SEE 2081_RE1031_LP

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 then 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. A solid object is made up of a cone and a cylinder is given in the figure.

   1. How many curved surfaces are there in the given solid object? Write it.
   2. Find the height of cone.
   3. Compare the volume of cone and cylinder.
7. The length, breadth and height of a rectangular classroom are 18 ft, 14 ft and 10 ft respectively. In the classroom, there are two windows with size 6 ft × 4 ft and two doors with size 6 ft × 3 ft.
   1. How much does it cost to paint four walls and ceiling of the classroom excluding doors and windows at the rate of Rs.40 per square feet? Find it.
   2. If a painter paints 202 square feet in a day, how many days will two painters take to paint the classroom? Find 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) = 5½
11. In the adjoining figure, ΔPQR, parallelograms PQRS and PQTU are standing on the same base PQ and between the same parallel lines PQ and UR.

    1. Write the relation between the area of parallelograms PQRS and PQTU.
    2. Prove that the area of ΔPQR is half of the area of parallelogram PQTU.
12. In the given figure, 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. (Experimentally verify that the opposite angles ABC and ADC of cyclic quadrilateral ABCD are supplementary. (Two circles with at least 3 cm radii are necessary.)
13. Construct a triangle CAT having sides AT = 4.4 cm, AC = 5.5 cm and ∠CAT = 60°. Construct another triangle BAT whose area is equal to the area of the given triangle, where AB = 6.2 cm.
    1. Why the area of ΔCAT and ΔBAT are equal? Give a reason.
    2. In the parallelogram ROSE, if P and Q are any points of sides ES and ER respectively, prove that ΔROP = ΔSOQ.
14. In the given figure, height of the electric pole (PQ) is 18 meter and height of a man (RS) is 1.5 meter. SQ represents the distance between electric pole and man, where ∠PRT = 30°.

    1. Define the angle of elevation.
    2. Find the value of PT.
    3. Find the distance between the electric pole and the man.
    4. By how many degrees will the angle of elevation be less or more when PT and TR are equal? Find it.
15. The marks obtained by 20 students in an examination with full marks 50 are given in the following table.

    Marks obtained	0–10	10–20	20–30	30–40	40–50
    No. of students	2	3	4	7	4

    1. Write the modal class of the given data.
    2. Find the median from the given data.
    3. Calculate the average mark from the given data.
    4. How many maximum number of students could be there who obtained the marks less than the average mark? Find it.
16. Two cards are drawn randomly one after another without replacement from a well shuffled deck of 52 cards.
    1. If P(A∩B) = P(A) × P(B), what type of events are A and B? Write it.
    2. Show the probability of all possible outcomes of getting and not getting king cards in a tree diagram.
    3. Find the probability of getting both king cards.
    4. Is the probability of getting both ace of diamond possible? Give reason.