FPC,Grouping ,identical objects ,circular ,begger''''s method ,divisors arrangements

If a group of n distinct objects,the number of arrangements of 4 object is 12 xx the number of arrangements of 2 objects,then the number of objects is (a) 10 (b) 8(c)6(d) none of these

Three identical rigid circular cylinder A B and C are arrenged on smooth inclined surfaces as shown in figure. The laest value of theta that prevent the arrangement from collapes is.

A monkey pulls the midpoint of a 10 cm long light inextensible string connecting two identical objects A and B lying on smooth table of masses 0.3 kg continuously along the perpendicular objects of line joining the masses .The masses are found to apporoach each other at a relative acceleration of 5 m s^(-2) when they are 6 cm apart .The constant force applied by monkey is

Two solid semi-circular disks fo equal masses m=10 kg collide and stick together. Their initial velocities are shown initially not rotating. The combined object is a circular disk of radius 0.1 m it is spinning with an angular velocity omega=10rad//s . how much mechanical energy (in J ) is lost in collision ?

The centripetal force required to hold 1 kg object in circular path by means of a string 1 m long, if the object is moving at constant speed of 2 m//s will be

A point object moves on a circular path such that distance covered by it is given by function S=(t^(2)/(2)+2t) meter ( t in second). The ratio of the magnitude of acceleration at t = 2 s and t = 5 s . is 1: 2 then the radius of the circle is