NTA JEE Main 9th April 2013 Online

Two simple pendulums of length 1 m and 4 m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to:

When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by :
$$y_1 = 0.05\cos(0.50\pi x - 100\pi t)$$
$$y_2 = 0.05\cos(0.46\pi x - 92\pi t)$$
where $$y_1$$, $$y_2$$ and x are in meters and t in seconds. The speed of sound in the medium is :

An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km, it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/s, then the speed of the engine is :

Two point dipoles of dipole moment $$\vec{p_1}$$ and $$\vec{p_2}$$ are at a distance x from each other and $$\vec{p_1} \| \vec{p_2}$$. The force between the dipoles is :

Two balls of same mass and carrying equal charge are hung from a fixed support of length $$l$$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between the balls is proportional to :

In a metre bridge experiment null point is obtained at 40 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then the new position of the null point from the same end, if one decides to balance a resistance of 3X against Y, will be close to :

A letter 'A' is constructed of a uniform wire with resistance 1.0$$\Omega$$ per cm. The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60°. The resistance between the ends of the legs is close to:

A shunt of resistance 1 $$\Omega$$ is connected across a galvanometer of 120 $$\Omega$$ resistance. A current of 5.5 ampere gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly :

A uniform electric field $$\vec{E}$$ exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to $$\vec{E}$$. The path of the particle between the plates is a:

An electric current is flowing through a circular coil of radius R. The ratio of the magnetic field at the centre of the coil and that at a distance $$2\sqrt{2}R$$ from the centre of the coil and on its axis is :