Questions

The length, breadth and height of a rectangular room are 13ft, 12ft, and 10ft respectively. There are 2 windows of size 3ft×4ft and a door of size 3ft×6ft.

1. How much does it cost to paint four walls and celling excluding door and windows at the rate of Rs. 40 per square ft? Find it.
2. By how much will the total cost of painting the same parts of the room be increased if the rate of cost per square feet is increased by 25%? Find it.

In the figure, cone is filled with ice-cream whose upper part is hemispherical. The slant height of the cone is 25cm and its radius is 7 cm.

1. Write the relation among the height (h), radius (r), and slant height (l) of the cone.
2. Find the total volume of ice-cream in conical and hemi spherical parts.
3. Compare the quantities of ice-cream in the conical and hemispherical parts.

The ratio of slant height and a side of base of square based pyramid is 5:6 and its total surface area is 1536 sq.cm.

1. Write the relation among base area (A), height(h), and volume(v) of the pyramid.
2. Compare the base area and the area of triangular surfaces.
3. Find the volume of the pyramid.

A merchant exchanged Rs.7,06,062 with pound sterling (£) at the rate of the pound sterling (£)1 = NRs. 168.11. After one week, the Nepali rupees is devaluated by 2%.

1. What amount of pound sterling (£) does the merchant exchange with the Nepali rupees he had? Find it.
2. What would be the new exchange rate after 2% devaluation of Nepali rupees? Find it.
3. How much rupees will the merchant gain or lose when he exchanged Nepali rupees with the sterling pound at the time of devaluation? Find it.

Rajiv has got Rs. 12,00,000. He purchased a motorcycle for Rs. 2,00,000 and a land for Rs. 10,00,000. The price of the motorcycle has been depreciating at a compound rate of 10% for 2 years, while the price of land has been increasing at the compound rate of 12%.

1. Write the formula to calculate compound growth.
2. What will be the price of land after 2 years? Find it.
3. Will the total price of the motorcycle and land after 2 years be Rs.15,00,000? Write with calculation.

Rita is a student studying in class 10. Her mother deposited Rs.50,000 for 2 years in fixed deposit of a bank at compound interest compounded annually for her study expenses and the compound amount at the end of one year is Rs. 56,000.

1. For principal Rs. 'P', time T years and rate of interest R% per year, write the formula to find yearly compound amount 'CA'.
2. Find the annual rate of compound interest offered by the bank.
3. What will be the compound amount that Rita gets at the end of 2 years? Find it.

In a survey of 200 people, 120 like to play football, 85 like to play volleyball and 30 like to play none of these two games.

1. If F and V denote the sets of people who like to play football and volleyball respectively, then write the cardinality of $n(\overline {F \cup V})$.
2. Present the above information in a Venn diagram.
3. How many people like to play volleyball only? Find it.
4. Compare the number of people who like to play both the games and the number of people who don't like any of these two games.

Construct a parallelogram in which one side AB = 5.5 cm. , diagonal AC = 8 cm, and diagonal BD = 6 cm. Construct a rectangle having equal area to this parallelogram.

Construct a parallelogram having a side 5.5 cm and whose area is equal to a rectangle of length 6.5 cm and breadth 5 cm.

Construct a $\triangle$LMN in which LM = 6.3 cm, $\angle$LNM=30$^{\circ}$ and $\angle$LMN=45$^{\circ}$. Also, construct another $\triangle$OLM having OL = 7.5 cm.