JEE Main 2019 (Online) 11th January Evening Slot

If  \(\left| {\matrix{ {a - b - c} & {2a} & {2a} \cr {2b} & {b - c - a} & {2b} \cr {2c} & {2c} & {c - a - b} \cr } } \right|\)
      = (a + b + c) (x + a + b + c)2, x \(\ne\) 0,
then x is equal to :

If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x – a2) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left( {{{mean\,\,of\,X} \over {s\tan dard\,\,deviation\,\,of\,X}}} \right...

Let  S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

Given \({{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}\) for a \(\Delta\)ABC with usual notation.
If   \({{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },\) then the ordered triad ($$\alpha...

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation x2
sin \(\theta\) – x(sin \(\theta\) cos \(\theta\) + 1) + cos \(\theta\) = 0 (0 < \(\theta\) < 45o), and \(\alpha\) < \(\beta\). Then $$\sum\limits_{n = 0}^\inft...

Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \({{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}}\) is :

If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the
equation of the diagonal AD is :

Let \(\sqrt 3 \widehat i + \widehat j,\)    \(\widehat i + \sqrt 3 \widehat j\)  and   \(\beta \widehat i + \left( {1 - \beta } \right)\widehat j\) respectively be the position vectors of the points A, B and C with respect to the origin O. ...

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is \(\lambda\). If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

Seven capacitors, each of capacitance 2 \(\mu\)F, are to be connected in a configuration to obtain an effective capacitance of \(\left( {{6 \over {13}}} \right)\mu F.\) Which of the combinations, shown in figures below, will achieve the de...

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a consta...

An amplitude modulated signal is plotted below :

Which one of the following best describes the above signal ?

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 \(\Omega\) resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that shoul...

In the circuit shown, the potential difference between A and B is :

A galvanometer having a resistance of 20 \(\Omega\) and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: (\({{{hc} \over e}}\) = 1240 nm eV)

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear
dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per
unit length of the frame ...

A 27 mW laser beam has a cross-sectional area of 10 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by :
[Given permittivity of space \(\in\)0 = 9 \(\times\) 10–12 SI units, Speed of light c = 3 $$...

The circuit shown below contains two ideal diodes, each with a forward resistance of 50 \(\Omega\). If the battery voltage is 6 V, the current through the 100 \(\Omega\) resistance (in Amperes) is :

An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \(\sqrt 3\), then the angle of incidence is:

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads...

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :...

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by \(\Delta\)T. The
amount of heat abso...

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the tempe...

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 \(\times\) 10–6 J/ T when a magnetic intensity of 60 \(\times\) 103 A/m is applied. Its magnetic susceptibility is

A particle of mass m and charge q is in an electric and magnetic field given by
\(\overrightarrow E = 2\widehat i + 3\widehat j;\,\,\,\overrightarrow B = 4\widehat j + 6\widehat k.\)
The charged particle is shifted from he origin to the p...

The region between y = 0 and y = d contains a magnetic field \(\overrightarrow B = B\widehat z\). A particle of mass m and charge q enters the region with a velocity \(\overrightarrow v = v\widehat i.\) If d \(=\) \({{mv} \over {2qB}},\)...

A particle moves from the point \(\left( {2.0\widehat i + 4.0\widehat j} \right)\) m, at t = 0, with an initial velocity \(\left( {5.0\widehat i + 4.0\widehat j} \right)\) ms\(-\)1. It is acted upon by a constant force which produces a cons...

A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO' ,passing through the cent...

The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5m, the angle between the force and the position vector is (in radians) :

A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular accele...

A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is...

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be :

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10–2 m. The relative change in the a...

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:

In a double-slit experiment, green light (5303\(\mathop A\limits^ \circ\)) falls on a double slit having a separation of 19.44 \(\mu\)m and awidht of 4.05 \(\mu\)m. The number of bright fringes between the first and the second diffracti...