JEE Main 2016 April 9 Paper & Solutions - JEE MCQ

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force W/20 on the car. While moving uphill on the road at a speed of 10 ms⁻¹, the car needs power P.  If it needs power P/2 while moving downhill at speed v then value of v is :

A cubical block of side 30 cm is moving with velocity 2 ms⁻¹ on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

​Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is 1/4 the area of the ellipse. (Seefigure) With db as the semimajor axis, and ca as the semiminor axis.  If t₁ is the time taken for planet to go over path abc and t₂ for path taken over cda then :

Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure).  Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure.
If the radius of the cross-section of water stream when it hits the ground is x. Then :

200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water=4184 J/kg/K) :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point.  The amplitude and time period for both particles are same and equal to A and T, respectively.  At time t=0 one particle  has displacement A while the other one has displacement -A/2 and they are moving towards each other.  If they cross each other at time t, then t is :

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz.  Calculate the frequency heard by driver of second engine before they pass each other.  Speed of sound is 330 m/sec :

The potential (in volts) of a charge distribution is given by

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ0 (in units of ∈_o) which is spread over a certain region, then choose the correct statement.

Three capacitors each of 4 µF are to be connected in such a way that the effective capacitance is 6 µF. This can be done by connecting them :

In the circuit shown, the resistance r is a variable resistance. If for r = f R, the heat generation in r is maximum then the value of f is:

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT.  The dipole attains stable equilibrium at an angle of 30º with this field.  The magnitude of the other field (in mT ) is close to :

A 50 Ω resistance  is connected to a battery of 5V. A galvanometer of resistance 100 Ω is to be used as an ammeter to measure current through the resistance, for this a resistance r_s is connected to the galvanometer.  Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit ?

A series LR circuit is connected to a voltage source with V(t)=V₀ sinΩt.  After very large time, current I(t) behaves as :

Microwave oven acts on the principle of :

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown.  For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :

In Young’s double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used.  A person standing near the slits is looking at the fringe pattern.  When the separation between the slits is varied, the interference pattern disappears for a particular distance d0 between the slits.  If the angular resolution of the eye is  1º/60 the value of d₀ is close to :

When photons of wavelength λ₁ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength  λ₂ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength  λ₃ is used then find the stopping potential for this case:

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon.  This photon strikes a doubly ionized lithium atom (z=3) in excited state and completely removes the orbiting electron.  The least quantum number for the excited state of the ion for the process is :

The truth table given in fig. represents :

An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz.  The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is: 

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC.  If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S.  If the coefficient of linear expansion of metal is α then the value of S is :

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L.  The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively.  The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end.  The equilibrium extended length, of this wire, would equal :

To know the resistance G of a galvanometer by half deflection method, a battery of emf V_E and resistance R is used to deflect the galvanometer by angle θ.  If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

To find the focal length of a convex mirror, a student records the following data :

The focal length of the convex lens is f₁ and that of mirror is f₂. Then taking index correction to be negligibly small,  f₁ and f₂ are close to :

An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of R=100 Ω, and a maximum power  of dissipation rating of 1 W.  The minimum voltage range of the DC source in the circuit is :

An unknown transistor needs to be identified as a npn or pnp type.  A multimeter, with +ve and −ve terminals, is used to measure resistance between different terminals of transistor.  If terminal 2 is the base of the transistor then which of the following is correct for a  pnp transistor ?