JEE Main 2019 (Online) 10th January Morning Slot

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards nu...

Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c \(\ne\) 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then t...

The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -

In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of...

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to :

A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of \(\Delta\)PQR is a line :

If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is :

The sum of all values of \(\theta\) \(\in\)\(\left( {0,{\pi \over 2}} \right)\) satisfying sin2 2\(\theta\) + cos4 2\(\theta\) = \({3 \over 4}\) is -

Let \(\overrightarrow a = 2\widehat i + {\lambda _1}\widehat j + 3\widehat k,\,\,\)   \(\overrightarrow b = 4\widehat i + \left( {3 - {\lambda _2}} \right)\widehat j + 6\widehat k,\)  and  $$\overrightarrow c = 3\widehat i + 6\widehat j ...

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = ...

A parallel plate capacitor is of area 6 cm2
and a separation 3 mm. The gap is filled with three dielectric
materials of equal thickness (see figure) with dielectric constants K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a mater...

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then...

A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode ? (Given : radius of earth = 6.4 ×...

A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is -

A uniform metallic wire has a resistance of 18 \(\Omega\) and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -

A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf \(\varepsilon\) and internal resistance r. A cell C having emf \(\varepsilon\)/2 and internal resistance 3r is connected. The length AJ at which the ...

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R1 and R2 respectively, are -

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to -

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perp...

If the magnetic field of a plane electromagnetic wave is given by (the speed of light = 3 × 108 B = 100 × 10–6
sin \(\left[ {2\pi \times 2 \times {{10}^{15}}\left( {t - {x \over c}} \right)} \right]\) then the maximum electric field assoc...

To get output 1 at R, for the given logic gate circuit the input values must be

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r ...

Two electric dipoles, A, B with respective dipole moments \({\overrightarrow d _A} = - 4qai\) and \({\overrightarrow d _B} = - 2qai\) are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both ...

A plano convex lens of refractive index \(\mu\)1 and focal length ƒ1 is kept in contact with another plano concave lens of refractive index \(\mu\)2 and focal length ƒ2. If the radius of curvature of their spherical faces is R each and ƒ1...

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic e...

A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK–1m–1, the energy flux through it in the steady state is -

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. The three engines ar...

A magnet of total magnetic moment 10-2 \({\widehat i}\) A-m2 is placed in a time varying magnetic field, B\({\widehat i}\) (cos \(\omega t\)) where B = 1 Tesla and \(\omega\) = 0.125 rad/s. The work done for reversing the direction of th...

An insulating thin rod of length \(l\) has a linear charge density \(\rho \left( x \right)\) = \({\rho _0}{x \over l}\) on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod make...

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the grou...

Water flows into a large tank with flat bottom at the rate of 10–4m3s–1. Water is also leaking out of a hole ofarea 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height is -

To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coeffi...

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -

The density of a material in SI units is 128 kg m–3
. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is -

In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -

In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle \({1 \over {40}}\) by using light of wavelength \(\lambda\)1. When the light of wavelength \(\lambda\)2 is used a bright fringe is s...

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ1. If the speed of the train is reduced to 17 m/s, the frequency registered is ƒ2. If speed of sound ...

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close t...

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time is -