SEE Mathematics Model Question Paper 2080 with Solutions - Set 2

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.

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.

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.

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.

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.

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 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.

The first and last term of an arithmetic series having some terms are 4 and 40 respectively. The sum of all terms is 220.

1. Write the formula to calculate the the sum of the first n terms of the series.
2. Find the total number of terms in the series.
3. What should be added to the third term of the series so that the first three terms form a geometric series? Find it.

The length of a rectangular plot is 8m more than its breadth. The area of the plot is 384 sq.m.

1. How many roots does the quadratic equation $\rm ax^2+bx+c=0, a\not = 0$ have? Write it.
2. What are length and breadth of the plot? Find it.
3. How long the plot should be decreased from its length to form it is a square plot? Calculate it.

Solve: $\rm 2^{x - 2}+ 3^{3 - x} = 3$

Simplify: $\rm \frac {1}{x^2 - 5x + 6} + \frac {2}{4x - x^2 - 3}$

Construct a quadrilateral ABCD in which AB=4.5cm, AC=CD=5cm, AD=6cm, and $\angle$BAC=60$^{\circ}$. Also, construct a triangle PBC whose area is equal to the area of the quadrilateral. Give the reason for being the area of the quadrilateral ABCD and the triangle PBC equal.

From a class having 12 boys and 18 girls, two students are selected randomly without sending the first student back to the class.

1. Define mutually exclusive events.
2. Show the probabilities of possible outcomes of selecting boys and girls in a tree diagram.
3. Find the probability of selecting both girls.
4. By how much the probability of getting at least one boy is less than the total probability? Calculate it.