NTA JEE Main 25th April 2013 Online - Physics

A block is placed on a rough horizontal plane. A time dependent horizontal force $$F = kt$$ acts on the block, where k is a positive constant. The acceleration - time graph of the block is :

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $$R_0 = 40$$ m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $$v = 20$$ m/s on a horizontal surface? ($$g = 10$$ m/s$$^2$$)

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $$v$$, the electrical power output will be most likely proportional to

A ring of mass M and radius R is rotating about its axis with angular velocity $$\omega$$. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :

Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is:

In an experiment, a small steel ball falls through a liquid at a constant speed of 10 cm/s. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward?

A mass of 50 g of water in a closed vessel, with surroundings at a constant temperature from 30°C to 25°C takes 2 minutes to cool. A mass of 100 g of another liquid in an identical vessel with identical surroundings takes the same time to cool from 30°C to 25°C. The specific heat of the liquid is : (The water equivalent of the vessel is 30 g.)

A sample of gas expands from $$V_1$$ to $$V_2$$. In which of the following, the work done will be greatest?

In the isothermal expansion of 10 g of gas from volume V to 2V the work done by the gas is 575 J. What is the root mean square speed of the molecules of the gas at that temperature?

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $$\sigma$$ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be :

In a transverse wave the distance between a crest and neighbouring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4 s. The maximum speed of the vibrating particles in the medium is:

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: No work is required to be done to move a test charge between any two points on an equipotential surface.
Statement 2: Electric lines of force at the equipotential surfaces are mutually perpendicular to each other.

The surface charge density of a thin charged disc of radius R is $$\sigma$$. The value of the electric field at the centre of the disc is $$\frac{\sigma}{2\epsilon_0}$$. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc:

The gravitational field in a region is given by: $$\vec{E} = (5N/kg)\hat{i} + (12N/kg)\hat{j}$$. If the potential at the origin is taken to be zero, then the ratio of the potential at the points (12 m, 0) and (0, 5 m) is :

A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance $$C_0$$. Now one-third of the material is replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area $$\frac{1}{3}$$ A, dielectric constant 2K and another with area $$\frac{2}{3}$$ A and dielectric constant K. If the capacitance of this new capacitor is C then $$\frac{C}{C_0}$$ is

Six equal resistances are connected between points P, Q and R as shown in the figure. Then net resistance will be maximum between :

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to $$8 \times 10^{22}$$ Am$$^2$$, the value of earth's magnetic field near the equator is close to (radius of the earth = $$6.4 \times 10^6$$ m)

One of the two small circular coils, (none of them having any self-inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a dc supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?

A metal sample carrying a current along X-axis with density $$J_x$$ is subjected to a magnetic field $$B_z$$ (along z-axis). The electric field $$E_y$$ developed along Y-axis is directly proportional to $$J_x$$ as well as $$B_z$$. The constant of proportionality has SI unit.

When resonance is produced in a series LCR circuit, then which of the following is not correct?

A series LR circuit is connected to an ac source of frequency $$\omega$$ and the inductive reactance is equal to 2R. A capacitance of capacitive reactance equal to R is added in series with L and R. The ratio of the new power factor to the old one is :

A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively. If the thickness of the bottom of glass is 1 cm and depth of water is 5 cm, how much the page will appear to be shifted if viewed from the top?

A thin glass plate of thickness $$\frac{2500}{3}\lambda$$ ($$\lambda$$ is wavelength of light used) and refractive index $$\mu = 1.5$$ is inserted between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant from the slits, the ratio of the intensities before and after the introduction of the glass plate is :

The source that illuminates the double-slit in 'double-slit interference experiment' emits two distinct monochromatic waves of wavelength 500 nm and 600 nm, each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to one wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in nm is:

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: Out of radio waves and microwaves, the radio waves undergo more diffraction.
Statement-2: Radio waves have greater frequency compared to microwaves.

In an experiment on photoelectric effect, a student plots stopping potential $$V_0$$ against reciprocal of the wavelength $$\lambda$$ of the incident light for two different metals A and B. These are shown in the figure.

Looking at the graphs, you can most appropriately say that:

A copper ball of radius 1 cm and work function 4.47 eV is irradiated with ultraviolet radiation of wavelength 2500 $$\text{Å}$$. The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is :

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. It will emit:

Which of the following circuits correctly represents the following truth table?

Which of the following modulated signal has the best noise-tolerance?