**“Madhyamik Suggestive Question Paper, 2015 – 16”**

*Time: 3:00 Hr**. **Mathematics***(X)**** F.M.:90**

**3. Answer any two of the following: 5+5=10**

(a) The ratios of Darjeeling tea and Assam tea in two different qualities of mixed tea are 2:7 and 1:5 respectively. In what ration must these two types of mixed tea be mixed, so that the mixture has Darjeeling tea and Assam tea in the ratio 1:4.

(b) Rustam mixes Assam tea at Rs. 120/kg with Darjeeling tea at Rs. 200/kg in the ratio of 5:3 and sells the mixture at Rs. 162/kg. What will be his percentage profit or loss ?

(c) The simple interest and compound interest of a certain sum of money for 2 years are Rs. 400 and Rs. 410 respectively. Find the sum of money and rate of interest.

(d) In how many years will RS. 100000 amount to Rs. 133100 at 10% per annum compound interest?

**6. ****Answer any one question: 4 **

(a) Anand went to market and saw that decrease of Rs. 6 per dozen in the price of banana will make 3 more bananas available in Rs. 30. Find the present price of banana.

(b) Area of a right angled triangle is 60 sq. meters and the difference between the lengths of its perpendicular and base is 7 m. Find the length of the hypotenuse.

**11. ****Answer any one question: 2x5=10 **

(a) If a perpendicular is drawn from the vertex containing the right angle of a right angled triangle on the hypotenuse, the triangle on each side of the perpendicular are similar to the triangle and to one another.

(b) Prove that the angle which an arc of a circle subtends at the centre, is double the angle subtended by it at any point in the remaining part of the circle.

(c) Prove that if two tangents be drawn to a circle from a point outside it, then the line segments joining the points of contact and the exterior point are equal and they subtend equal angles at the centre.