SEE 2081_RE1031_GP

1. In a survey of 450 people, 200 people liked tea and 250 people liked coffee. But 50 people did not like any of these two drinks.
   1. If T and C denote the set of people who like tea and coffee respectively, write the cardinality of n(T ∪ C).
   2. Present the above information in a Venn diagram.
   3. Find the number of people who liked tea only.
   4. Compare the number of people who like both tea and coffee with the number of people who like coffee only.
2. A farmer deposited Rs.50,000 in a co-operative for 2 years to get the annual compound interest at the rate of 8% per annum.
   1. How many times the interest is calculated in the quarterly compound interest in one year? Write it.
   2. How much annual compound interest will the farmer receive at the end of 2 years? Find it.
   3. By how much the semi-annual compound interest is more than the annual compound interest of the same sum at the same rate and for the same period of time? Find it.
3. An electric bus is purchased for Rs.45,00,000. Using the bus for 2 years Rs.12,00,000 is earned. The value of the bus depreciates at the rate of 10% per annum.
   1. If the initial price of bus is V₀, annual rate of depreciation is R and price of the bus after T years is Vₜ, express Vₜ in terms of V₀, R and T.
   2. How much the price of the bus depreciated in first year? Find it.
   3. If the bus will be sold after 2 years, what will be the percentage of profit or loss? Find it.
4. Nabin went to bank to exchange American dollars to visit abroad. In that day the buying rate of 1 dollar was Rs.138.23 and selling rate was Rs.138.83.
   1. By how much the selling rate is more than the buying rate? Find it.
   2. How much Nepali rupees can be exchanged with American dollar 500? Find it.
   3. After some days the selling rate of dollar 1 becomes Rs.139.80 then by what percent the Nepali currency was devaluated? Find it.
5. The vertical height of a square based pyramid is 12 cm and its base side is 10 cm.

   1. How many triangular surfaces are there in a square based pyramid? Write it.
   2. Find the volume of the pyramid.
   3. Find the total surface area of the pyramid.
6. In the given figure, a combined solid object is formed with the combination of cylinder and cone having same radius. In the solid object, the length of cylindrical part is 28 cm and the slant height of conical part is 17 cm. The volume of the cylindrical part is 5632 cubic cm.

   1. What type is the shape of the base of solid object? Write it.
   2. Compare the height of conical part and the length of cylindrical part.
   3. Is the volume of cylindrical part five times the volume of conical part? Justify with calculation.
7. The length, breadth and height of a rectangular room are 12 m, 8 m and 3 m respectively. There are two square windows with edges 2 m and a door of size 1.5 m × 1 m in the room.
   1. Find the area of the floor of the room.
   2. How much does it cost to coloring the four walls and ceiling of the room excluding the area occupied by the windows and door at the rate of Rs.15 per square meter? Calculate it.
8. There are 7 arithmetic means between 3 and 27.
   1. Write the formula to calculate arithmetic mean between a and b.
   2. What is the 5th mean of the given sequence? Find it.
   3. Which one is greater by how much in arithmetic mean and geometric mean between 3 and 27? Compare it.
9. The perimeter and area of a rectangular ground are 44 meter and 120 square meters respectively.
   1. Write the formula to solve the quadratic equation ax² + bx + c = 0, a ≠ 0.
   2. Find the length and breadth of the ground.
   3. If the ground is made a square by reducing the length side, by what percent the area will be increased or decreased? Find it.
10. 1. Simplify: a/(a−b) + b/(b−a)
    2. Solve: 2ˣ + 1/(2ˣ) = 2½
11. In the given figure, EC // AB, DA // CB and DF ⟂ BC.

    1. Write the relation between areas of triangle and parallelogram standing on the same base and between same parallel lines.
    2. If BC = 6 cm and DF = 8 cm find the area of ΔABE.
    3. In the given figure, if area of ΔAOB and area of ΔCOD are equal, then prove that AD ∥ BC.
12. In the given diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral.

    1. Write the relationship between angle ∠QRS and reflex ∠QOS.
    2. If ∠QPS = 46°, find the value of ∠QOS.
    3. Verify experimentally that: ∡QPS + ∡QRS = 180°. (Two circles having radii more than 3 cm are necessary.)
13. In quadrilateral PQRS, PQ = 5 cm, QR = 4.5 cm, RS = SP = 6 cm and QS = 6.5 cm.
    1. Construct quadrilateral PQRS according to the above measurements and then construct a triangle which is equal to the quadrilateral in area.
    2. Why the area of the quadrilateral and triangle are equal? Give reason.
14. In the given figure, from the top of a tower AB 30 meter high, the angle of depression of the roof of a house is 30°. The distance between tower and house is 10√3 meter.

    1. Write the definition of the angle of elevation.
    2. What is the angle of elevation of the top of the tower from the roof of the house? Write it.
    3. Find the height of the house.
    4. What is the value of ∠CAH when AE = EC? Give reason.
15. The marks obtained by 15 students in an examination with full mark 50 are given in table.

    Obtained Marks	0–10	10–20	20–30	30–40	40–50
    Number of Students	5	3	4	2	1

    1. Write the formula to calculate the first quartile of continuous series.
    2. Find the first quartile of the given data.
    3. Calculate the mean of the given data.
16. A bag contains 7 black and 4 red balls of same shape and size. Two balls are drawn randomly one after another without replacement.
    1. If B and R be two independent events then 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 the probability of getting both red balls is more or less than the probability of getting both black balls? Find it.