As promised, here is another problem from our ALM110 major exam:

The diagram is self-descriptive. The 'hoop' rolls without slipping and its center moves to the right with a velocity 'V'. The radius of the hoop is 'R'.

Find the angular velocity of the rod.

Note: I have added a diagram describing the connection between the 'rod' and the 'hoop'.

Probability:

Consider a collection of families, each of which has exactly two children. Each of the four possible combinations of boys and girls, bg, gb, bb, gg, occurs with the same frequency. A family is chosen uniformly at random, and we are told that it contains at least one boy. What is the (conditional) probability that the other child is a boy?

AML110 major:

You could have probably solved at least two problems from our AML110 major exam.

Here's the first:
A rod is constrained to move b/w two fixed cylinders. The cylinders however are free to rotate about their natural axes.

Find the acceleration of the rod.

Radius of the larger cylinder = .6m.
Radius of the smaller cylinder= .3m.

Boating:

A 100kg man(standing on shore) wishes to start his journey in a 200kg row-boat (parked in the water near the shore) with good initial speed. What he does is this:
1)He heaves the boat forward (with great effort) providing it with 2 units speed.

2)Next, he sprints on the beach sand, and jumps into the boat (his running direction coincides with the boats motion), with a velocity 5 units.

What is the final speed of the boat??

You'll encounter similar questions in your JEE.

The rod (weight=W) is hinged at A. It is released from rest from the position shown in black.

1)What is the reaction from the hinge at this instant??

2)What is the reaction when the rod has rotated by 45 degrees?

CSL105 quiz2:

A bag contains either a 100 Rs note or a 500 Rs note, with equal probability.
I add a 100 Rs note to the bag. (I'm rich).

'A' draws a note from the bag and it is Rs 100. 'A' keeps it.

'B' draws a note now. What is the probability that 'B' draws a 100 Rs note?

Answer=2/3.

The upper rod is hinged to the roof; the lower rod is hinged to the upper rod.
Mass of both rods=9kg; length=1m each.

Now, a force 45N is applied to the upper rod as shown. At this instant, find the angular acceleration of the lower rod.