NTA JEE Main 11th April 2015 Online

A vector $$\vec{A}$$ is rotated by a small angle $$\Delta\theta$$ radians $$(\Delta\theta \ll 1)$$ to get a new vector $$\vec{B}$$. In that case $$\left|\vec{B} - \vec{A}\right|$$ is:

A beaker contains a fluid of density $$\rho$$ $$\frac{kg}{m^3}$$, specific heat $$S$$ $$\frac{J}{kg \cdot ^\circ C}$$ and viscosity $$\eta$$. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $$\left(\frac{Q}{A}\right)$$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $$\eta$$, $$\left(\frac{S\Delta\theta}{h}\right)$$ and $$\left(\frac{1}{\rho g}\right)$$ when $$\Delta\theta$$ (in $$^\circ C$$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $$\left(\frac{Q}{A}\right)$$ is:

If electronic charge $$e$$, electron mass $$m$$, speed of light in vacuum $$c$$ and Planck's constant $$h$$ are taken as fundamental quantities, the permeability of vacuum $$\mu_0$$ can be expressed in units of:

From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $$g = 32$$ m/s$$^2$$, is:

A large number $$(n)$$ of identical beads, each of mass $$m$$ and radius $$r$$ are strung on a thin smooth rigid horizontal rod of length $$L(L \gg r)$$ and are at rest at random positions. The rod is mounted between two rigid supports (see the figure below). If one of the beads is now given a speed $$v$$, the average force experienced by each support after a long time is (assume all collisions are elastic):

A particle is moving in a circle of radius $$r$$ under the action of a force $$F = \alpha r^2$$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy = 0 for $$r = 0$$):

A uniform thin rod AB of length $$L$$ has linear mass density $$\mu(x) = a + \frac{bx}{L}$$, where $$x$$ is measured from A. If the CM of the rod lies at a distance of $$\left(\frac{7}{12}L\right)$$ from A, then $$a$$ and $$b$$ are related as:

A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad s$$^{-1}$$, the magnitude of its angular momentum about a point on the ground right under the center of the circle is:

Which of the following most closely depicts the correct variation of the gravitation potential, $$V(r)$$ with distance $$r$$ due to a large planet of radius $$R$$ and uniform mass density? (figures are not drawn to scale)

An experiment takes 10 min to raise the temperature of water in a container from 0$$^\circ$$C to 100$$^\circ$$C and another 55 min to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of the water to be 1 cal (g$$^\circ$$C)$$^{-1}$$, the heat of vaporization according to this experiment will come out to be: