SEE 2081_RE1031_MP

1. A survey conducted among 160 people showed that the number of people who like only apple and only orange are 75 and 45 respectively. Among them, 23 people do not like any of these two fruits.
   1. If ‘A’ represents the set of people who like apple and ‘O’ represents the set of people who like orange, write the cardinality notation of the number of people who don’t like any of these fruits.
   2. Present the above information in a Venn diagram.
   3. Find the number of people who like apple.
   4. Compare the number of people who like apple and who like orange.
2. Neeraj took a loan of Rs. 4,00,000 for 2 years at the rate of 10% annual compound interest. He paid Rs. 2,40,000 at the end of the first year.
   1. Write the relation among principal (P), annual compound interest rate (R), time (T) and compound interest (CI).
   2. Find the compound interest of the first year.
   3. How much total interest was paid by Neeraj in two years? Find it.
3. Neelam bought a machine for Rs. 40,000. The price of the machine depreciates at the rate of 5% annually. The machine is sold for Rs. 36,100 after using for some years.
   1. By how much does the price of the machine depreciate in the first year? Find it.
   2. After how many years was the machine sold? Find it.
   3. Find the profit or loss percentage from selling the machine if she earns Rs. 4,900 from the rent of the machine.
4. Ramesh had NRs. 2,07,345. When he went to the bank the exchange rate was as follows:

   Buying rate of $1 = Rs. 138.23

   Selling rate of $1 = Rs. 138.83

   1. Which exchange rate is used when Ramesh exchanges American dollar to Nepali rupees? Write it.
   2. Find the American dollar obtained from NRs. 2,07,345.
   3. By what percent Nepali currency is devaluated when the selling rate of 1 US dollar is Rs. 140.2183? Find it.
5. The volume of a square based pyramid is 512 cubic cm and the length of the side of its base is 16 cm.
   1. How many plane surfaces are counted to find the total surface area of a square based pyramid? Write it.
   2. Find the vertical height of the pyramid.
   3. Find the total surface area of the pyramid.
6. Jyoti bought a tank made up of a cylinder and a hemisphere from the local market. The total height of the tank is 3.5 meter and the radius of the base is 1.05 meter.
   1. How many curved surfaces are there in a combined solid made of a cylinder and a hemisphere? Write it.
   2. Find the volume of the tank.
   3. How much maximum liters of water is contained in the tank? Find it.
7. The length, breadth and height of a rectangular room are 16 ft, 12 ft and 9 ft respectively. There are two square windows of dimension 4 ft × 4 ft and one door of dimension 6 ft × 2 ft.
   1. How much does it cost for carpeting the room at the rate of Rs.300 per sq. ft.? Find it.
   2. If the cost of coloring four walls and ceiling excluding doors and windows of the room is Rs.19,560, find the rate of coloring per square feet.
8. Hari deposited Rs.1,000, Rs.2,000 and Rs.3,000 in bank on his son Aashish's first, second and third birthday respectively. In this way, he increases the deposit by Rs.1,000 on every birthday.
   1. Define mean in arithmetic series.
   2. How much total money is deposited up to 10^th birthday? Find it.
9. Kriti wants to fence her field having length twice of breadth. The area of the field is 800 square feet.
   1. Write down the standard form of quadratic equation.
   2. How much length of wire is required to fence the field once with wire? Find it.
10. 1. Simplify: \(\frac{x}{xy - y^{2}} + \frac{y}{xy - x^{2}}\)
    2. \(2^x + \frac{16}{2^x} = 10\)
11. In the given figure, parallelograms PQRS and PQUT are standing on the same base PQ and between the same parallel lines PQ and TR.

    1. Write the relation between the areas of parallelograms PQRS and PQUT.
    2. Prove that area of ΔPQT is half of the area of parallelogram PQRS.
    3. Are the areas of ΔAPD and ΔBPQ equal in the given figure? Write with reason.
12. In the given figure, O is the centre of the circle. The points M, N, P and L are on the circumference of the circle.

    1. Define inscribed angle.
    2. If the central angle ∠LOP = (9x + 2)° and the inscribed angle ∠LMP = (4x + 5)°, find the value of x.
    3. Verify experimentally that angles ∠LMP and ∠LNP are equal. (Two circles having at least 3 cm radii are necessary.)
13. 1. Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 5.6 cm, RS = 5.4 cm, SP = 6.8 cm and ∡PQR = 75°. Then construct a triangle PSM equal in area to the quadrilateral PQRS.
    2. In the given adjoining paralle- logram ABCD, AE = BE. What percentage of area of a paralle logram ABCD is occupied by the triangle BEC? Find it.
14. In the given situation, PQ represents the height of the house, RS represents the height of the tower and QS represents the distance between the house and the tower.

    1. Write the name of the angle of elevation of the top of the tower as observed from the roof of the house.
    2. Find the value of TR.
    3. Find the distance between the house and the tower.
    4. Is the angle of depression of 30° formed when the roof of the house is observed from a point 28 m below the top of the tower? Give reason.
15. The following table represents the marks obtained by students in an internal examination of Mathematics with full marks 50. The median of the data is 29.
    
    

    Obtained Marks	0–10	10–20	20–30	30–40	40–50
    Number of Students	3	7	10	x	10

    1. Write the median class.
    2. Find the value of x.
    3. Find the mean mark of the given data.
    4. Find the ratio of students obtaining marks less than 20 and students obtaining marks 20 or more than 20.
16. A bag contains 7 black balls and 4 red balls. Two balls are drawn randomly one after another without replacement.
    1. If B and R are two independent events, write the formula of P(B ∩ R).
    2. Show the probability of all possible outcomes in a tree diagram.
    3. Find the probability of getting both black balls.
    4. By how much is the probability of getting both red balls less than the probability of getting both black balls? Find it.