JEE Main 2015 April 10 Paper & Solutions - JEE MCQ

A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms^-1 . The total initial energy of the spring is :

A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is :

Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then :

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then :

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter cm then the Reynolds number for the flow is (density of water =10³ kg/m³ and viscosity of water = 10^-3 Pa.s) close to :

If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by :

An ideal gas goes through a reversible cycle a → b → c → d has the V - T diagram shown below. Process d → a and b → c are adiabatic.

The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T^q . A good estimate for q is :

A simple harmonic oscillator of angular frequency 2 rad s^-1 is acted upon by an external force F = sint N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to : 

A bat moving at 10 ms^-1 towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = 320 ms^-1)

A thin disc of radius b = 2a has a concentric hole of radius 'a' in it (see figure). It carries uniform surface charge 'σ' on it. If the electric field on its axis at height 'h' (h << a) from its centre is given as 'Ch' then value of 'C' is :

Shown in the figure are two point charges +Q and -Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ₁ is the surface charge on the inner surface and Q₁ net charge on it and σ₂ the surface charge on the outer surface and Q₂ net charge on it then :

If the capacitance of a nanocapacitor is measured in terms of a unit 'u' made by combining the electronic charge 'e', Bohr radius 'a₀', Planck's constant 'h' and speed of light 'c' then :

Suppose the drift velocity v_d in a material varied with the applied electric field E as . Then V - I graph for a wire made of such a material is best given by :

A 10V battery with internal resistance 1Ω and a 15V battery with internal resistance 0.6Ω are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to :

A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd'. If 'α' be the angle of deviation of proton from initial direction of motion (see figure), the value of sin α will be :

A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization (magnetic moment/volume), then is:

When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self - inductance of the coil is :

In the circuits (a) and (b) switches S₁ and S₂ are closed at t=0 and are kept closed for a long time. The variation of currents in the two circuits for t ≥ 0 are roughly shown by (figures are schematic and not drawn to scale) :
  

An electromagnetic wave travelling in the x-direction has frequency of 2 x 10¹⁴ Hz and electric field amplitude of 27 Vm^-1 .From the options given below, which one describes the magnetic field for this wave ?

You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum p_y in the y-direction then for a majority of electrons passing through the slit (h is Planck's constant) :

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is θ, then θ is close to :

de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to (|e| = 1.6 x 10^-19 C, m_e = 9.1 x 10^-31 kg, h = 6.6 x 10^-34 Js) : 

If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n^th level will be :

In an unbiased n-p junction electrons diffuse from n - region to p - region because :

Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :

If the zero error is -0.03cm, then mean corrected diameter is :