NTA JEE Main 10th April 2015 Online

If the capacitance of a nanocapacitor is measured in terms of a unit $$u$$, made by combining the electronic charge $$e$$, Bohr radius $$a_0$$, Planck's constant $$h$$ and speed of light $$c$$ then

A block of mass $$m = 10$$ kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed $$v$$, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed $$\frac{v}{10}$$ after being dropped from height $$H$$, then neglecting energy losses and taking $$g = 10$$ m s$$^{-2}$$, the value of $$H$$ is close to

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 $$\left(\frac{x}{2}\right)$$ from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity 3 m s$$^{-1}$$. The total initial energy of the spring is:

If a body moving in a circular path maintains constant speed of 10 m s$$^{-1}$$, then which of the following correctly describes the relation between acceleration and radius?

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 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:

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 the star is $$T$$ and its distance from the galaxy's axis is $$r$$, then

If two glass plates have water between them and are separated by very small distance (see the figure below), 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:

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $$\frac{2}{\sqrt{\pi}}$$ cm then the Reynolds number for the flow is (density of water = $$10^3$$ kg/m$$^3$$ and viscosity of water = $$10^{-3}$$ Pa.s) close to:

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

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