NTA JEE Main 6th April 2014 Offline

The current voltage relation of diode is given by $$I = (e^{1000V/T} - 1)$$ mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring $$\pm 0.01$$ V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = \frac{x^3}{6}$$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $$F = ax + bx^2$$ where a and b are constants. The work done in stretching the unstretched rubber-band by L is:

A mass $$m$$ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

A bob of mass m attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $$\omega$$ rad/s about the vertical. About the point of suspension:

Four particles, each of mass $$M$$ and equidistant from each other, move along a circle of radius $$R$$ under the action of their mutual gravitational attraction. The speed of each particle is:

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $$d_1$$ and $$d_2$$ are filled in the tube. Each liquid subtends 90° angle at centre. Radius joining their interface makes an angle $$\alpha$$ with vertical. Ratio $$\frac{d_1}{d_2}$$ is:

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If $$r \ll R$$, and the surface tension of water is T, value of r just before bubbles detach is: (density of water is $$\rho_w$$)

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)