JEE (Advanced) 2010 Paper-2

A biconvex lens of focal length 15 cmis in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force Fit) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

A tiny spherical oil drop carrying a net charge q is balanced instill air with a vertical uniform electric field of strength $$\frac{81 \pi}{7} \times 10^5 Vm^{-1}$$. When the field switched off, the drop is observed to fall with terminal velocity $$2 \times 10^{-3} m s^{-1}$$. Given $$g = 9.8 m s^{-2}$$, viscosity of the air = $$1.8 \times 10^{-5} Ns m^{-2}$$ and the density of oil = $$900 kg m^{-3}$$, the magnitude of q is

A uniformly charged thin spherical shell of radius R carries uniform surface charge density of $$\sigma$$ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to

A diatomic ideal gas is compressed adiabatically to $$\frac{1}{32}$$ of its initial volume. In the initial temperature of the gas is $$T_i$$(in Kelvin) and the final temperature is $$aT_i$$, the value of a is

At time t = O, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?
[Take : $$\ln 5 = 1.6, \ln 3 = 1.1$$]

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $$\frac{25}{3} m$$ to $$\frac{50}{7} m$$ in 30 seconds. What is the speed of the object in km per hour ?

A large glass slab $$(\mu = \frac{5}{3})$$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

To determine the half life of a radioactive element, a student plots a graph of $$\ln \mid \frac{dN(t)}{dt} \mid$$ versus t. Here $$\frac{dN(t)}{dt}$$ is the rate of radioactive decay at time t If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is

If the radius of the opening of the dropperis r, the vertical force due to the surface tension on the drop of radius R (assuming $$r \ll R$$) is