Two thin metallic spherical shells of radii r₁ and r₂ (r₁ < r₂) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$₁ and the outer shell at temperature $$\theta$$₂($$\theta$$₁ < $$\theta$$₂). The rate at which heat flows radially through the material is :-

If V_A and V_B are the input voltages (either 5V or 0V) and V₀ is the output voltage then the two gates represented in the following circuit (A) and (B) are :-

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $${1 \over 4}$$ times that of the bob and the length of the thread is increased by 1/3^rd of the original length, then the time period of the simple harmonic oscillations will be :-