Bholi had many apprehensions about going to school. She remembered how their old cow, Lakshmi, had been turned out of the house and sold. When she got a clean dress, was bathed and her hair were properly done with oil,only then she felt that she was going to a better place than her home.?
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 
On the day of her examination, Riya sharpened her pencil from both ends as shown below. 
The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.