SEE 2081_RE1031_SP

1. In a survey conducted among 120 students studying in class Ten of a secondary school, it was found that 60 students liked cricket game, 55 students liked basketball game and 20 students did not like any of these games.
   1. If C and B denote the sets of students who liked cricket and basketball game respectively, write the cardinality of n(B ∪ C).
   2. Present the above information in a Venn-diagram.
   3. Find the number of students who liked cricket game only.
   4. Compare the number of students who liked cricket game only and who liked basketball game only.
2. Aatmik wants to deposit Rs.4,00,000 in a bank for 2 years. The bank offers 10% per annum compound interest to Aatmik with three alternatives (annual compound interest, semi-annual compound interest and quarterly compound interest).
   1. Which option among the above three alternatives Aatmik has to use to get more interest? Write it.
   2. How much compound interest does he receive at the end of 2 years compounded semi annually? Find it.
3. A photocopy machine is purchased for Rs.80,000. After using it for 2 years, only Rs.30,000 is earned. The price of machine depreciates annually at the rate of 20% and the machine is sold after 2 years.
   1. The initial price of a machine is V₀, annual rate of compound depreciation is R and the price of machine after T years is Vₜ, express Vₜ in terms of V₀, R and T.
   2. Find the total profit or loss amount on selling the machine.
   3. If he had sold the machine after using it one year more, by how much the selling price is less or more than the purchased price? Compare it.
4. A businessman exchanged Australian dollars with NRs.1,29,090 at the exchange rate of Australian dollar 1 NRs.86.06. After some days, Nepali currency was revaluated by 2% in comparison to Australian dollar and on that day he exchanged the Australian dollars into Nepali currency again.
   1. How many Australian dollars did the businessman exchange? Find it.
   2. How many Nepali rupees did the businessman receive when he exchanged Australian dollar after revaluation in Nepali currency? Find it.
   3. What profit or loss percent did the businessman make in that transaction? Find it.
5. The vertical height of the square based pyramid is 24 cm and the length of one side of base is 20 cm.
   1. Write the formula to find the volume of the pyramid.
   2. Find the total surface area of the pyramid.
6. In the figure, a metallic solid made of hemisphere and cone is given, where the height of cone is 24 cm and diameter of base is 14 cm.

   1. Write the formula to find the slant height of cone when vertical height and radius of base are given.
   2. Find the volume of the solid object.
   3. If the solid object is melted and turned into a cylindrical object of radius 7 cm, what is the height of cylinder? Calculate it.
7. The volume and height of a square based room are 75 cubic meter and 3 meter respectively. The area occupied by a door and two windows in the room is 6 square meter.
   1. What is the total cost of plastering the four walls without door and windows at the rate of Rs.200 per square meter? Find it.
   2. If the rate of plastering per square meter is increased by one-forth, then what will be the increment in the total cost of plastering the walls? Find it.
8. Hira collected following sum of money in the first 5 days of month Baishakh.

   Baishakh-1	Baishakh-2	Baishakh-3	Baishakh-4	Baishakh-5
   Rs.10	Rs.20	Rs.40	Rs.80	Rs.160

   1. What is the mean value of the amount collected on 2nd Baishakh and 4th Baishakh? Write it.
   2. How much money will be collected by 10th day? Find using formula.
   3. Up to how many days of Baishakh can Rs.1,63,830 be collected? Find it.
9. The length of rectangular field is twice of its breadth and its area is 200 square meter.
   1. Write the standard form of quadratic equation.
   2. Find the length and breadth of the rectangular field.
   3. How many maximum numbers of pieces having size 5 m × 4 m can be made in the field? Also present diagram.
10. 1. Simplify: 1/(x−y) − 1/(x+y)
    2. If x² = 3^2/3 + 3^−2/3 − 2, prove that: 3x³ + 9x = 8
11. In the given figure, parallelogram EBCF and square ABCD are on the same base BC and between the same parallel lines AF and BC.

    1. Write the relation between the areas of parallelograms standing on the same base and between same parallel lines.
    2. Prove that: Area of parallelogram EBCF = Area of square ABCD.
    3. In the given figure PQRS is a parallelogram and M is the mid-point of TR. Prove that: ΔTQM = 1/2 (ΔPQT + ΔSRT)
12. 1. Construct a triangle ABC having BC = 6.4 cm, AB = 5.6 cm and AC = 6 cm. Also construct a triangle DAB having one side 7 cm equal in area to ΔABC.
    2. Why the area of ΔABC and ΔDAB are equal? Give reason.
13. Central angle AOB and inscribed angles ADB and ACB are standing on the same arc AB in a circle with center O.
    1. Write the relation between the inscribed angles standing on the same arc.
    2. Experimentally verify that, the central angle AOB is double of the inscribed angle ACB.
    3. The measure of central angle is (5x)° and the measure of inscribed angle is (2x + 10)° standing on the same arc in a circle, find the value of x.
14. A tree x meter high is broken by the wind, at the height 6 meter from the ground so that its top touches the ground and makes an angle 30° with the ground.
    1. What is called the angle of elevation? Write it.
    2. Express the length broken part of the tree in terms of x.
    3. What was the height of the tree before broken? Find it.
    4. What height should the tree be broken so that its top makes an angle of 45° with ground? Find it.
15. The first quartile of the given data is 35.

    Obtained Marks	0-20	20-40	40-60	60-80	80-100
    Number of students	2	x	8	5	1

    1. Illustrate the class where the first quartile lies.
    2. Find the value of x.
    3. Find the mode from the given data.
    4. Find the ratio of students who are above and below the first quartile class.
16. A married couple has given birth of two children in the interval of five years.
    1. Define independent events.
    2. Show all the possible outcomes in a tree diagram.
    3. Find the probability of having both daughters.
    4. By how much the probability of getting both children son is less or more than the maximum probability? Calculate it.