONE of these four options corresponds to the correct answer.
For each question, choose the option corresponding to the correct answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −1 In all other cases.
PARAGRAPH “X”
In electromagnetic theory, the electric and magnetic phenomena are related to each other.
Therefore, the dimensions of electric and magnetic quantities must also be related to each
other. In the questions below, [𝐸] and [𝐵] stand for dimensions of electric and magnetic
fields respectively, while [𝜖0] and [𝜇0] stand for dimensions of the permittivity and
permeability of free space respectively. [𝐿] and [𝑇] are dimensions of length and time
respectively. All the quantities are given in SI units.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.15 The relation between [𝐸] and [𝐵] is
(A) [𝐸] = [𝐵] [𝐿] [𝑇] (B) [𝐸] = [𝐵] [𝐿]−1
[𝑇]
(C) [𝐸] = [𝐵] [𝐿] [𝑇]−1
(D) [𝐸] = [𝐵] [𝐿]−1
[𝑇]−1
10. JEE (Advanced) 2018 Paper 1
10/12
PARAGRAPH “X”
In electromagnetic theory, the electric and magnetic phenomena are related to each other.
Therefore, the dimensions of electric and magnetic quantities must also be related to each
other. In the questions below, [𝐸] and [𝐵] stand for dimensions of electric and magnetic
fields respectively, while [𝜖0] and [𝜇0] stand for dimensions of the permittivity and
permeability of free space respectively. [𝐿] and [𝑇] are dimensions of length and time
respectively. All the quantities are given in SI units.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.16 The relation between [𝜖0] and [𝜇0] is
(A) [𝜇0] = [𝜖0] [𝐿]2
[𝑇]−2
(B) [𝜇0] = [𝜖0] [𝐿]−2
[𝑇]2
(C) [𝜇0] = [𝜖0]−1
[𝐿]2
[𝑇]−2
(D) [𝜇0] = [𝜖0]−1
[𝐿]−2
[𝑇]2
11. JEE (Advanced) 2018 Paper 1
11/12
PARAGRAPH “A”
If the measurement errors in all the independent quantities are known, then it is possible to
determine the error in any dependent quantity. This is done by the use of series expansion
and truncating the expansion at the first power of the error. For example, consider the relation
𝑧 = 𝑥/𝑦. If the errors in 𝑥, 𝑦 and 𝑧 are Δ𝑥, Δ𝑦 and Δ𝑧, respectively, then
𝑧 ± Δ𝑧 =
𝑥±Δ𝑥
𝑦±Δ𝑦
=
𝑥
𝑦
(1 ±
Δ𝑥
𝑥
) (1 ±
Δ𝑦
𝑦
)
−1
.
The series expansion for (1 ±
Δ𝑦
𝑦
)
−1
, to first power in Δ𝑦/𝑦, is 1 ∓ (Δ𝑦/𝑦). The relative
errors in independent variables are always added. So the error in 𝑧 will be
Δ𝑧 = 𝑧 (
Δ𝑥
𝑥
+
Δ𝑦
𝑦
).
The above derivation makes the assumption that Δ𝑥/𝑥 ≪1, Δ𝑦/𝑦 ≪1. Therefore, the higher
powers of these quantities are neglected.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)
Q.17
Consider the ratio 𝑟 =
(1−𝑎)
(1+𝑎)
to be determined by measuring a dimensionless quantity 𝑎.
If the error in the measurement of 𝑎 is Δ𝑎 (Δ𝑎/𝑎 ≪ 1) , then what is the error Δ𝑟 in
determining 𝑟?
(A)
Δ𝑎
(1+𝑎)2
(B)
2Δ𝑎
(1+𝑎)2
(C)
2Δ𝑎
(1−𝑎2)
(D)
2𝑎Δ𝑎
(1−𝑎2)
12. JEE (Advanced) 2018 Paper 1
12/12
PARAGRAPH “A”
If the measurement errors in all the independent quantities are known, then it is possible to
determine the error in any dependent quantity. This is done by the use of series expansion
and truncating the expansion at the first power of the error. For example, consider the relation
𝑧 = 𝑥/𝑦. If the errors in 𝑥, 𝑦 and 𝑧 are Δ𝑥, Δ𝑦 and Δ𝑧, respectively, then
𝑧 ± Δ𝑧 =
𝑥±Δ𝑥
𝑦±Δ𝑦
=
𝑥
𝑦
(1 ±
Δ𝑥
𝑥
) (1 ±
Δ𝑦
𝑦
)
−1
.
The series expansion for (1 ±
Δ𝑦
𝑦
)
−1
, to first power in Δ𝑦/𝑦, is 1 ∓ (Δ𝑦/𝑦). The relative
errors in independent variables are always added. So the error in 𝑧 will be
Δ𝑧 = 𝑧 (
Δ𝑥
𝑥
+
Δ𝑦
𝑦
).
The above derivation makes the assumption that Δ𝑥/𝑥 ≪1, Δ𝑦/𝑦 ≪1. Therefore, the higher
powers of these quantities are neglected.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)
Q.18 In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40
nuclei decayed in the first 1.0 𝑠. For |𝑥| ≪ 1, ln(1 + 𝑥) = 𝑥 up to first power in 𝑥. The error
Δ𝜆, in the determination of the decay constant 𝜆, in 𝑠−1
, is
(A) 0.04 (B) 0.03 (C) 0.02 (D) 0.01
13. JEE (Advanced) 2018 Paper 1
1/12
JEE (ADVANCED) 2018 PAPER 1
PART II-CHEMISTRY
SECTION 1 (Maximum Marks: 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +𝟒 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +𝟑 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +𝟐 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +𝟏 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −𝟐 In all other cases.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option) ,without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in -2 marks.
Q.1 The compound(s) which generate(s) N2 gas upon thermal decomposition below 300C
is (are)
(A) NH4NO3
(B) (NH4)2Cr2O7
(C) Ba(N3)2
(D) Mg3N2
Q.2 The correct statement(s) regarding the binary transition metal carbonyl compounds is (are)
(Atomic numbers: Fe = 26, Ni = 28)
(A) Total number of valence shell electrons at metal centre in Fe(CO)5 or Ni(CO)4 is 16
(B) These are predominantly low spin in nature
(C) Metal–carbon bond strengthens when the oxidation state of the metal is lowered
(D) The carbonyl C−O bond weakens when the oxidation state of the metal is increased
14. JEE (Advanced) 2018 Paper 1
2/12
Q.3 Based on the compounds of group 15 elements, the correct statement(s) is (are)
(A) Bi2O5 is more basic than N2O5
(B) NF3 is more covalent than BiF3
(C) PH3 boils at lower temperature than NH3
(D) The N−N single bond is stronger than the P−P single bond
Q.4 In the following reaction sequence, the correct structure(s) of X is (are)
(A) (B)
(C) (D)
15. JEE (Advanced) 2018 Paper 1
3/12
Q.5 The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)
(A)
(B)
(C)
(D)
16. JEE (Advanced) 2018 Paper 1
4/12
Q.6 A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure,
volume and temperature, respectively. The thermodynamic parameters q, w, H and U are
heat, work, enthalpy and internal energy, respectively.
The correct option(s) is (are)
(A) 𝑞 𝐴𝐶 = ∆𝑈 𝐵𝐶 and 𝑤 𝐴𝐵 = 𝑃2(𝑉2 − 𝑉1)
(B) 𝑤 𝐵𝐶 = 𝑃2(𝑉2 − 𝑉1) and 𝑞 𝐵𝐶 = ∆𝐻𝐴𝐶
(C) ∆𝐻 𝐶𝐴 < ∆𝑈 𝐶𝐴 and 𝑞 𝐴𝐶 = ∆𝑈 𝐵𝐶
(D) 𝑞 𝐵𝐶 = ∆𝐻𝐴𝐶 and ∆𝐻 𝐶𝐴 > ∆𝑈 𝐶𝐴
17. JEE (Advanced) 2018 Paper 1
5/12
SECTION 2 (Maximum Marks: 24)
This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE.
For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off
to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the
on-screen virtual numeric keypad in the place designated to enter the answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct numerical value is entered as answer.
Zero Marks : 0In all other cases.
Q.7 Among the species given below, the total number of diamagnetic species is ___.
H atom, NO2 monomer, O2
−
(superoxide), dimeric sulphur in vapour phase,
Mn3O4, (NH4)2[FeCl4], (NH4)2[NiCl4], K2MnO4, K2CrO4
Q.8 The ammonia prepared by treating ammonium sulphate with calcium hydroxide is
completely used by NiCl2.6H2O to form a stable coordination compound. Assume that both
the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl2.6H2O
are used in the preparation, the combined weight (in grams) of gypsum and the nickel-
ammonia coordination compound thus produced is ____.
(Atomic weights in g mol-1
: H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)
18. JEE (Advanced) 2018 Paper 1
6/12
Q.9 Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit
cell is constructed from the unit cell of MX following the sequential instructions given
below. Neglect the charge balance.
(i) Remove all the anions (X) except the central one
(ii) Replace all the face centered cations (M) by anions (X)
(iii) Remove all the corner cations (M)
(iv) Replace the central anion (X) with cation (M)
The value of
number of anions
number of cations
in Z is ____.
Q.10 For the electrochemical cell,
Mg(s) Mg2+
(aq, 1 M) Cu2+
(aq, 1 M) Cu(s)
the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg2+
is changed
to 𝒙 M, the cell potential changes to 2.67 V at 300 K. The value of 𝒙 is ____.
(given,
𝐹
𝑅
= 11500 K V−1
, where 𝐹 is the Faraday constant and 𝑅 is the gas constant,
ln(10) = 2.30)
19. JEE (Advanced) 2018 Paper 1
7/12
Q.11 A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal
gas). The partition separating the two compartments is fixed and is a perfect heat insulator
(Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat
but does NOT allow the gas to leak across (Figure 2), the volume (in m3
) of the compartment
A after the system attains equilibrium is ____.
Q.12 Liquids A and B form ideal solution over the entire range of composition. At temperature T,
equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same
temperature, a new solution of A and B having mole fractions 𝑥 𝐴 and 𝑥 𝐵, respectively, has
vapour pressure of 22.5 Torr. The value of 𝑥 𝐴/𝑥 𝐵 in the new solution is ____.
(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)
20. JEE (Advanced) 2018 Paper 1
8/12
Q.13 The solubility of a salt of weak acid (AB) at pH 3 is Y×103
mol L−1
. The value of Y is ____.
(Given that the value of solubility product of AB (𝐾𝑠𝑝) = 2×1010
and the value of ionization
constant of HB (𝐾𝑎) = 1×108
)
Q.14 The plot given below shows 𝑃 − 𝑇 curves (where P is the pressure and T is the temperature)
for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely
dissociates in both the solvents.
On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of
these solvents, the elevation of boiling point of solvent X is three times that of solvent Y.
Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is
0.7 in solvent Y, the degree of dimerization in solvent X is ____.
21. JEE (Advanced) 2018 Paper 1
9/12
SECTION 3 (Maximum Marks: 12)
This section contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions.
Each question has FOUR options. ONLY ONE of these four options corresponds to the correct answer.
For each question, choose the option corresponding to the correct answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −1 In all other cases.
PARAGRAPH “X”
Treatment of benzene with CO/HCl in the presence of anhydrous AlCl3/CuCl
followed by reaction with Ac2O/NaOAc gives compound X as the major product.
Compound X upon reaction with Br2/Na2CO3, followed by heating at 473 K with
moist KOH furnishes Y as the major product. Reaction of X with H2/Pd-C, followed
by H3PO4 treatment gives Z as the major product.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.15 The compound Y is
(A)
(B)
(C)
(D)
22. JEE (Advanced) 2018 Paper 1
10/12
PARAGRAPH “X”
Treatment of benzene with CO/HCl in the presence of anhydrous AlCl3/CuCl
followed by reaction with Ac2O/NaOAc gives compound X as the major product.
Compound X upon reaction with Br2/Na2CO3, followed by heating at 473 K with
moist KOH furnishes Y as the major product. Reaction of X with H2/Pd-C, followed
by H3PO4 treatment gives Z as the major product.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.16 The compound Z is
(A) (B)
(C)
(D)
23. JEE (Advanced) 2018 Paper 1
11/12
PARAGRAPH “A”
An organic acid P (C11H12O2) can easily be oxidized to a dibasic acid which reacts with
ethyleneglycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic
ketone as one of the products. P undergoes the following reaction sequences to furnish
R via Q. The compound P also undergoes another set of reactions to produce S.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)
Q.17 The compound R is
(A)
(B)
(C) (D)
24. JEE (Advanced) 2018 Paper 1
12/12
PARAGRAPH “A”
An organic acid P (C11H12O2) can easily be oxidized to a dibasic acid which reacts with
ethyleneglycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic
ketone as one of the products. P undergoes the following reaction sequences to furnish
R via Q. The compound P also undergoes another set of reactions to produce S.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)
Q.18 The compound S is
(A)
(B) (C) (D)
25. JEE (Advanced) 2018 Paper 1
1/8
JEE (ADVANCED) 2018 PAPER 1
PART-III MATHEMATICS
SECTION 1 (Maximum Marks: 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s)
is (are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +𝟒 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +𝟑 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +𝟐 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +𝟏 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −𝟐 In all other cases.
For Example: If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option) ,without selecting any incorrect option (second
option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in -2 marks.
26. JEE (Advanced) 2018 Paper 1
2/8
Q.1 For a non-zero complex number 𝑧, let arg(𝑧) denote the principal argument with
− 𝜋 < arg(𝑧) ≤ 𝜋. Then, which of the following statement(s) is (are) FALSE?
(A) arg(−1 − 𝑖) =
𝜋
4
, where 𝑖 = √−1
(B) The function 𝑓: ℝ → (−𝜋, 𝜋], defined by 𝑓(𝑡) = arg(−1 + 𝑖𝑡) for all 𝑡 ∈ ℝ, is
continuous at all points of ℝ, where 𝑖 = √−1
(C) For any two non-zero complex numbers 𝑧1 and 𝑧2,
arg (
𝑧1
𝑧2
) − arg( 𝑧1) + arg( 𝑧2)
is an integer multiple of 2𝜋
(D) For any three given distinct complex numbers 𝑧1, 𝑧2 and 𝑧3, the locus of the
point 𝑧 satisfying the condition
arg (
(𝑧−𝑧1) (𝑧2−𝑧3)
(𝑧−𝑧3) (𝑧2−𝑧1)
) = 𝜋,
lies on a straight line
Q.2 In a triangle 𝑃𝑄𝑅, let ∠𝑃𝑄𝑅 = 30°
and the sides 𝑃𝑄 and 𝑄𝑅 have lengths 10√3 and 10,
respectively. Then, which of the following statement(s) is (are) TRUE?
(A) ∠𝑄𝑃𝑅 = 45°
(B) The area of the triangle 𝑃𝑄𝑅 is 25√3 and ∠𝑄𝑅𝑃 = 120°
(C) The radius of the incircle of the triangle 𝑃𝑄𝑅 is 10√3 − 15
(D) The area of the circumcircle of the triangle 𝑃𝑄𝑅 is 100 𝜋
27. JEE (Advanced) 2018 Paper 1
3/8
Q.3 Let 𝑃1: 2𝑥 + 𝑦 − 𝑧 = 3 and 𝑃2: 𝑥 + 2𝑦 + 𝑧 = 2 be two planes. Then, which of the
following statement(s) is (are) TRUE?
(A) The line of intersection of 𝑃1 and 𝑃2 has direction ratios 1, 2, −1
(B) The line
3𝑥 − 4
9
=
1 − 3𝑦
9
=
𝑧
3
is perpendicular to the line of intersection of 𝑃1 and 𝑃2
(C) The acute angle between 𝑃1 and 𝑃2 is 60°
(D) If 𝑃3 is the plane passing through the point (4, 2, −2) and perpendicular to the line
of intersection of 𝑃1 and 𝑃2, then the distance of the point (2, 1, 1) from the plane
𝑃3 is
2
√3
Q.4 For every twice differentiable function 𝑓: ℝ → [−2, 2] with (𝑓(0))2
+ (𝑓′(0))
2
= 85,
which of the following statement(s) is (are) TRUE?
(A) There exist 𝑟, 𝑠 ∈ ℝ, where 𝑟 < 𝑠, such that 𝑓 is one-one on the open interval (𝑟, 𝑠)
(B) There exists 𝑥0 ∈ (−4, 0) such that |𝑓′(𝑥0)| ≤ 1
(C) lim
𝑥→∞
𝑓(𝑥) = 1
(D) There exists 𝛼 ∈ (−4, 4) such that 𝑓(𝛼) + 𝑓′′(𝛼) = 0 and 𝑓′(𝛼) ≠ 0
Q.5 Let 𝑓: ℝ → ℝ and 𝑔: ℝ → ℝ be two non-constant differentiable functions. If
𝑓′(𝑥) = (𝑒(𝑓(𝑥)−𝑔(𝑥))
)𝑔′(𝑥) for all 𝑥 ∈ ℝ,
and 𝑓(1) = 𝑔(2) = 1, then which of the following statement(s) is (are) TRUE?
(A) 𝑓(2) < 1 − loge 2 (B) 𝑓(2) > 1 − loge 2
(C) 𝑔(1) > 1 − loge 2 (D) 𝑔(1) < 1 − loge 2
28. JEE (Advanced) 2018 Paper 1
4/8
Q.6 Let 𝑓: [0, ∞) → ℝ be a continuous function such that
𝑓(𝑥) = 1 − 2𝑥 + ∫ 𝑒 𝑥−𝑡
𝑓(𝑡)𝑑𝑡
𝑥
0
for all 𝑥 ∈ [0, ∞). Then, which of the following statement(s) is (are) TRUE?
(A) The curve 𝑦 = 𝑓(𝑥) passes through the point (1, 2)
(B) The curve 𝑦 = 𝑓(𝑥) passes through the point (2, −1)
(C) The area of the region {(𝑥, 𝑦) ∈ [0, 1] × ℝ ∶ 𝑓( 𝑥) ≤ 𝑦 ≤ √1 − 𝑥2 } is
𝜋−2
4
(D) The area of the region {(𝑥, 𝑦) ∈ [0,1] × ℝ ∶ 𝑓( 𝑥) ≤ 𝑦 ≤ √1 − 𝑥2 } is
𝜋−1
4
29. JEE (Advanced) 2018 Paper 1
5/8
SECTION 2 (Maximum Marks: 24)
This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE.
For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off
to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the
on-screen virtual numeric keypad in the place designated to enter the answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct numerical value is entered as answer.
Zero Marks : 0In all other cases.
Q.7 The value of
((log2 9)2)
1
log2 (log2 9) × (√7)
1
log4 7
is ______ .
Q.8 The number of 5 digit numbers which are divisible by 4, with digits from the set
{1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .
Q.9 Let 𝑋 be the set consisting of the first 2018 terms of the arithmetic progression
1, 6, 11, … , and 𝑌 be the set consisting of the first 2018 terms of the arithmetic
progression 9, 16, 23, … . Then, the number of elements in the set 𝑋 ∪ 𝑌 is _____.
Q.10 The number of real solutions of the equation
sin−1
(∑ 𝑥 𝑖+1
∞
𝑖=1
− 𝑥 ∑ (
𝑥
2
)
𝑖
∞
𝑖=1
) =
𝜋
2
− cos−1
(∑ (−
𝑥
2
)
𝑖
−
∞
𝑖=1
∑(−𝑥)𝑖
∞
𝑖=1
)
lying in the interval (−
1
2
,
1
2
) is _____ .
(Here, the inverse trigonometric functions sin−1
𝑥 and cos−1
𝑥 assume values in [−
𝜋
2
,
𝜋
2
]
and [0, 𝜋], respectively.)
Q.11 For each positive integer 𝑛, let
𝑦𝑛 =
1
𝑛
((𝑛 + 1)(𝑛 + 2) ⋯ (𝑛 + 𝑛))
1
𝑛
.
For 𝑥 ∈ ℝ, let [𝑥] be the greatest integer less than or equal to 𝑥. If lim
𝑛→∞
𝑦𝑛 = 𝐿, then the
value of [𝐿] is _____ .
30. JEE (Advanced) 2018 Paper 1
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Q.12 Let 𝑎⃗ and 𝑏⃗⃗ be two unit vectors such that 𝑎⃗ ⋅ 𝑏⃗⃗ = 0. For some 𝑥, 𝑦 ∈ ℝ, let
𝑐⃗ = 𝑥 𝑎⃗ + 𝑦 𝑏⃗⃗ + (𝑎⃗ × 𝑏⃗⃗). If |𝑐⃗| = 2 and the vector 𝑐⃗ is inclined at the same angle 𝛼 to
both 𝑎⃗ and 𝑏⃗⃗, then the value of 8 cos2
𝛼 is _____ .
Q.13 Let 𝑎, 𝑏, 𝑐 be three non-zero real numbers such that the equation
√3 𝑎 cos 𝑥 + 2 𝑏 sin 𝑥 = 𝑐, 𝑥 ∈ [−
𝜋
2
,
𝜋
2
],
has two distinct real roots 𝛼 and 𝛽 with 𝛼 + 𝛽 =
𝜋
3
. Then, the value of
𝑏
𝑎
is _____ .
Q.14 A farmer 𝐹1 has a land in the shape of a triangle with vertices at 𝑃(0, 0), 𝑄(1, 1) and
𝑅(2, 0). From this land, a neighbouring farmer 𝐹2 takes away the region which lies
between the side 𝑃𝑄 and a curve of the form 𝑦 = 𝑥 𝑛
(𝑛 > 1). If the area of the region
taken away by the farmer 𝐹2 is exactly 30% of the area of ∆𝑃𝑄𝑅, then the value of 𝑛 is
_____ .
31. JEE (Advanced) 2018 Paper 1
7/8
SECTION 3 (Maximum Marks: 12)
This section contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions.
Each question has FOUR options. ONLY ONE of these four options corresponds to the correct answer.
For each question, choose the option corresponding to the correct answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : −1 In all other cases.
PARAGRAPH “X”
Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation 𝑥2
+ 𝑦2
= 4.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.15 Let 𝐸1 𝐸2 and 𝐹1 𝐹2 be the chords of 𝑆 passing through the point 𝑃0 (1, 1) and parallel to the
x-axis and the y-axis, respectively. Let 𝐺1 𝐺2 be the chord of S passing through 𝑃0 and
having slope −1. Let the tangents to 𝑆 at 𝐸1 and 𝐸2 meet at 𝐸3, the tangents to 𝑆 at 𝐹1 and
𝐹2 meet at 𝐹3, and the tangents to 𝑆 at 𝐺1 and 𝐺2 meet at 𝐺3. Then, the points 𝐸3, 𝐹3, and
𝐺3 lie on the curve
(A) 𝑥 + 𝑦 = 4 (B) (𝑥 − 4)2
+ (𝑦 − 4)2
= 16
(C) (𝑥 − 4)(𝑦 − 4) = 4 (D) 𝑥𝑦 = 4
PARAGRAPH “X”
Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation 𝑥2
+ 𝑦2
= 4.
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)
Q.16 Let 𝑃 be a point on the circle 𝑆 with both coordinates being positive. Let the tangent to 𝑆 at
𝑃 intersect the coordinate axes at the points 𝑀 and 𝑁. Then, the mid-point of the line
segment 𝑀𝑁 must lie on the curve
(A) (𝑥 + 𝑦)2
= 3𝑥𝑦 (B) 𝑥2/3
+ 𝑦2/3
= 24/3
(C) 𝑥2
+ 𝑦2
= 2𝑥𝑦 (D) 𝑥2
+ 𝑦2
= 𝑥2
𝑦2
32. JEE (Advanced) 2018 Paper 1
8/8
Q.17 The probability that, on the examination day, the student 𝑆1 gets the previously allotted seat
𝑅1, and NONE of the remaining students gets the seat previously allotted to him/her is
(A)
3
40
(B)
1
8
(C)
7
40
(D)
1
5
PARAGRAPH “A”
There are five students 𝑆1, 𝑆2, 𝑆3, 𝑆4 and 𝑆5 in a music class and for them there are
five seats 𝑅1, 𝑅2, 𝑅3, 𝑅4 and 𝑅5 arranged in a row, where initially the seat 𝑅𝑖 is
allotted to the student 𝑆𝑖, 𝑖 = 1, 2, 3, 4, 5. But, on the examination day, the five
students are randomly allotted the five seats.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)
Q.18 For 𝑖 = 1, 2, 3, 4, let 𝑇𝑖 denote the event that the students 𝑆𝑖 and 𝑆𝑖+1 do NOT sit adjacent
to each other on the day of the examination. Then, the probability of the event
𝑇1 ∩ 𝑇2 ∩ 𝑇3 ∩ 𝑇4 is
(A)
1
15
(B)
1
10
(C)
7
60
(D)
1
5
END OF THE QUESTION PAPER
PARAGRAPH “A”
There are five students 𝑆1, 𝑆2, 𝑆3, 𝑆4 and 𝑆5 in a music class and for them there are
five seats 𝑅1, 𝑅2, 𝑅3, 𝑅4 and 𝑅5 arranged in a row, where initially the seat 𝑅𝑖 is
allotted to the student 𝑆𝑖, 𝑖 = 1, 2, 3, 4, 5. But, on the examination day, the five
students are randomly allotted the five seats.
(There are two questions based on PARAGRAPH “A”, the question given below is one of them)