JEE Main 2016 April 10 Paper & Solutions - JEE MCQ

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is:

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then BC/AB is close to :

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R , while its mass is M. The gravitational pull F_G on the astronaut is :

A bottle has an opening of radius a and length b.  A cork of length b and radius (a+∆a) where (∆a<<a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is µ then the force needed to push the cork into  the bottle is :

A Carnot freezer takes heat from water at 0ºC inside it and rejects it to the room at a temperature of 27ºC. The latent heat of ice is 336×10³Jkg⁻¹. If 5 kg of water at 0ºC is converted into ice at 0ºC by the freezer, then the energy consumed by the freezer is close to :

Which of the following shows the correct relationship between the pressure ‘P’ and density ρ of an ideal gas at constant temperature?

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased.The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall.An observer, towards whom the toy car is moving, is able to hear 5 beats per second.If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :

Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential V₀, V₀+∆V, V₀+2∆V, .......... V₀+N∆V  (∆V>0), are drawn and have increasing radii r₀, r₁, r₂,..........r_N, respectively. If the difference in the radii of the surfaces is constant for all values of V₀ and ∆V then :

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 µF is

The resistance of an electrical toaster has a temperature dependence given by R(T)=R₀ [1+α(T−T₀)] in its range of operation.  At T₀=300 K, R=100 Ω and at T=500 K, R=120 Ω. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s.  The total work done in raising the temperature is :

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ‘ v ’ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities σ1 and σ2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is 240 ms⁻¹.The earth’s magnetic field over Delhi is 5×10⁻⁵ T with the declination angle ~0º and dip of θ such that sin θ = 2/3. If the voltage developed is V_B between the lower and upper side of the plane and VW between the tips of the wings then V_B and V_W are close to:

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as , where B₀ and τ are constants, at time t=0.  If the resistance of the loop is R then the heat generated in the loop after a long time (t →∞) is :

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen :
 

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :

A photoelectric surface is illuminated successively by monochromatic light of wavelengths λ and λ/2 . If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state.The minimum kinetic energy of the neutron for which inelastic collision will take place is :

To get an output of 1 from the circuit shown in figure the input must be :

A modulated signal C_m(t) has the form C_m( t ) = 30 sin 300πt + 10 (cos 200πt −cos 400πt). The carrier frequency f_c, the modulating frequency (message frequency) f_ω, and the modulation index µ are respectively given by :

A particle of mass m is acted upon by a force F given by the empirical law . If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot:

A thin 1 m long rod has a radius of 5 mm. A force of 50 πkN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known.If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R = 2400 Ω.  Deflection becomes 20 divisions when resistance taken from resistance box is 4900 Ω. Then we can conclude :

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :

A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a common emitter transistor configuration is :

The ratio (R) of output resistance r₀, and the input resistance r_i in measurements of input and output characteristics of a transistor is typically in the range :