Angular Momentum

A particle is projected with speed 'v' at an angle 'Q' with the horizontal. Find its angular momentum about the point of projection after time 't'.

7 elastic beads for the Dwarf-lords, in their halls of stone

Seven identical beads are sliding on a meter rod as shown. Their positions and velocities are listed. A positive velocity indicates motion to the right.

When a bead slides off the meter rod, a Dragon awakes. Presently, its t=0.

At what times does a Dragon awake? Note that a total of 7 Dragons will wake up. List all the 7 time instants.

Click the image to enlarge and notice the minus signs.

Integral Calculus

Let f : R -> (0,∞) be a decreasing function. For n ∈ N.

We define,     a(n) = f(1) + f(2) + ... +f(n) - ₁ ∫ ⁿ f .
Show that the infinite sequence (a(n)) is a bounded, monotonic one, and hence it converges.

Poison

Evaluate this limit.

Next, solve this question:

A typist makes about 1 error in 200 words. What is the probability that he types the 1st 2500 word without error?