JEE Main 2019 — 9 Jan Shift 2 (Previous Year Paper) with Answer Key

more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v

is equal to:","text":"In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$v

more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v

is equal to:","acceptedAnswer":{"@type":"Answer","text":"B. $\\sqrt{a_1a_2}\\,t$"},"suggestedAnswer":[{"@type":"Answer","text":"A. $\\sqrt{2a_1a_2}\\,t$"},{"@type":"Answer","text":"C. $\\frac{a_1 + a_2}{2}\\,t$"},{"@type":"Answer","text":"D. $\\frac{2a_1a_2}{a_1 + a_2}\\,t$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a\\cos\\omega t$, $y = a\\sin\\omega t$ and $z = a\\omega t$. The speed of the particle is:","text":"The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a\\cos\\omega t$, $y = a\\sin\\omega t$ and $z = a\\omega t$. The speed of the particle is:","acceptedAnswer":{"@type":"Answer","text":"C. $\\sqrt{2}\\,a\\omega$"},"suggestedAnswer":[{"@type":"Answer","text":"A. $a\\omega$"},{"@type":"Answer","text":"B. $2a\\omega$"},{"@type":"Answer","text":"D. $\\sqrt{3}\\,a\\omega$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($g = 10$ m s$^{-2}$)","text":"A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($g = 10$ m s$^{-2}$)","acceptedAnswer":{"@type":"Answer","text":"A. 100 N"},"suggestedAnswer":[{"@type":"Answer","text":"B. 200 N"},{"@type":"Answer","text":"C. 140 N"},{"@type":"Answer","text":"D. 70 N"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A force acts on a 2 kg object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in first 5 seconds?","text":"A force acts on a 2 kg object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in first 5 seconds?","acceptedAnswer":{"@type":"Answer","text":"B. 900 J"},"suggestedAnswer":[{"@type":"Answer","text":"A. 950 J"},{"@type":"Answer","text":"C. 875 J"},{"@type":"Answer","text":"D. 850 J"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$^{-1}$) will be ($g = 10$ m s$^{-2}$)","text":"A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$^{-1}$) will be ($g = 10$ m s$^{-2}$)","acceptedAnswer":{"@type":"Answer","text":"A. $\\sqrt{30}$"},"suggestedAnswer":[{"@type":"Answer","text":"B. $\\sqrt{\\frac{30}{2}}$"},{"@type":"Answer","text":"C. $\\frac{\\sqrt{30}}{2}$"},{"@type":"Answer","text":"D. $\\frac{\\sqrt{20}}{3}$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = $6.4 \\times 10^3$ km) is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of h for which $E_1$ and $E_2$ are equal, is:","text":"The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = $6.4 \\times 10^3$ km) is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of h for which $E_1$ and $E_2$ are equal, is:","acceptedAnswer":{"@type":"Answer","text":"D. $3.2 \\times 10^3$ km"},"suggestedAnswer":[{"@type":"Answer","text":"A. $1.28 \\times 10^4$ km"},{"@type":"Answer","text":"B. $6.4 \\times 10^3$ km"},{"@type":"Answer","text":"C. $1.6 \\times 10^3$ km"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:","text":"The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:","acceptedAnswer":{"@type":"Answer","text":"A. 4.8 m"},"suggestedAnswer":[{"@type":"Answer","text":"B. 9.6 m"},{"@type":"Answer","text":"C. 2.9 m"},{"@type":"Answer","text":"D. 6.0 m"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1$ (= 600 K) and rejects to a reservoir at temperature $T_2$. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3$ (= 400 K). Calculate the temperature $T_2$ if the work outputs of the two engines are equal:","text":"Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1$ (= 600 K) and rejects to a reservoir at temperature $T_2$. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3$ (= 400 K). Calculate the temperature $T_2$ if the work outputs of the two engines are equal:","acceptedAnswer":{"@type":"Answer","text":"C. 500 K"},"suggestedAnswer":[{"@type":"Answer","text":"A. 300 K"},{"@type":"Answer","text":"B. 400 K"},{"@type":"Answer","text":"D. 600 K"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take R = 8.3 J/K mole]","text":"A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take R = 8.3 J/K mole]","acceptedAnswer":{"@type":"Answer","text":"C. 10 kJ"},"suggestedAnswer":[{"@type":"Answer","text":"A. 0.9 kJ"},{"@type":"Answer","text":"B. 6 kJ"},{"@type":"Answer","text":"D. 14 kJ"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:","text":"A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:","acceptedAnswer":{"@type":"Answer","text":"C. 666 Hz"},"suggestedAnswer":[{"@type":"Answer","text":"A. 333 Hz"},{"@type":"Answer","text":"B. 500 Hz"},{"@type":"Answer","text":"D. 753 Hz"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:","text":"A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:","acceptedAnswer":{"@type":"Answer","text":"C. $\\frac{A}{\\sqrt{2}}$"},"suggestedAnswer":[{"@type":"Answer","text":"A. A"},{"@type":"Answer","text":"B. $\\frac{A}{2}$"},{"@type":"Answer","text":"D. $\\frac{A}{2\\sqrt{2}}$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant K will be:","text":"A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant K will be:","acceptedAnswer":{"@type":"Answer","text":"B. $K = \\frac{(K_1 + K_3)(K_2 + K_4)}{K_1 + K_2 + K_3 + K_4}$"},"suggestedAnswer":[{"@type":"Answer","text":"A. $K = \\frac{(K_1 + K_2)(K_3 + K_4)}{K_1 + K_2 + K_3 + K_4}$"},{"@type":"Answer","text":"C. $K = \\frac{(K_1 + K_4)(K_2 + K_3)}{2(K_1 + K_2 + K_3 + K_4)}$"},{"@type":"Answer","text":"D. $K = \\frac{(K_1 + K_2)(K_3 + K_4)}{2(K_1 + K_2 + K_3 + K_4)}$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"Charge is distributed within a sphere of radius R with a volume charge density $\\rho(r) = \\frac{A}{r^2}e^{-2r/a}$, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:","text":"Charge is distributed within a sphere of radius R with a volume charge density $\\rho(r) = \\frac{A}{r^2}e^{-2r/a}$, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:","acceptedAnswer":{"@type":"Answer","text":"B. $\\frac{a}{2}\\log\\left(\\frac{1}{1 - \\frac{Q}{2\\pi aA}}\\right)$"},"suggestedAnswer":[{"@type":"Answer","text":"A. $\\frac{a}{2}\\log\\left(1 - \\frac{Q}{2\\pi aA}\\right)$"},{"@type":"Answer","text":"C. $a\\log\\left(1 - \\frac{Q}{2\\pi aA}\\right)$"},{"@type":"Answer","text":"D. $a\\log\\left(\\frac{1}{1 - \\frac{Q}{2\\pi aA}}\\right)$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"Two point charges $q_1$ ($\\sqrt{10}$ μC) and $q_2$ (−25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, $\\left[\\text{take } \\frac{1}{4\\pi\\epsilon_0} = 9 \\times 10^9 \\text{ Nm}^2\\text{C}^{-2}\\right]$","text":"Two point charges $q_1$ ($\\sqrt{10}$ μC) and $q_2$ (−25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, $\\left[\\text{take } \\frac{1}{4\\pi\\epsilon_0} = 9 \\times 10^9 \\text{ Nm}^2\\text{C}^{-2}\\right]$","acceptedAnswer":{"@type":"Answer","text":"B. $(63\\hat{i} - 27\\hat{j}) \\times 10^2$"},"suggestedAnswer":[{"@type":"Answer","text":"A. $(-63\\hat{i} + 27\\hat{j}) \\times 10^2$"},{"@type":"Answer","text":"C. $(81\\hat{i} - 81\\hat{j}) \\times 10^2$"},{"@type":"Answer","text":"D. $(-81\\hat{i} + 81\\hat{j}) \\times 10^2$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"In the given circuit the internal resistance of the 18 V cell is negligible. If $R_1 = 400\\ \\Omega$, $R_3 = 100\\ \\Omega$ and $R_4 = 500\\ \\Omega$ and the reading of an ideal voltmeter across $R_4$ is 5 V, then the value of $R_2$ will be:","text":"In the given circuit the internal resistance of the 18 V cell is negligible. If $R_1 = 400\\ \\Omega$, $R_3 = 100\\ \\Omega$ and $R_4 = 500\\ \\Omega$ and the reading of an ideal voltmeter across $R_4$ is 5 V, then the value of $R_2$ will be:","acceptedAnswer":{"@type":"Answer","text":"D. 300 Ω"},"suggestedAnswer":[{"@type":"Answer","text":"A. 550 Ω"},{"@type":"Answer","text":"B. 230 Ω"},{"@type":"Answer","text":"C. 450 Ω"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:","text":"A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:","acceptedAnswer":{"@type":"Answer","text":"C. $5.17 \\times 10^2$ J"},"suggestedAnswer":[{"@type":"Answer","text":"A. $5.65 \\times 10^2$ J"},{"@type":"Answer","text":"B. $2.26 \\times 10^3$ J"},{"@type":"Answer","text":"D. $3.39 \\times 10^3$ J"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop ($B_L$) to that at the centre of the coil ($B_C$), i.e. $\\frac{B_L}{B_C}$ will be:","text":"One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop ($B_L$) to that at the centre of the coil ($B_C$), i.e. $\\frac{B_L}{B_C}$ will be:","acceptedAnswer":{"@type":"Answer","text":"C. $\\frac{1}{N^2}$"},"suggestedAnswer":[{"@type":"Answer","text":"A. N"},{"@type":"Answer","text":"B. $N^2$"},{"@type":"Answer","text":"D. $\\frac{1}{N}$"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = $1.6 \\times 10^{-19}$ C)","text":"A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = $1.6 \\times 10^{-19}$ C)","acceptedAnswer":{"@type":"Answer","text":"B. $2.0 \\times 10^{-24}$ kg"},"suggestedAnswer":[{"@type":"Answer","text":"A. $9.1 \\times 10^{-31}$ kg"},{"@type":"Answer","text":"C. $1.6 \\times 10^{-19}$ kg"},{"@type":"Answer","text":"D. $1.6 \\times 10^{-27}$ kg"}]},{"@type":"Question","eduQuestionType":"Multiple choice","name":"A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:","text":"A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:","acceptedAnswer":{"@type":"Answer","text":"C. 45 A"},"suggestedAnswer":[{"@type":"Answer","text":"A. 35 A"},{"@type":"Answer","text":"B. 50 A"},{"@type":"Answer","text":"D. 25 A"}]}]}

is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sqrt{2a_1a_2}\\,t$","is_correct":false},{"key":"B","content":"$\\sqrt{a_1a_2}\\,t$","is_correct":true},{"key":"C","content":"$\\frac{a_1 + a_2}{2}\\,t$","is_correct":false},{"key":"D","content":"$\\frac{2a_1a_2}{a_1 + a_2}\\,t$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":3,"question":"The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a\\cos\\omega t$, $y = a\\sin\\omega t$ and $z = a\\omega t$. The speed of the particle is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$a\\omega$","is_correct":false},{"key":"B","content":"$2a\\omega$","is_correct":false},{"key":"C","content":"$\\sqrt{2}\\,a\\omega$","is_correct":true},{"key":"D","content":"$\\sqrt{3}\\,a\\omega$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":4,"question":"A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($g = 10$ m s$^{-2}$)","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"100 N","is_correct":true},{"key":"B","content":"200 N","is_correct":false},{"key":"C","content":"140 N","is_correct":false},{"key":"D","content":"70 N","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":5,"question":"A force acts on a 2 kg object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in first 5 seconds?","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"950 J","is_correct":false},{"key":"B","content":"900 J","is_correct":true},{"key":"C","content":"875 J","is_correct":false},{"key":"D","content":"850 J","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":6,"question":"A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$^{-1}$) will be ($g = 10$ m s$^{-2}$)","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q6.png","type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sqrt{30}$","is_correct":true},{"key":"B","content":"$\\sqrt{\\frac{30}{2}}$","is_correct":false},{"key":"C","content":"$\\frac{\\sqrt{30}}{2}$","is_correct":false},{"key":"D","content":"$\\frac{\\sqrt{20}}{3}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":7,"question":"The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = $6.4 \\times 10^3$ km) is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of h for which $E_1$ and $E_2$ are equal, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$1.28 \\times 10^4$ km","is_correct":false},{"key":"B","content":"$6.4 \\times 10^3$ km","is_correct":false},{"key":"C","content":"$1.6 \\times 10^3$ km","is_correct":false},{"key":"D","content":"$3.2 \\times 10^3$ km","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":8,"question":"The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"4.8 m","is_correct":true},{"key":"B","content":"9.6 m","is_correct":false},{"key":"C","content":"2.9 m","is_correct":false},{"key":"D","content":"6.0 m","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":9,"question":"Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1$ (= 600 K) and rejects to a reservoir at temperature $T_2$. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3$ (= 400 K). Calculate the temperature $T_2$ if the work outputs of the two engines are equal:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"300 K","is_correct":false},{"key":"B","content":"400 K","is_correct":false},{"key":"C","content":"500 K","is_correct":true},{"key":"D","content":"600 K","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":10,"question":"A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take R = 8.3 J/K mole]","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"0.9 kJ","is_correct":false},{"key":"B","content":"6 kJ","is_correct":false},{"key":"C","content":"10 kJ","is_correct":true},{"key":"D","content":"14 kJ","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":11,"question":"A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"333 Hz","is_correct":false},{"key":"B","content":"500 Hz","is_correct":false},{"key":"C","content":"666 Hz","is_correct":true},{"key":"D","content":"753 Hz","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":12,"question":"A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"A","is_correct":false},{"key":"B","content":"$\\frac{A}{2}$","is_correct":false},{"key":"C","content":"$\\frac{A}{\\sqrt{2}}$","is_correct":true},{"key":"D","content":"$\\frac{A}{2\\sqrt{2}}$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":13,"question":"A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant K will be:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q14.png","type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$K = \\frac{(K_1 + K_2)(K_3 + K_4)}{K_1 + K_2 + K_3 + K_4}$","is_correct":false},{"key":"B","content":"$K = \\frac{(K_1 + K_3)(K_2 + K_4)}{K_1 + K_2 + K_3 + K_4}$","is_correct":true},{"key":"C","content":"$K = \\frac{(K_1 + K_4)(K_2 + K_3)}{2(K_1 + K_2 + K_3 + K_4)}$","is_correct":false},{"key":"D","content":"$K = \\frac{(K_1 + K_2)(K_3 + K_4)}{2(K_1 + K_2 + K_3 + K_4)}$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":14,"question":"Charge is distributed within a sphere of radius R with a volume charge density $\\rho(r) = \\frac{A}{r^2}e^{-2r/a}$, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{a}{2}\\log\\left(1 - \\frac{Q}{2\\pi aA}\\right)$","is_correct":false},{"key":"B","content":"$\\frac{a}{2}\\log\\left(\\frac{1}{1 - \\frac{Q}{2\\pi aA}}\\right)$","is_correct":true},{"key":"C","content":"$a\\log\\left(1 - \\frac{Q}{2\\pi aA}\\right)$","is_correct":false},{"key":"D","content":"$a\\log\\left(\\frac{1}{1 - \\frac{Q}{2\\pi aA}}\\right)$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":15,"question":"Two point charges $q_1$ ($\\sqrt{10}$ μC) and $q_2$ (−25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, $\\left[\\text{take } \\frac{1}{4\\pi\\epsilon_0} = 9 \\times 10^9 \\text{ Nm}^2\\text{C}^{-2}\\right]$","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$(-63\\hat{i} + 27\\hat{j}) \\times 10^2$","is_correct":false},{"key":"B","content":"$(63\\hat{i} - 27\\hat{j}) \\times 10^2$","is_correct":true},{"key":"C","content":"$(81\\hat{i} - 81\\hat{j}) \\times 10^2$","is_correct":false},{"key":"D","content":"$(-81\\hat{i} + 81\\hat{j}) \\times 10^2$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":16,"question":"In the given circuit the internal resistance of the 18 V cell is negligible. If $R_1 = 400\\ \\Omega$, $R_3 = 100\\ \\Omega$ and $R_4 = 500\\ \\Omega$ and the reading of an ideal voltmeter across $R_4$ is 5 V, then the value of $R_2$ will be:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q17.png","type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"550 Ω","is_correct":false},{"key":"B","content":"230 Ω","is_correct":false},{"key":"C","content":"450 Ω","is_correct":false},{"key":"D","content":"300 Ω","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":17,"question":"A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$5.65 \\times 10^2$ J","is_correct":false},{"key":"B","content":"$2.26 \\times 10^3$ J","is_correct":false},{"key":"C","content":"$5.17 \\times 10^2$ J","is_correct":true},{"key":"D","content":"$3.39 \\times 10^3$ J","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":18,"question":"One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop ($B_L$) to that at the centre of the coil ($B_C$), i.e. $\\frac{B_L}{B_C}$ will be:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"N","is_correct":false},{"key":"B","content":"$N^2$","is_correct":false},{"key":"C","content":"$\\frac{1}{N^2}$","is_correct":true},{"key":"D","content":"$\\frac{1}{N}$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":19,"question":"A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = $1.6 \\times 10^{-19}$ C)","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$9.1 \\times 10^{-31}$ kg","is_correct":false},{"key":"B","content":"$2.0 \\times 10^{-24}$ kg","is_correct":true},{"key":"C","content":"$1.6 \\times 10^{-19}$ kg","is_correct":false},{"key":"D","content":"$1.6 \\times 10^{-27}$ kg","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":20,"question":"A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"35 A","is_correct":false},{"key":"B","content":"50 A","is_correct":false},{"key":"C","content":"45 A","is_correct":true},{"key":"D","content":"25 A","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":21,"question":"The energy associated with electric field is ($U_E$) and with magnetic field is ($U_B$) for an electromagnetic wave in free space. Then:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$U_E > U_B$","is_correct":false},{"key":"B","content":"$U_E \u003c U_B$","is_correct":false},{"key":"C","content":"$U_E = U_B$","is_correct":true},{"key":"D","content":"$U_E = \\frac{U_B}{2}$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":22,"question":"Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror ($M_1$) and parallel to the second mirror ($M_2$) is finally reflected from the second mirror ($M_2$) parallel to the first mirror ($M_1$). The angle between the two mirrors will be:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"45°","is_correct":false},{"key":"B","content":"60°","is_correct":true},{"key":"C","content":"75°","is_correct":false},{"key":"D","content":"90°","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":23,"question":"In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\\lambda = 500$ nm is incident on the slits. The total number of bright fringes that are observed in the angular range $-30° \\le \\theta \\le 30°$ is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"320","is_correct":false},{"key":"B","content":"321","is_correct":false},{"key":"C","content":"640","is_correct":false},{"key":"D","content":"641","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":24,"question":"The magnetic field associated with a light wave is given, at the origin, by $B = B_0[\\sin(3.14 \\times 10^7)ct + \\sin(6.28 \\times 10^7)ct]$. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? ($c = 3 \\times 10^8$ m s$^{-1}$, $h = 6.6 \\times 10^{-34}$ J-s)","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"7.72 eV","is_correct":true},{"key":"B","content":"8.52 eV","is_correct":false},{"key":"C","content":"12.5 eV","is_correct":false},{"key":"D","content":"6.82 eV","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":25,"question":"At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio $\\frac{R_B}{R_A}$ of their activities after time t itself decays with time t as $e^{-3t}$. If the half-life of A is $\\ln 2$, the half-life of B is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{\\ln 2}{4}$","is_correct":true},{"key":"B","content":"$\\frac{\\ln 2}{2}$","is_correct":false},{"key":"C","content":"$2\\ln 2$","is_correct":false},{"key":"D","content":"$4\\ln 2$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":26,"question":"Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of $V_o$ changes by: (assume that the Ge diode has large breakdown voltage)","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q27.png","type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"0.4 V","is_correct":true},{"key":"B","content":"0.2 V","is_correct":false},{"key":"C","content":"0.6 V","is_correct":false},{"key":"D","content":"0.8 V","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":27,"question":"In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accomodated for transmitting TV signals of band width 6 MHz are (Take velocity of light $c = 3 \\times 10^8$ m/s, $h = 6.6 \\times 10^{-34}$ J-s)","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$6.25 \\times 10^5$","is_correct":true},{"key":"B","content":"$3.86 \\times 10^6$","is_correct":false},{"key":"C","content":"$4.87 \\times 10^5$","is_correct":false},{"key":"D","content":"$3.75 \\times 10^6$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":28,"question":"A carbon resistance has a following colour code (bands, from left: Green, Orange, Yellow, Golden). What is the value of the resistance?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q29.png","type":"mcq_single","difficulty":"easy","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"6.4 MΩ ± 5%","is_correct":false},{"key":"B","content":"530 kΩ ± 5%","is_correct":true},{"key":"C","content":"64 kΩ ± 10%","is_correct":false},{"key":"D","content":"5.3 MΩ ± 5%","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":29,"question":"The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Physics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"5.725 mm","is_correct":false},{"key":"B","content":"5.755 mm","is_correct":true},{"key":"C","content":"5.950 mm","is_correct":false},{"key":"D","content":"5.740 mm","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":30,"question":"The major product of the following reaction is: γ-butyrolactone + o-cresol (2-methylphenol) $\\xrightarrow{\\text{AlCl}_3,\\ \\Delta}$ ?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q31.png","type":"mcq_single","difficulty":"hard","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"A 1-indanone fused to the phenol ring: OH and CH$_3$ on the benzene ring, with the CH$_3$ ortho to the C=O-bearing ring fusion, and a methyl on the five-membered ring","is_correct":false},{"key":"B","content":"A 1-tetralone (six-membered ketone ring fused to benzene) with OH and CH$_3$ on the aromatic ring (CH$_3$ ortho to OH, OH meta to the ring carbonyl side as drawn)","is_correct":true},{"key":"C","content":"A 1-indanone with OH and CH$_3$ on the aromatic ring (OH para to the ring-fusion) and a methyl on the five-membered ring","is_correct":false},{"key":"D","content":"A 1-tetralone with OH and CH$_3$ on the aromatic ring, OH para to the carbonyl-bearing ring fusion (C=O at the bottom as drawn)","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":31,"question":"Which of the following compounds is not aromatic?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q32.png","type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"Pyridine","is_correct":false},{"key":"B","content":"Pyrrole","is_correct":false},{"key":"C","content":"Cyclopentadienyl cation","is_correct":true},{"key":"D","content":"Cyclopentadienyl anion","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":32,"question":"The major product of the following reaction is: 2-ethylbenzamide (a benzene ring bearing $-\\text{CONH}_2$ and an ortho $-\\text{CH}_2\\text{CH}_3$) $\\xrightarrow{\\text{(i) Br}_2/h\\nu\\text{; (ii) KOH (dil)}}$ ?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q33.png","type":"mcq_single","difficulty":"hard","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"3,4-dihydroisoquinolin-1(2H)-one (six-membered lactam: C=O, NH, CH$_2$, CH$_2$ fused to benzene)","is_correct":false},{"key":"B","content":"3-methylisoindolin-1-one (five-membered lactam: C=O, NH, CH(CH$_3$) fused to benzene)","is_correct":true},{"key":"C","content":"Isoindoline-type ring without carbonyl: benzene fused to a five-membered ring containing NH","is_correct":false},{"key":"D","content":"Benzene fused to a four-membered ring containing NH and a CH bearing CH$_3$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":33,"question":"The products formed in the reaction of cumene with $\\text{O}_2$ followed by treatment with dil. HCl are:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q34.png","type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"Phenol and propan-2-ol ($\\text{CH}_3\\text{CH(OH)CH}_3$)","is_correct":false},{"key":"B","content":"Phenol and acetone ($\\text{CH}_3\\text{COCH}_3$)","is_correct":true},{"key":"C","content":"Benzene and acetone","is_correct":false},{"key":"D","content":"Acetophenone ($\\text{C}_6\\text{H}_5\\text{COCH}_3$) and methanol ($\\text{CH}_3\\text{OH}$)","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":34,"question":"The major product formed in the following reaction is: $\\text{CH}_3\\text{CHO}$ + $\\text{C}_6\\text{H}_5\\text{COCH}_3$ $\\xrightarrow{\\text{dil. NaOH}}$ ?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q35.png","type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{CH}_3\\text{CH(OH)CH}_2\\text{CHO}$","is_correct":false},{"key":"B","content":"$\\text{CH}_3\\text{CH(OH)CH}_2\\text{COC}_6\\text{H}_5$","is_correct":true},{"key":"C","content":"$\\text{OHC}-\\text{CH}_2-\\text{C(OH)(CH}_3)\\text{C}_6\\text{H}_5$","is_correct":false},{"key":"D","content":"$\\text{C}_6\\text{H}_5\\text{CO}-\\text{CH}_2-\\text{C(OH)(CH}_3)\\text{C}_6\\text{H}_5$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":35,"question":"The increasing basicity order of the following compounds is: (A) $\\text{CH}_3\\text{CH}_2\\text{NH}_2$ (B) $(\\text{CH}_3\\text{CH}_2)_2\\text{NH}$ (C) $(\\text{CH}_3)_3\\text{N}$ (D) $\\text{Ph}-\\text{NH}-\\text{CH}_3$","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"(A) \u003c (B) \u003c (D) \u003c (C)","is_correct":false},{"key":"B","content":"(D) \u003c (C) \u003c (B) \u003c (A)","is_correct":false},{"key":"C","content":"(D) \u003c (C) \u003c (A) \u003c (B)","is_correct":true},{"key":"D","content":"(A) \u003c (B) \u003c (C) \u003c (D)","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":36,"question":"The correct sequence of amino acids present in the tripeptide given below is:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q37.png","type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"Leu - Ser - Thr","is_correct":false},{"key":"B","content":"Thr - Ser - Leu","is_correct":false},{"key":"C","content":"Val - Ser - Thr","is_correct":true},{"key":"D","content":"Thr - Ser - Val","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":37,"question":"The tests performed on compound X and their inferences are: (a) 2,4-DNP test — Coloured precipitate; (b) Iodoform test — Yellow precipitate; (c) Azo-dye test — No dye formation. Compound 'X' is:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q38.png","type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"2-aminophenyl substituted secondary alcohol: benzene with $-\\text{NH}_2$ and ortho $-\\text{CH(OH)CH}_3$","is_correct":false},{"key":"B","content":"Benzene with $-\\text{N(CH}_3)_2$ and ortho $-\\text{COCH}_3$ (2-(dimethylamino)acetophenone)","is_correct":true},{"key":"C","content":"Benzene with $-\\text{NH}_2$ and ortho $-\\text{CH}_2\\text{CHO}$","is_correct":false},{"key":"D","content":"Benzene with $-\\text{N(CH}_3)_2$ and ortho $-\\text{CH}_2\\text{CHO}$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":38,"question":"The major product obtained in the following reaction is: 2-amino-1-phenylpropan-1-ol ($\\text{C}_6\\text{H}_5-\\text{CH(OH)}-\\text{CH(NH}_2)-\\text{CH}_3$) $\\xrightarrow[\\text{room temp.}]{(\\text{CH}_3\\text{CO})_2\\text{O/pyridine (1 eqv.)}}$ ?","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q39.png","type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{C}_6\\text{H}_5-\\text{CH(OCOCH}_3)-\\text{CH(NH}_2)-\\text{CH}_3$","is_correct":false},{"key":"B","content":"$\\text{C}_6\\text{H}_5-\\text{CH(OH)}-\\text{CH(NHCOCH}_3)-\\text{CH}_3$","is_correct":true},{"key":"C","content":"$\\text{C}_6\\text{H}_5-\\text{C(CH}_3)=\\text{C(CH}_3)-\\text{NHCOCH}_3$ type enamide (C=C in the chain, N-acetyl)","is_correct":false},{"key":"D","content":"Ring-acetylated product: $\\text{COCH}_3$ on the benzene ring ortho to the side chain, with OH and $\\text{NH}_2$ unchanged","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":39,"question":"The correct match between Item I and Item II is: Item I: (A) Benzaldehyde, (B) Alumina, (C) Acetonitrile. Item II: (P) Mobile phase, (Q) Adsorbent, (R) Adsorbate.","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"(A)→(P); (B)→(R); (C)→(Q)","is_correct":false},{"key":"B","content":"(A)→(Q); (B)→(P); (C)→(R)","is_correct":false},{"key":"C","content":"(A)→(Q); (B)→(R); (C)→(P)","is_correct":false},{"key":"D","content":"(A)→(R); (B)→(Q); (C)→(P)","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":40,"question":"When the first electron gain enthalpy ($\\Delta_{eg}H$) of oxygen is −141 kJ/mol, its second electron gain enthalpy is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"a positive value","is_correct":true},{"key":"B","content":"a more negative value than the first","is_correct":false},{"key":"C","content":"negative, but less negative than the first","is_correct":false},{"key":"D","content":"almost the same as that of the first","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":41,"question":"The correct statement regarding the given Ellingham diagram is:","image_url":"https://gyanvapi.kineticsoftwaresolution.com/storage/questions/jee-main/jee-main-2019-jan-09-shift2/q42.png","type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"Coke cannot be used for the extraction of Cu from Cu$_2$O.","is_correct":false},{"key":"B","content":"At 1400°C, Al can be used for the extraction of Zn from ZnO","is_correct":true},{"key":"C","content":"At 500°C, coke can be used for the extraction of Zn from ZnO","is_correct":false},{"key":"D","content":"At 800°C, Cu can be used for the extraction of Zn from ZnO.","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":42,"question":"The temporary hardness of water is due to:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{CaCl}_2$","is_correct":false},{"key":"B","content":"$\\text{Ca(HCO}_3)_2$","is_correct":true},{"key":"C","content":"NaCl","is_correct":false},{"key":"D","content":"$\\text{Na}_2\\text{SO}_4$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":43,"question":"The metal that forms nitride by reacting directly with $\\text{N}_2$ of air, is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"K","is_correct":false},{"key":"B","content":"Rb","is_correct":false},{"key":"C","content":"Cs","is_correct":false},{"key":"D","content":"Li","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":44,"question":"Good reducing nature of $\\text{H}_3\\text{PO}_2$ is attributed to the presence of:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"One P−H bond","is_correct":false},{"key":"B","content":"Two P−H bonds","is_correct":true},{"key":"C","content":"One P−OH bond","is_correct":false},{"key":"D","content":"Two P−OH bonds","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":45,"question":"The transition element that has lowest enthalpy of atomisation, is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"V","is_correct":false},{"key":"B","content":"Cu","is_correct":false},{"key":"C","content":"Zn","is_correct":true},{"key":"D","content":"Fe","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":46,"question":"The complex that has highest crystal field splitting energy ($\\Delta$), is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{K}_2[\\text{CoCl}_4]$","is_correct":false},{"key":"B","content":"$\\text{K}_3[\\text{Co(CN)}_6]$","is_correct":true},{"key":"C","content":"$[\\text{Co(NH}_3)_5\\text{Cl}]\\text{Cl}_2$","is_correct":false},{"key":"D","content":"$[\\text{Co(NH}_3)_5(\\text{H}_2\\text{O})]\\text{Cl}_3$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":47,"question":"Homoleptic octahedral complexes of a metal ion '$\\text{M}^{3+} more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v

is equal to:","text":"In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$v

more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v

with three monodentate ligands $L_1$, $L_2$ and $L_3$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$L_1 \u003c L_2 \u003c L_3$","is_correct":false},{"key":"B","content":"$L_3 \u003c L_2 \u003c L_1$","is_correct":false},{"key":"C","content":"$L_2 \u003c L_1 \u003c L_3$","is_correct":false},{"key":"D","content":"$L_3 \u003c L_1 \u003c L_2$","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":48,"question":"Which of the following conditions in drinking water causes methemoglobinemia?","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"> 100 ppm of sulphate","is_correct":false},{"key":"B","content":"> 50 ppm of lead","is_correct":false},{"key":"C","content":"> 50 ppm of nitrate","is_correct":true},{"key":"D","content":"> 50 ppm of chloride","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":49,"question":"The pH of rain water, is approximately:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"7.0","is_correct":false},{"key":"B","content":"7.5","is_correct":false},{"key":"C","content":"6.5","is_correct":false},{"key":"D","content":"5.6","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":50,"question":"For the following reaction, the mass of water produced from 445 g of $\\text{C}_{57}\\text{H}_{110}\\text{O}_6$ is: $2\\text{C}_{57}\\text{H}_{110}\\text{O}_6(s) + 163\\text{O}_2(g) \\rightarrow 114\\text{CO}_2(g) + 110\\text{H}_2\\text{O}(l)$","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"445 g","is_correct":false},{"key":"B","content":"495 g","is_correct":true},{"key":"C","content":"490 g","is_correct":false},{"key":"D","content":"890 g","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":51,"question":"At 100°C, copper (Cu) has FCC unit cell structure with cell edge length of $x$ Å. What is the approximate density of Cu (in g cm$^{-3}$) at this temperature? [Atomic Mass of Cu = 63.55 u]","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{105}{x^3}$","is_correct":false},{"key":"B","content":"$\\frac{211}{x^3}$","is_correct":false},{"key":"C","content":"$\\frac{422}{x^3}$","is_correct":true},{"key":"D","content":"$\\frac{205}{x^3}$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":52,"question":"Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? (a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. (b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number. (c) According to wave mechanics, the ground state angular momentum is equal to $\\frac{h}{2\\pi}$. (d) The plot of $\\psi$ Vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value.","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"(a), (b)","is_correct":false},{"key":"B","content":"(a), (c)","is_correct":false},{"key":"C","content":"(b), (c)","is_correct":false},{"key":"D","content":"(a), (d)","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":53,"question":"In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{NO} \\rightarrow \\text{NO}^+$","is_correct":true},{"key":"B","content":"$\\text{O}_2 \\rightarrow \\text{O}_2^+$","is_correct":false},{"key":"C","content":"$\\text{O}_2 \\rightarrow \\text{O}_2^{2-}$","is_correct":false},{"key":"D","content":"$\\text{N}_2 \\rightarrow \\text{N}_2^+$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":54,"question":"The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are 4.2 kJ K$^{-1}$kg$^{-1}$ and 2.0 kJ K$^{-1}$kg$^{-1}$; heat of liquid fusion and vapourisation of water are 334 kJ kg$^{-1}$ and 2491 kJ kg$^{-1}$, respectively). (log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)","image_url":null,"type":"mcq_single","difficulty":"hard","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"2.64 kJ kg$^{-1}$K$^{-1}$","is_correct":false},{"key":"B","content":"8.49 kJ kg$^{-1}$K$^{-1}$","is_correct":false},{"key":"C","content":"7.90 kJ kg$^{-1}$K$^{-1}$","is_correct":false},{"key":"D","content":"9.26 kJ kg$^{-1}$K$^{-1}$","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":55,"question":"A solution containing 62 g ethylene glycol in 250 g water is cooled to −10°C. If $K_f$ for water is 1.86 K kg mol$^{-1}$, the amount of water (in g) separated as ice is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"16","is_correct":false},{"key":"B","content":"32","is_correct":false},{"key":"C","content":"48","is_correct":false},{"key":"D","content":"64","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":56,"question":"Consider the following reversible chemical reactions: $\\text{A}_2(g) + \\text{B}_2(g) \\overset{K_1}{\\rightleftharpoons} 2\\text{AB}(g)$ ..... (1); $6\\text{AB}(g) \\overset{K_2}{\\rightleftharpoons} 3\\text{A}_2(g) + 3\\text{B}_2(g)$ ..... (2). The relation between $K_1$ and $K_2$ is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$K_2 = K_1^{-3}$","is_correct":true},{"key":"B","content":"$K_2 = K_1^3$","is_correct":false},{"key":"C","content":"$K_1K_2 = 3$","is_correct":false},{"key":"D","content":"$K_1K_2 = \\frac{1}{3}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":57,"question":"If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction $\\text{Zn}(s) + \\text{Cu}^{2+}(aq) \\rightleftharpoons \\text{Zn}^{2+}(aq) + \\text{Cu}(s)$ at 300 K is approximately ($R = 8$ JK$^{-1}$mol$^{-1}$, $F = 96000$ C mol$^{-1}$)","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$e^{-80}$","is_correct":false},{"key":"B","content":"$e^{320}$","is_correct":false},{"key":"C","content":"$e^{-160}$","is_correct":false},{"key":"D","content":"$e^{160}$","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":58,"question":"For the reaction, $2\\text{A} + \\text{B} \\rightarrow$ products, when the concentrations of A and B both were doubled, the rate of the reaction increased from 0.3 mol L$^{-1}$s$^{-1}$ to 2.4 mol L$^{-1}$s$^{-1}$. When the concentration of A alone is doubled, the rate increased from 0.3 mol L$^{-1}$s$^{-1}$ to 0.6 mol L$^{-1}$s$^{-1}$. Which one of the following statements is correct?","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"Order of the reaction with respect to B is 2","is_correct":true},{"key":"B","content":"Total order of the reaction is 4","is_correct":false},{"key":"C","content":"Order of the reaction with respect to A is 2","is_correct":false},{"key":"D","content":"Order of the reaction with respect to B is 1","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":59,"question":"For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Chemistry","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\text{AlCl}_3$","is_correct":true},{"key":"B","content":"$\\text{BaCl}_2$","is_correct":false},{"key":"C","content":"NaCl","is_correct":false},{"key":"D","content":"$\\text{Na}_3\\text{PO}_4$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":60,"question":"Let $A = \\{x \\in \\mathbb{R} : x \\text{ is not a positive integer}\\}$. Define a function $f: A \\rightarrow \\mathbb{R}$ as $f(x) = \\frac{2x}{x-1}$, then $f$ is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"not injective","is_correct":false},{"key":"B","content":"injective but not surjective","is_correct":true},{"key":"C","content":"surjective but not injective","is_correct":false},{"key":"D","content":"neither injective nor surjective","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":61,"question":"Let $z_0$ be a root of the quadratic equation, $x^2 + x + 1 = 0$. If $z = 3 + 6iz_0^{81} - 3iz_0^{93}$, then $\\arg z$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{\\pi}{4}$","is_correct":true},{"key":"B","content":"$\\frac{\\pi}{6}$","is_correct":false},{"key":"C","content":"$\\frac{\\pi}{3}$","is_correct":false},{"key":"D","content":"0","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":62,"question":"The number of all possible positive integral values of $\\alpha$ for which the roots of the quadratic equation, $6x^2 - 11x + \\alpha = 0$ are rational numbers is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"2","is_correct":false},{"key":"B","content":"3","is_correct":true},{"key":"C","content":"4","is_correct":false},{"key":"D","content":"5","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":63,"question":"If $A = \\begin{bmatrix} e^t & e^{-t}\\cos t & e^{-t}\\sin t \\\\ e^t & -e^{-t}\\cos t - e^{-t}\\sin t & -e^{-t}\\sin t + e^{-t}\\cos t \\\\ e^t & 2e^{-t}\\sin t & -2e^{-t}\\cos t \\end{bmatrix}$, then A is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"invertible only if $t = \\pi$.","is_correct":false},{"key":"B","content":"invertible only if $t = \\frac{\\pi}{2}$.","is_correct":false},{"key":"C","content":"invertible for all $t \\in \\mathbb{R}$.","is_correct":true},{"key":"D","content":"not invertible for any $t \\in \\mathbb{R}$.","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":64,"question":"If the system of linear equations $x - 4y + 7z = g$, $3y - 5z = h$, $-2x + 5y - 9z = k$ is consistent, then:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$2g + h + k = 0$","is_correct":true},{"key":"B","content":"$g + 2h + k = 0$","is_correct":false},{"key":"C","content":"$g + h + 2k = 0$","is_correct":false},{"key":"D","content":"$g + h + k = 0$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":65,"question":"The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"372","is_correct":false},{"key":"B","content":"375","is_correct":false},{"key":"C","content":"374","is_correct":true},{"key":"D","content":"250","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":66,"question":"The coefficient of $t^4$ in the expansion of $\\left(\\frac{1 - t^6}{1 - t}\\right)^3$ is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"12","is_correct":false},{"key":"B","content":"10","is_correct":false},{"key":"C","content":"15","is_correct":true},{"key":"D","content":"14","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":67,"question":"Let a, b and c be the 7$^{\\text{th}}$, 11$^{\\text{th}}$ and 13$^{\\text{th}}$ terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then $\\frac{a}{c}$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"4","is_correct":true},{"key":"B","content":"2","is_correct":false},{"key":"C","content":"$\\frac{7}{13}$","is_correct":false},{"key":"D","content":"$\\frac{1}{2}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":68,"question":"The sum of the following series $1 + 6 + \\frac{9(1^2 + 2^2 + 3^2)}{7} + \\frac{12(1^2 + 2^2 + 3^2 + 4^2)}{9} + \\frac{15(1^2 + 2^2 + \\ldots + 5^2)}{11} + \\ldots$ up to 15 terms, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"7510","is_correct":false},{"key":"B","content":"7820","is_correct":true},{"key":"C","content":"7830","is_correct":false},{"key":"D","content":"7520","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":69,"question":"For each $x \\in \\mathbb{R}$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\\lim_{x \\to 0^-} \\frac{x([x] + |x|)\\sin[x]}{|x|}$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sin 1$","is_correct":false},{"key":"B","content":"0","is_correct":false},{"key":"C","content":"$-\\sin 1$","is_correct":true},{"key":"D","content":"1","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":70,"question":"If $x = 3\\tan t$ and $y = 3\\sec t$, then the value of $\\frac{d^2y}{dx^2}$ at $t = \\frac{\\pi}{4}$, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{1}{6}$","is_correct":false},{"key":"B","content":"$\\frac{1}{6\\sqrt{2}}$","is_correct":true},{"key":"C","content":"$\\frac{1}{3\\sqrt{2}}$","is_correct":false},{"key":"D","content":"$\\frac{3}{2\\sqrt{2}}$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":71,"question":"If both the roots of the quadratic equation $x^2 - mx + 4 = 0$ are real and distinct and they lie in the interval [1, 5], then m lies in the interval:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$(-5, -4)$","is_correct":false},{"key":"B","content":"$(3, 4)$","is_correct":false},{"key":"C","content":"$(4, 5)$","is_correct":true},{"key":"D","content":"$(5, 6)$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":72,"question":"Let $f$ be a differentiable function from $\\mathbb{R}$ to $\\mathbb{R}$ such that $|f(x) - f(y)| \\le 2|x - y|^{3/2}$, for all $x, y \\in \\mathbb{R}$. If $f(0) = 1$ then $\\int_0^1 f^2(x)\\,dx$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"0","is_correct":false},{"key":"B","content":"1","is_correct":true},{"key":"C","content":"$\\frac{1}{2}$","is_correct":false},{"key":"D","content":"2","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":73,"question":"If $f(x) = \\int \\frac{5x^8 + 7x^6}{(x^2 + 1 + 2x^7)^2}\\,dx$, $(x \\ge 0)$, and $f(0) = 0$, then the value of $f(1)$ is:","image_url":null,"type":"mcq_single","difficulty":"hard","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$-\\frac{1}{2}$","is_correct":false},{"key":"B","content":"$\\frac{1}{4}$","is_correct":true},{"key":"C","content":"$\\frac{1}{2}$","is_correct":false},{"key":"D","content":"$-\\frac{1}{4}$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":74,"question":"If $\\int_0^{\\pi/3} \\frac{\\tan\\theta}{\\sqrt{2k\\sec\\theta}}\\,d\\theta = 1 - \\frac{1}{\\sqrt{2}}$, $(k > 0)$, then the value of k is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"2","is_correct":true},{"key":"B","content":"1","is_correct":false},{"key":"C","content":"4","is_correct":false},{"key":"D","content":"$\\frac{1}{2}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":75,"question":"The area of the region $A = \\{(x, y) : 0 \\le y \\le x|x| + 1 \\text{ and } -1 \\le x \\le 1\\}$ in sq. units, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{2}{3}$","is_correct":false},{"key":"B","content":"$\\frac{1}{3}$","is_correct":false},{"key":"C","content":"$\\frac{4}{3}$","is_correct":false},{"key":"D","content":"2","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":76,"question":"Let $f: [0, 1] \\rightarrow \\mathbb{R}$ be such that $f(xy) = f(x) \\cdot f(y)$, for all $x, y \\in [0, 1]$, and $f(0) \\ne 0$. If $y = y(x)$ satisfies the differential equation, $\\frac{dy}{dx} = f(x)$ with $y(0) = 1$, then $y\\left(\\frac{1}{4}\\right) + y\\left(\\frac{3}{4}\\right)$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"2","is_correct":false},{"key":"B","content":"3","is_correct":true},{"key":"C","content":"4","is_correct":false},{"key":"D","content":"5","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":77,"question":"Let S be the set of all triangles in the $xy$-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"9","is_correct":false},{"key":"B","content":"18","is_correct":false},{"key":"C","content":"36","is_correct":true},{"key":"D","content":"32","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":78,"question":"Let the equations of two sides of a triangle be $3x - 2y + 6 = 0$ and $4x + 5y - 20 = 0$. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is:","image_url":null,"type":"mcq_single","difficulty":"hard","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$122y - 26x - 1675 = 0$","is_correct":false},{"key":"B","content":"$26x - 122y - 1675 = 0$","is_correct":true},{"key":"C","content":"$26x + 61y + 1675 = 0$","is_correct":false},{"key":"D","content":"$122y + 26x + 1675 = 0$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":79,"question":"If the circles $x^2 + y^2 - 16x - 20y + 164 = r^2$ and $(x - 4)^2 + (y - 7)^2 = 36$ intersect at two distinct points, then:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$1 \u003c r \u003c 11$","is_correct":true},{"key":"B","content":"$0 \u003c r \u003c 1$","is_correct":false},{"key":"C","content":"$r = 11$","is_correct":false},{"key":"D","content":"$r > 11$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":80,"question":"Let A(4, −4) and B(9, 6) be points on the parabola, $y^2 = 4x$. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $\\Delta$ACB is maximum. Then, the area (in sq.units) of $\\Delta$ACB, is:","image_url":null,"type":"mcq_single","difficulty":"hard","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$31\\frac{1}{4}$","is_correct":true},{"key":"B","content":"$30\\frac{1}{2}$","is_correct":false},{"key":"C","content":"32","is_correct":false},{"key":"D","content":"$31\\frac{3}{4}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":81,"question":"A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the $x$-axis. Then the eccentricity of the hyperbola is:","image_url":null,"type":"mcq_single","difficulty":"easy","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sqrt{3}$","is_correct":false},{"key":"B","content":"$\\frac{2}{\\sqrt{3}}$","is_correct":true},{"key":"C","content":"2","is_correct":false},{"key":"D","content":"$\\frac{3}{2}$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":82,"question":"If the lines $x = ay + b$, $z = cy + d$ and $x = a'z + b'$, $y = c'z + d'$ are perpendicular, then:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$ab' + bc' + 1 = 0$","is_correct":false},{"key":"B","content":"$bb' + cc' + 1 = 0$","is_correct":false},{"key":"C","content":"$aa' + c + c' = 0$","is_correct":true},{"key":"D","content":"$cc' + a + a' = 0$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":83,"question":"The equation of the plane containing the straight line $\\frac{x}{2} = \\frac{y}{3} = \\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\\frac{x}{3} = \\frac{y}{4} = \\frac{z}{2}$ and $\\frac{x}{4} = \\frac{y}{2} = \\frac{z}{3}$ is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$x + 2y - 2z = 0$","is_correct":false},{"key":"B","content":"$3x + 2y - 3z = 0$","is_correct":false},{"key":"C","content":"$x - 2y + z = 0$","is_correct":true},{"key":"D","content":"$5x + 2y - 4z = 0$","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":84,"question":"Let $\\vec{a} = \\hat{i} + \\hat{j} + \\sqrt{2}\\hat{k}$, $\\vec{b} = b_1\\hat{i} + b_2\\hat{j} + \\sqrt{2}\\hat{k}$ and $\\vec{c} = 5\\hat{i} + \\hat{j} + \\sqrt{2}\\hat{k}$ be three vectors such that the projection vector of $\\vec{b}$ on $\\vec{a}$ is $\\vec{a}$. If $\\vec{a} + \\vec{b}$ is perpendicular to $\\vec{c}$, then $|\\vec{b}|$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"6","is_correct":true},{"key":"B","content":"4","is_correct":false},{"key":"C","content":"$\\sqrt{22}$","is_correct":false},{"key":"D","content":"$\\sqrt{32}$","is_correct":false}],"correct_answer":"A","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":85,"question":"A data consists of n observations: $x_1, x_2, \\ldots, x_n$. If $\\sum_{i=1}^{n}(x_i + 1)^2 = 9n$ and $\\sum_{i=1}^{n}(x_i - 1)^2 = 5n$, then the standard deviation of this data is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sqrt{7}$","is_correct":false},{"key":"B","content":"$\\sqrt{5}$","is_correct":true},{"key":"C","content":"5","is_correct":false},{"key":"D","content":"2","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":86,"question":"An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\frac{27}{49}$","is_correct":false},{"key":"B","content":"$\\frac{21}{49}$","is_correct":false},{"key":"C","content":"$\\frac{26}{49}$","is_correct":false},{"key":"D","content":"$\\frac{32}{49}$","is_correct":true}],"correct_answer":"D","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":87,"question":"If $0 \\le x \u003c \\frac{\\pi}{2}$, then the number of values of $x$ for which $\\sin x - \\sin 2x + \\sin 3x = 0$, is:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"3","is_correct":false},{"key":"B","content":"4","is_correct":false},{"key":"C","content":"2","is_correct":true},{"key":"D","content":"1","is_correct":false}],"correct_answer":"C","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":88,"question":"If $x = \\sin^{-1}(\\sin 10)$ and $y = \\cos^{-1}(\\cos 10)$, then $y - x$ is equal to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"0","is_correct":false},{"key":"B","content":"$\\pi$","is_correct":true},{"key":"C","content":"10","is_correct":false},{"key":"D","content":"$7\\pi$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"},{"number":89,"question":"The logical statement $[\\sim(\\sim p \\vee q) \\vee (p \\wedge r)] \\wedge (\\sim q \\wedge r)$ is equivalent to:","image_url":null,"type":"mcq_single","difficulty":"medium","subject":"Mathematics","marks":4,"negative_marks":1,"options":[{"key":"A","content":"$\\sim p \\vee r$","is_correct":false},{"key":"B","content":"$(p \\wedge r) \\wedge \\sim q$","is_correct":true},{"key":"C","content":"$(p \\wedge \\sim q) \\vee r$","is_correct":false},{"key":"D","content":"$(\\sim p \\wedge \\sim q) \\wedge r$","is_correct":false}],"correct_answer":"B","explanation":null,"source":"JEE Main 2019 official paper","shown_locale":"en"}]}} more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v

is equal to:","text":"In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$v

more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then '$v