JEE Advanced 2012 Paper 1, Question 12
For the resistance network shown in the figure, choose the correct option(s).
- The current through
is zero. 
A.- The potential at
is less than that at 
. 
A.
Solution
We can speed up the solution by noticing the mirror symmetry of the circuit. Let the current 
split into two parts 
and 
at the node 
(see figure). Similarly, let the currents going into node 
be 
and 
. If we were to reverse the polarity of the 
battery connected to the circuit, all currents would simply reverse direction, but their magnitudes would remain the …
and 
as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field 
points into the plane of the paper. At 
, the loop starts rotating about the common diameter as axis with a constant angular velocity 
in the magnetic field. Which of the following options is/are correct?
has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at 
, in a co-ordinate system fixed to the table. A point mass 
is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is 
and the velocity is 
. At that instant, which of the following options is/are correct?
, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)
and same refractive index 
are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (
). If 
, and 
are the apparent depths of a point 
