JEE Main 2019 January 10 Shift 1 Paper & Solutions - JEE MCQ

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 material which when fully inserted in above capacitor, gives same capacitance would be :

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 :

In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ₁. When the light of wavelength λ₂ is used a bright fringe is seen at the same angle in the same set up. Given that λ₁ and λ₂ are in visible range (380 nm to 740 nm), their values are :

A magnet of total magnetic moment 10^-2 î A-m² is placed in a time varying magnetic field, B î (costωt) where B = l Tesla and ω = 0.125 rad/ s. The work done for reversing the direction of the magnetic moment at t = 1 second, 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 coefficient of friction between the mop and the floor is μ the torque, applied by the machine on the mop is :

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 = 6 seconds is close to:

If the magnetic field of a plane electromagnetic wave is given by (The speed of light = 3 × 10⁸/m/s)
 then the maximum electric field associated with it is :

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 < a, would be :

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

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 the maximum height to which the combined system reaches above the top of the building before falling below is : (g =10ms^–2)

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 :

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

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

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

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 in LOS(Line of Sight) mode ? (Given : radius of earth = 6.4 x 10⁶m).

A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in fig. shows no deflection is:

An insulating thin rod of length ℓ has a x linear charge density λ (x) =  on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

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 ground is :

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 to :

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 f₁. If the speed of the train is reduced to 17 m/s, the frequency registered is f₂. If speed of sound is 340 m/s, then the ratio f₁/f₂ is :

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^–12m, the minimum electron energy required is close to :

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:

A plano convex lens of refractive index µ₁ and focal length f₁ is kept in contact with another plano concave lens of refractive index µ₂ and focal length f₂. If the radius of curvature of their spherical faces is R each and f₁ = 2f₂, then µ1 and µ₂ are related as 

Two electric dipoles, A, B with respective dipole moments and placed on the x-axis with a separation R, as shown in the figure

The distance from A at which both of them produce the same potential is :

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

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:

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 T₂ > T₂ > T₃ > T₄ . The three engines are equally efficient if: