NTA JEE Main 7th April 2013 Online

Let $$[\epsilon_0]$$ denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

A projectile is given an initial velocity of $$(\hat{i} + 2\hat{j})$$ m s$$^{-1}$$, where $$\hat{i}$$ is along the ground and $$\hat{j}$$ is along the vertical upward. If $$g = 10$$ m s$$^{-2}$$, the equation of its trajectory is :

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. The extension $$x_0$$ of the spring when it is in equilibrium is :

This question has Statement - I and Statement - II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I: A point particle of mass $$m$$ moving with speed $$v$$ collides with stationary point particle of mass $$M$$. If the maximum energy loss possible is given as $$f\left(\frac{1}{2}mv^2\right)$$ then $$f = \left(\frac{m}{M+m}\right)$$.
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A hoop of radius r and mass m rotating with an angular velocity $$\omega_0$$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is T, the density of the liquid is $$\rho$$ and L is its latent heat of vaporisation.)

If a piece of metal is heated to temperature $$\theta$$ and then allowed to cool in a room which is at temperature $$\theta_0$$, the graph between the temperature T of the metal and time t will be closest to :

The below P-V diagram represents the thermodynamic cycle of an engine, operating with an ideal mono-atomic gas. The amount of heat, extracted from the source in a single cycle, is:

Two charges, each equal to q, are kept at $$x = -a$$ and $$x = a$$ on the x-axis. A particle of mass m and charge $$q_0 = -\frac{q}{2}$$ is placed at the origin. If charge $$q_0$$ is given a small displacement ($$y << a$$) along the y-axis, the net force acting on the particle is proportional to :