JEE Main 2019 Question Paper with Solutions

The distance of the point having position vector $- \widehat i + 2\widehat j + 6\widehat k$ from the straight line passing through the point (2, 3, – 4) and parallel to the vector, $6\widehat i + 3\widehat j - 4\widehat k$ is :

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5s, is close to :

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given ; Mass of planet = 8 × 10 22 kg, Radius of planet = 2 × 10 6 m, Gravitational constant G = 6.67 × 10 –11 Nm 2 /kg 2 ]

One mole of ideal gas passes through a process where pressure and volume obey the relation $P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$ . Here P 0 and V 0 are constants. Calculate the change in the temperature of the gas if its volume changes form V 0 to 2V 0

The correct statements among (a) to (d) are : (a) saline hydrides produce H 2 gas when reacted with H 2 O. (b) reaction of LiAlH 4 with BF 3 leads to B 2 H 6 . (c) PH 3 and CH 4 are electron - rich and electron - precise hydrides, respectively. (d) HF and CH 4 are called as molecular

The minimum amount of O 2 (g) consumed per gram of reactant is for the reaction : (Given atomic mass : Fe = 56, O = 16, Mg = 24, P = 31, C = 12, H = 1)

The difference between $\Delta$ H and $\Delta$ U ( $\Delta$ H – $\Delta$ U), when the combustion of one mole of heptane(l) is carried out at a temperature T, is equal to :

The pH of a 0.02 M NH 4 Cl solution will be : [given K b (NH 4 OH) = 10 –5 and log 2 = 0.301]

For the reaction, 2SO 2 (g) + O 2 (g) = 2SO 3 (g), Δ H = –57.2 kJ mol –1 and K C = 1.7 × 10 16 Which of the following statement is incorrect ?

The smallest natural number n, such that the coefficient of x in the expansion of ${\left( {{x^2} + {1 \over {{x^3}}}} \right)^n}$ is n C 23 , is :

Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance ${3 \over 5}$ from the origin. Then which one of the following points lies on any of these lines ?

If 5x + 9 = 0 is the directrix of the hyperbola 16x 2 – 9y 2 = 144, then its corresponding focus is :

The number of real roots of the equation 5 + |2 x – 1| = 2 x (2 x – 2) is

The negation of the Boolean expression ~ s ∨ (~r ∧ s) is equivalent to :

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity $\rho$ . The resistance between the two spheres will be :

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, R L = 4k Ω . The series resistance of the circuit is R i = 1 k Ω . If the battery voltage V B varies from 8 V to 16 V, what are the minimum and maximum values of the current through Zener diode?

A coil of self inductance 10 mH and resistance 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω . After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [take ln 5 = 1.6]

In a Young's double slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant h = 6.6 × 10 –34 Js, speed of light c = 3.0 × 10 8 m/s]

Let $\lambda$ be a real number for which the system of linear equations x + y + z = 6, 4x + $\lambda$ y – $\lambda$ z = $\lambda$ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation:

Let f(x) = log e (sin x), (0 < x < π ) and g(x) = sin –1 (e –x ), (x ≥ 0). If α is a positive real number such that a = (fog)'( α ) and b = (fog)( α ), then :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm 3 /min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

The integral $\int\limits_{\pi /6}^{\pi /3} {{{\sec }^{2/3}}} x\cos e{c^{4/3}}xdx$ is equal to :

The correct match between Item-I and Item-II is : .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-s6z2{text-align:center} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-s268{text-align:left} .tg .tg-0lax{text-align:left;vertical-align:top} Item - I Item - II (a) High density polythene (I) Peroxide catalyst (b) Polyacrylonitrile (II) Condensation at high temperature & pressure (c) Novolac (III) Ziegler-Natta Catalyst (d) Nylon 6 (IV) Acid or base catalyst

The major product 'Y' in the following reactions is :

For the reaction of H 2 with I 2 , the rate constant is 2.5 × 10 –4 dm 3 mol –1 s –1 at 327°C and 1.0 dm 3 mol –1 at 527°C. The activation energy for the reaction, in kJ mole –1 is : (R = 8.314 JK –1 mol –1 )

The highest possible oxidation states of uranium and plutonium, respectively are :

Which one of the following graphs between molar conductivity ( ${\Lambda _m}$ ) versus $\sqrt C$ is correct ?