JEE Advanced Model Paper 12 with solutions for online practice

The bob of a simple pendulum, which is in the shape of a hollow cylinder of mass 'M' radius 'r ’ and length ’h ’ is suspended by a long string (the mass of the base and lid of the cylinder are negligible). The cylinder is filled with a liquid of density ' ρ ’ upto a height of ’x ’ . Then the value of ’ for which the time period of the pendulum is maximum is given by which of the following equations (use A = πr2ρ)