SEE 2080_RE1031_SP

1. A survey was conducted among 45 students of grade X asking them about preference of two subjects Mathematics and English. Findings are presented below:
   1. 11 students like Mathematics only.
   2. 13 students like English only.
   3. 6 students do not like any of them.
   1. Write the set of students who don't like any of these both subjects in cardinal notation by letting set of students who like Mathematics by \(M\) and English by \(E\).(1)
   2. Illustrate the above information in a Venn diagram.(1)
   3. Find the number of students who like Mathematics.(3)
   4. If all students, who like English, belong to the set who like Mathematics, what effect can be shown in the cardinality of the set \((M \cap E)\)? Write it.(1)
2. Indira planned to deposit Rs. 10,000 in the bank. Bank A and bank B have announced a new interest rate offer as shown below.

   Bank A	Bank B
   Yearly rate of compound interest: 10%	Half yearly rate of compound interest: 8%

   1. Write the formula for finding yearly compound interest.(1)
   2. How much amount can Indira receive in 2 years when she deposits the money in bank A? Calculate it.(1)
   3. If Indira withdraws the amount accumulated in 1 year according to bank A and deposits it in bank B, how much amount can she receive at the end of second year from bank B? Calculate it.(2)
   4. In which bank would you advise Indira to deposit the amount between bank A and bank B? Give reason.(2)
3. The population of a village is 10,000. The population grows by 2% annually in the village.
   1. Write the formula used to find the population after \(T\) years.(1)
   2. After how many years the population of the village will be 10,404? Find it.(2)
   3. If the population increases at the rate of 4% per annum, by what number will the population of that village be increased in 2 years? Find it.(1)
4. On Bhadra 13, B.S. 2076, Reena exchanged NRs. 11,45,900 with U.S. dollars at the rate of 1 U.S. dollar = NRs. 114.59. She sent the dollars to her brother, who lives in America. Next day her brother sent 9000 pound sterling to her. She exchanged the pound sterling at the rate of NRs. 139.85 = 1 Pound Sterling.
   1. Which amount is more between the amount Reena sent and the amount she received? Find it.(2)
   2. Compare the exchange rate between US dollar and pound sterling.(1)
5. The volume of the square based pyramid as shown in the figure is 384 cubic cm and the length of the side of the base is 12 cm.
   1. How many triangle's area are counted to find the lateral surface area of the square based pyramid?(1)
   2. Find the total surface area of the pyramid.(3)
   3. Compare the area of the triangular faces and the area of the base of the pyramid.(1)
6. In the figure, the total height of the combined solid metal is 180 cm and radius of the base is 42 cm. \([\pi = \frac{22}{7}]\)
   1. Write the formula for finding total surface area of the cone.(1)
   2. Find the volume of the combined solid object.(2)
   3. How much rupees is required to make the solid metal at the rate of 10 paisa per cubic centimeter? Find it.(1)
7. A water plant company built a reserve water tank whose lower part is cylindrical and upper part is hemi-spherical with equal diameter. The inner diameter and total height of the tank are 4.2 meter and 4.5 meter respectively. \([\pi = \frac{22}{7}]\)
   1. Find the volume of the tank.(2)
   2. How many maximum number of water tanks of 1000 liter capacity can be filled by the full water of reserve tank? Find it.(2)
8. There are 7 terms in an arithmetic sequence. The first term is 7 and the last term is -17.
   1. If the first term of an arithmetic sequence is \(a\) and the third term is \(b\), write the formula to find the mean.(1)
   2. Find all the arithmetic means of the sequence.(2)
   3. If 5 terms are added to that sequence, then calculate the sum of the terms of the new sequence.(2)
9. Ramesh purchased a rectangular field to make a house in Surkhet. The area of the field is 180 square meter and its perimeter is 56 meter.
   1. Write the standard form of the quadratic equation.(1)
   2. What is the breadth of the field? Find it.(2)
   3. Can he make a 21 meter long straight wall in the field? Write with reason.(2)
10. 1. Simplify: \(\frac{1}{a + 2b} + \frac{2a}{a^2 - 4b^2}\) (2)
    2. Solve: \(4 \times 3^{x+1} - 9^x = 27\) (3)
11. In the given figure, \(FE \parallel GH\), \(EI \parallel FG\) and \(FJ \parallel GI\).
    1. Write the relationship between the areas of parallelograms standing on the same base and between the same parallel lines. (1)
    2. Prove that: Area of \(\triangle EFJ = \) Area of \(\triangle HGI\) (2)
    3. When the parallelogram \(EFGH\) is made as a rectangle lying on the same base \(FG\), will it make any change in the area? Write with reason. (1)
12. 1. In a quadrilateral \(PQRS\), \(PQ = QR = 4.8 \text{ cm}\), \(RS = PS = 5.8 \text{ cm}\) and \(\angle QPS = 60^\circ\). Construct the quadrilateral \(PQRS\) and then construct a triangle which is equal to the quadrilateral in area. (3)
    2. In the figure, \(ABCD\) is a parallelogram. \(F\) is the mid-point of \(AB\) and the area of \(\triangle AFE\) is \(8 \text{ square cm}\). Prove that: Area of parallelogram \(ABCD = 32 \text{ square cm}\). (2)
13. A circle with center \(O\) has central angle \(\angle EOG = 110^\circ\) and \(EFGH\) is a cyclic quadrilateral.
    1. Write the relation between the opposite angles of a cyclic quadrilateral.(1)
    2. Find the value of \(\angle EHG\).(1)
    3. Verify experimentally that opposite angles \(\angle EFG\) and \(\angle EHG\) of the cyclic quadrilateral \(EFGH\) are supplementary. (Two circles having at least 3 cm radii are necessary.)(2)
14. The distance between a tower and a house is 25 feet. The height of the tower is 75 feet and the angle of depression from the top of the tower to the roof of the house is \(45^\circ\).
    1. Define angle of depression.(1)
    2. Find the height of the house.(1)
    3. How many feet the tower is higher than the house? Find it.(1)
    4. If the angle of elevation formed by viewing just below the top of tower from the roof of the house is \(30^\circ\), at what distance below the top of the tower is viewed? Find it.(1)
15. The daily wage of workers of a paper factory is given in the table below:

    Wages in Rs.	500-600	600-700	700-800	800-900	900-1000	1000-1100
    Number of workers	3	5	6	2	3	1

    1. What is the modal class of the given data? Write it.(1)
    2. Find the median class of the given data.(2)
    3. What is the average daily income of a worker? Calculate it.(2)
    4. Do the median and modal class lie always in the same class? Write with reason.(1)
16. A box contains 10 red and 15 black balls of same shape and size. Two balls are drawn at random one after another without replacement.
    1. What do you mean by independent events? Write it.(1)
    2. Show the probability of all the possible outcomes in a tree diagram.(2)
    3. Find the probability of getting both black balls.(1)
    4. Compare the difference between the probability that both balls are black and both balls are red.(1)