JEE Main 2019 January 12 Shift 1 Paper & Solutions - JEE MCQ

A straight rod of length L extends from x = a to x=L + a. The gravitational force is exerted on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx², is given by:

A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30V/m, then the amplitude of the electric field for the wave propogating in the glass medium will be:

The output of the given logic circuit is :

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:

A particle of mass m moves in a circular orbit in a central potential field   If Bohr's
quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as:

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P₁ and P₂ respectively, then:

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.
The subsequent motion of the combined body will be :

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:

A passeng er train o f leng th 60m travels a t a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr.
The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction, and (ii) in the opposite directions is :

An ide al gas occupies a volu me of 2m³ at a pressure of 3 × 10⁶ Pa. The energy of the gas is:

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

The galvanometer deflection, when key K₁ is closed but K₂ is open, equals θ₀ (see figure).
On closing K₂ also and adjusting R₂ to 5Ω, the deflection in galvanometer becomes  

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position.
If is the speed of sound, speed of the plane is :

A proton and an a-particle (with their masses in the ratio of 1:4 and charges in the ratio of 1:2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii r_p : r_α of the circular paths described by them will be :

A point source of light, S is pla ce d at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall.
A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is :

“The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 micrometer diameter of a wire is ”

A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ₀. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ₁. Then M is given by :

What is the position and nature of image formed by lens combination shown in figure? (f₁, f₂ are focal lengths)

In the figure shown, a circuit contains two identical resistors with resistance R = 5W and an inductance with L = 2mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?

Determine the electric di pole mo ment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

The position vector of the centre of mass of a symmetric uniform bar of negligible area of cross-section as shown in figure is :

As sh own i n t he fi gure, tw o i nfi ni tel y lon g, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10^–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be (μ₀ = 4π × 10^–7 NA^{– 2}) :

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation  of its resistance R with length ℓ is  Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?

For the given cyclic process CAB as shown for a gas, the work done is :

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5W.The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire, is :

A part icle A of mass 'm' and charg e 'q ' is accelerated by a potential difference of 50 V.Another particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths  is close to:

There is a uniform spher ically sym metric surface charge density at a distance R₀ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R (t) is :