Describe the process of drawing one tangent to a circle from an external point.

Draw a circle of radius 4 cm. Draw a tangent on this circle from an external point at a distance 9 cm from the centre of the circle.

Asha buys ₹ 20 shares of a company which pays 9% dividend at such a price that she gets a return of 12% on her investment. At what price did she buy each share? (a) ₹ 20 (b) ₹ 15 (c) ₹ 25 (d) ₹ 18

If A = , then A² is equal to: (a) (b) (c) (d)

The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term is 128. Find its: (a) common ratio (b) first term

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Rohit and Vinay both opened a recurring deposit account in a bank for 2 years at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit’s interest was ₹ 800 more than Vinay’s interest. Find: (a) interest earned by Vinay. (b) sum deposited by Rohit every month.

(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is : (a) −1 (b) 1 (c) −5 (d) 5

Kabir bought 120 shares of a company with nominal value ₹100, available at a premium of ₹25. Find: (a) the money invested by Kabir in buying these shares. (b) the rate of dividend, if he received ₹1,080 as dividend from these shares after one year. (c) his rate of return.

In the given diagram, DE ∥ BC and AD : DB = 2 : 3. (a) Prove that: ΔADE ~ ΔABC and hence find DE : BC. (b) Prove: ΔDFE ~ ΔCFB. (c) Given, area of ΔDFE = 16 square units, find the area of ΔCFB.

If x = , a ≠ b, (a) Find: (b) Using properties of proportion, find:

A flagpole is erected at the top of a building. The angle of elevation of the top and foot of the flagpole from a point 100 m away, on the same level as that of the foot of the building, are 33° and 31° respectively. Find the height of the flagpole. Give your answer correct to the nearest metre.