**Date of submission: 5 Jan., 2015**

1. A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digits interchange their places. Find the number.

2. Show that the product of the 2^{nd} and 3^{rd} terms of an A.P exceeds the product of the 1^{st} and 4^{th} by twice the square of the difference between the 1^{st} and 2^{nd}.

3. In a circle, ∆ABC touches the sides BC, CA and AB at D, E, F, respectively. Show that AF+BD+CE=AE+BF+CD=Perimeter of ∆ABC

4. ∆ABC is a right triangle in which AB = 3.2 cm, BC = 3.2 cm, Angle B = 90˚. BD is perpendicular from B to AC. The circle Through BCD is drawn. Construct tangents from A to this circle.

5. Prepare and answer 5 questions from Quadratic Equations, Arithmetic Progressions, Circles and Constructions (Other exercise questions)

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