SEE 2081_RE1031_KOP

1. In a survey of a group of 360 students, 100 students like basketball game, 60 like cricket game only and 100 do not like any of the two games.
   1. Using symbols B (basketball) and C (cricket), write the given information in terms of set notation.
   2. Present the above information in a Venn-diagram.
   3. Find the number of students who like both basketball and cricket games.
   4. If everyone who is not interested in any game liked cricket game in the second survey and others remained the same, what would be the number of students who like cricket game?
2. Rajan borrowed a loan of Rs 10,000 from Ram for 2 years at the rate of 10% simple interest. Immediately, Rajan lent the same amount for the same time at 10% simple interest.
   1. According to the given context, which interest is more: simple interest or compound interest for 2 years? Write it.
   2. Find the profit Rajan got during the transaction of 2 years.
   3. How much more interest should Shyam need to pay to Rajan if Rajan lent the amount at semi-annual compound interest? Find it.
3. The population of a village is 20,000. The population increases by 2% annually in the village.
   1. If the initial population is P and the annual rate of population growth is R% per annum, express the population after T years as P_T.
   2. After how many years will the population of the village be 20,808? Find it.
   3. If the population increases at the rate of 3% per annum, by what number will the population of the village be increased in 2 years? Find it.
4. An American dollar to the currency exchange rate is NRs 136.13 and selling rate was NRs 137.25 in a certain day.
   1. Which buying or selling rate is used when you exchange American dollar into Nepali rupees? Write it.
   2. How many Nepali rupees will he get by exchanging 1000 dollars? Find it.
   3. The American tourist spent NRs 1,01,817.50 and returned back with remaining Nepali rupees. How many American dollars can he/she exchange from remaining Nepali rupees, while returning back to own country? Find it.
5. A group of students constructed a square based pyramid shaped tent having length of base side 24 meter and vertical height 5 meter.
   1. How many triangular surfaces are there in the square based pyramid? Write it.
   2. Find the slant height of the above square based tent.
   3. What is the total cost of cloths required to make triangular surfaces at the rate of Rs.125 per square metre? Find it.
6. In the given figure, wooden cylinder and cone having equal base are shown.
   1. Write the formula to find the volume of a cone.
   2. Find the volume of the cone in the given objects.
   3. If the given wooden cylinder is drilled out in the conical shape, what will be the volume of remaining wood in the cylinder? Find it.
7. The length of a wall is 10 m, width is 0.5 m and height is 2 m. Bricks of size 25 cm × 12 cm × 8 cm are used to build the wall. Also, \(\dfrac{1}{10}\) part of the wall is occupied by the clay joints.
   1. How many bricks are required to construct the wall? Find it.
   2. If 1000 bricks cost Rs 14,500, estimate the cost of bricks used in the wall at the rate of Rs 14,500 per 1000 bricks.
8. Ramesh deposits money in a co-operative for 7 days by increasing the amount every day. He deposits Rs 10 on the first day, Rs 20 on the second day, Rs 40 on the third day and so on till the 7th day.
   1. What type of series is formed from the deposit amount according to the above context? Write it.
   2. How much amount will Ramesh deposit by the end of 7 days? Find it using formula.
   3. If Ramesh withdraws the amount deposited in the first day, how much amount will he receive at the end of the 7th days? Find it.
9. The longer side of a rectangular field is 40 m more than the shorter side and its diagonal is 40 m more than its longer side.
   1. Write the relation among the length (l), breadth (b) and diagonal (d) of the field according to the above context.
   2. Find the length of the shorter side and longer side of the rectangular field.
   3. How many maximum numbers of plots of size 30 m × 20 m can be made from the rectangular field?
10. 1. Simplify:
       \(\frac{p+q}{pq} - \frac{q+r}{qr} - \frac{r+p}{rp}\)
    2. Solve:
       \( 3^{y} + 3^{-y} = 9{\frac{1}{9}} \)
11. In the given figure, ∆ABC and ∆BCD are standing on same base BC and between same parallel lines AD and BC. From the point B, a perpendicular BP is drawn to the line AC.
    1. Write the name of triangle whose area is equal to area of ∆BAD in the given figure.
    2. If AC = 9 cm and BP = 6 cm, find the area of triangle BCD.
    3. In the given figure, PQRS is a trapezium, where PQ//SR. M and N are the mid points of the diagonals PR and QS respectively. Prove that: ∆MSR=∆NSR.
12. In a triangle QR, ∡ QR 60°, QR 8 cm and Q 6 cm are given.)
    1. Construct a ∆ QR according to above measurements and also construct a rectangle RITA equal in area to the triangle.
    2. Why the areas of triangle and rectangle so formed are equal? Write reason.
13. O is the centre of the given circle. Inscribed angles PAQ and PBQ are standing on the same arc PQ.
    1. Write the relationship between the circumference angles PAQ and PBQ.
    2. If the measures of central angle POQ is (12x + 4)° and the measures of inscribed angle PAQ is (3x + 20)°, find the value of x.
    3. Verify experimentally that central angle is double of the inscribed angle in the same arc. (Two circles having radii more than 3 cm are necessary.)
14. In the given figure, height of the tower AB is 24.5 meter and height of a house CD is 4.5 meter. BC denotes the distance between tower and house.
    1. Define the angle of elevation.
    2. Find the value of AE.
    3. If ∠ADE = 30°, find the distance between the tower and the house.
    4. By how many degrees is the angle of elevation less or more when AE and ED are equal?Compare it.
15. The marks obtained by the students in an exam of mathematics of 75 full marks are given in the following table.

    Obtained Marks	0–15	15–30	30–45	45–60	60–75
    Number of Students	2	5	4	6	3

    1. Illustrate the modal class from the above data.
    2. Find the median from the above table.
    3. Find the mean from the above table.
    4. Among all the participants in the exam, what percentage of students obtained marks below the modal class? Find it.
16. A box contains 6 white and 10 black balls of same shape and size. Two balls are drawn at random one after another with replacement.
    1. If A and B are two independent events, write the multiplication law of probability.
    2. Show the probability of all the possible outcomes in a tree diagram.
    3. Find the probability of getting both balls of same color.
    4. By how much the the probability of getting both balls of different color is less or more than probability of getting both balls of white color? Find it.