SEE 2080_RE1031_LP

1. Out of the people who participated in a survey, 80 people liked oranges, 85 people liked mangoes and 75 people liked both, while 50 people did not like any of these fruits.
   1. Assuming the set of people who like oranges as \(O\) and mangoes as \(M\), write the set of people who like both fruits in the cardinality notation.(1)
   2. Present the above information in a Venn diagram.(1)
   3. Find the total number of people who participated in the survey by using Venn diagram.(3)
   4. Compare the number of people who like only one fruit and the number of people who like both the fruits.(1)
2. 2. The difference between the yearly compound interest for 2 years and half yearly compound interest on a sum of money for the same time at the interest rate of 20% per annum is Rs 482.
   1. Which is higher in yearly compound interest and half-yearly compound interest of an amount for keeping the same interest rate and time? Write it.(1)
   2. Find the principal.(2)
   3. Find the quarterly compound interest of the same principal in 1 year at the same rate of interest.(2)
3. 3. The initial population of Rampur was 2,40,000 and that of Laxmanpur was 2,30,000. The population of Rampur increases by 4% per year and the population of Laxmanpur decreases by 5% per year.
   1. Write the formula for finding population after \(T\) years.(1)
   2. After 2 years which place has more population and by how much? Find it.(2)
   3. By what percentage should the population of Laxmanpur increase in 2 years to reach the same population as the initial population of Rampur? Find it.(1)
4. 4. On a day, the exchange rate of US dollar ($) 1 was NRs. 133.63.
   1. How much Nepalese rupees can be exchanged with $ 1000? Find it. (1)
   2. While Nepalese currency is devaluated by 1.5% as comparison to dollar, what will be the Nepalese rupees equal with $ 1? Find it. (1)
   3. If Nepalese currency is revaluated by 1.5% instead of devaluation of 1.5%, what would be the difference in Nepalese rupees while exchanging $ 1000? Find it. (2)
5. 5. The radius of the base and vertical height of a conical tent are 8 meter and 6 meter respectively. [\(\pi = \frac{22}{7}\)]
   1. Write the formula for finding the curved surface area of a cone. (1)
   2. Find the cost of the canvas used in the tent at the rate of Rs. 50 per square meter. (3)
6. 6. The solid object shown in the picture is made up of cuboid and pyramid with a square base. Where, the length of the base side is 12 cm, height of the cuboid is 9 cm and slant height of the pyramid is 10 cm.
   1. How do you find the vertical height of the square based pyramid when slant height and length of the base are given? Write it. (1)
   2. Find the volume of the pyramid. (1)
   3. How much is the volume of the pyramid less or more than the volume of the cuboid? Compare it. (1)
7. 7. As shown in the picture, 30 rings made of cement with internal diameter of 91 cm and height of 30 cm each are placed to make a well. 3 workers can build the well in 7 days. The cost of one ring is Rs. 900 and the daily wage per worker is Rs. 1500.
   1. How much does it cost to build a well? Find it. (2)
   2. How many maximum liters of water can be stored in the well? Find it. (2)
   3. If there is 4000 liter of water in that well, how many rings are completely under the water level? Find it. (2)
8. 8. A civil servant decided to deposit certain amount of his salary in a cooperative in the arithmetic sequence. He deposited Rs. 6000 in the first month, Rs. 6100 in the second month, Rs. 6200 in the third month and so on.
   1. Write the formula to find the sum of the terms of an arithmetic sequence. (1)
   2. How much amount does he save within a year in the cooperative? Find it. (2)
   3. How many months will he take to deposit Rs. 64,500? Calculate it. (3)
9. 9. The ages of father and his daughter were 48 years and 17 years respectively in 2079 B.S.
   1. What will be the age of the father and his daughter after $x$ years? Write it. (1)
   2. Prove that the product of the ages of father in 3 years ago and the age of daughter 3 years hence is a square number. (1)
   3. In which year (B.S.), the numerical product of their ages will be 1020? Calculate it by forming quadratic equation. (2)
10. 10.
    1. Simplify: $\frac{m+n}{m-n} - \frac{m-n}{m+n}$ (2)
    2. Solve: $6^x + 6^{-x} = 6\frac{1}{6}$ (3)
11. 11. In the given figure, $PQRS$ is a parallelogram.
    1. Write the relationship between the area of parallelogram and area of triangle standing on the same base and between the same parallel lines. (1)
    2. If the area of $\triangle PQT$ is $20 \text{ sq. cm}$, what is the area of $\triangle PQS$? Find it. (1)
    3. Prove that: Area of $\triangle PQT$ = area of $\triangle QRS$. (2)
12. 12. In the quadrilateral \(ABCD\), \(AB = 4.2 \text{ cm}\), \(BC = 5.6 \text{ cm}\), \(CD = 5 \text{ cm}\), \(DA = 4.8 \text{ cm}\) and \(BD = 6.5 \text{ cm}\).
    1. Construct the quadrilateral \(ABCD\) according to above measurements and then construct a triangle which is equal to the quadrilateral in area.(3)
    2. Why the area of triangle and quadrilateral so formed are equal? Give reason.(1)
13. 13. In the figure, \(O\) is the center of the circle. Where \(AB\) is the diameter, \(\angle BEC = 70^\circ\) and \(AB \parallel CD\).
    1. What is the measure of an angle in the semi-circle? Write it.(1)
    2. Find the value of \(X\).(2)
    3. Verify experimentally that the angles on the circumference standing on the same arc are equal by making two circles having at least 3 cm radii.(2)
14. 14. A person 1.68 meter tall observing upward to the top of a tower \(30\sqrt{3}\) meter away from him, found the angle to be \(30^\circ\).
    1. What type of the given angle \(30^\circ\) is either angle of elevation or depression? Write it.(1)
    2. Sketch the required figure from the above context.(1)
    3. Find the height of the tower.(1)
    4. If the man looks at the top of the tower and to form the angle \(45^\circ\), how many meters should he move towards the tower? Find it.(1)
15. 15. In the table given below, the ages (in year) of the 30 players are mentioned.

    Age in years	0-10	10-20	20-30	30-40	40-50
    Number of players	6	4	5	4	11

    1. What is the modal class of the given data? Write it.(1)
    2. Find the median class of the given data.(1)
    3. Calculate the first quartile of the given data.(2)
    4. What is the average age of players under 20 years? Calculate it.(1)
16. 16. There are 2 red and 4 white balls of the same shape and size in a bag. Two balls are drawn randomly one after another without replacement.
    1. What is the independent events? Write it.(1)
    2. Show the probability of all the possible outcomes in a tree diagram.(2)
    3. What is the probability of getting both red balls? Find it.(2)
    4. How much the probability of getting both balls of different color is less or more than the probability of getting both balls of red color? Find it.(1)