JEE Main 2014 April 19 Paper & Solutions - JEE MCQ

A body is in simple harmonic motion with time period half second (T = 0.5 s) and amplitude one cm (A = 1 cm). Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

A bullet looses of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :

Long range radio transmission is possible when the radiowaves are reflected from the ionosphere.For this to happen the frequency of the radiowaves must be in the range :

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is θ_iC and the Brewster's angle of incidence is θ_iB, such that sinθ_iC/sinθ_iB = η = 1.28. The relative refractive index of the two media is :

If denote microwaves, X rays, infrared, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength :

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C¹⁴ is 5730 years, then age of the wooden piece placed in the museum is approximately :

​A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 ms^–1 (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is :

Given : A and B are input terminals.
Logic 1 = > 5 V
Logic 0 = < 1 V
Which logic gate operation, the following circuit does ?

The gravitational field in a region is given by . The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7m, –3 m) is :

Match List-I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists.

Match List-I (Experiment performed ) with List-II (Phenomena discovered/ associated) and select the correct option from the options given below the lists :

A heavy box is to be dragged along a rough horizontal floor. To do so, person A pushes it at an angle 30° from the horizontal and requires a minimum force F_A, while person B pulls the box at an angle 60° from the horizontal and needs minimum force F_B. If the coefficient of friction between the box and the floor is , the ratio is :

A gas is compressed from a volume of 2 m³ to a volume of 1m³ at a constant pressure of 100 N/m². Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle φ with the horizontal. Then :

In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm² and 10 mm² respectively. The rate at which water flows through the tube is (g = 10 ms^–2)

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_friction at point P ? It is assumed that the cylinder does not slip.

A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of liquid T, density r)

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from at one plate toat the other. The capacitance of capacitor is :

A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth, (kB is Boltzmann constant)

​The electric field in a region of space is given by, The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly

A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 ms^–1. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 ms^–2)

In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure.
Q. What is the value of g at the place?

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field Bs inside the superconductor will be such that :

The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common frequency with which three parts can vibrate?

A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature T₀. The initial temperature of the sphere is 3T₀. If the specific heat of the material of the sphere varies as  αT³ per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature 2T₀ will be (σ is Stefan Boltzmann constant) 

Figure shows a circular area of radius R where a uniform magnetic field is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

The diameter of the objective lens of microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope.