**1.**Let be positive integer and be an odd positive integer.Find the highest power of 2 which divides {\large .}

**2.**Let be two complex numbers which are linearly independent over .Conside the lattice generated over

Show that the Weirestrass elliptic function{\large } is absolutely and uniformly convergent on any compact subset of the complex plane which doesn’t contain any points of .Also,show that is meromorphic with a double pole only at points in .

**3.**The *deleted infinite broom* is the set of all line segments joining to and the point .Note that the segment between and through the X-axis is not included.

Prove that the deleted infinite broom is connected but not path-connected.

The closure of the deleted infinite broom is called the *infinite broom*.Prove that the infinite broom is path-connected.

**4.**Show that the roots of Legendre Polynomial in the interval are distinct.