SEE 2082 Bagmati Province — Maths Past Paper

Full marks: 75 · Time: 3 hours · With step-by-step model answers in Nepali & English.

1. Q1.

   In a survey conducted among 120 students of a school, the ratio of the students who liked to play football only and volleyball only was found to be 2:1. Also there were 20 students who liked to play both football and volleyball and 10 students who did not like any of these two games.

   • (a) If F and V are the sets of students who like to play football and volleyball respectively, write the set of students who like to play both games in cardinality notation.
   • (b) Present the given information in a Venn-diagram.
   • (c) Find the number of students who like to play football.
   • (d) By what percentage the number of students who like to play volleyball is more or less than the number of students who like to play football? Compare it.
2. Q2.

   The difference between annual compound amounts of a sum of money in 1 year and 2 years at the rate of 10% annual compound interest is Rs.47,250.

   • (a) Find the sum.
   • (b) By how much the quarterly compound interest is more than the semi-annual compound interest of the same sum in one year? Find it.
3. Q3.

   The current price of a machine is Rs. 50,000. Its price depreciates at the rate of 20% annually.

   • (a) Define compound depreciation.
   • (b) How much price of the machine is depreciated in first year? Find it.
   • (c) Will it be possible to buy that machine at half of its current price after 3 years? Give logic with calculation.
4. Q4.

   According to the exchange rate of Nepal Rastra Bank on the date of 11/25/2025, the buying rate and selling rate of 1 US dollar were NRs. 142.48 and NRs. 143.08 respectively.

   • (a) Among the buying rate and selling rate, which one is used while exchanging US dollar into Nepalese rupees? Write it.
   • (b) How many Nepalese rupees can an American tourist get while exchanging 3,000 dollars? Find it.
   • (c) Compare the buying rate and selling rate after 0.5% devaluation in Nepali currency.
   • (d) How much will the tourist gain while exchanging the 3,000 American dollars into Nepalese rupees after devaluation? Find it.
5. Q5.

   The volume of a square based pyramid is 960 cubic cm. and its vertical height is 5 cm.

   • (a) What does a denote in the formula V = (1/3)a²h to find the volume of the square based pyramid? Write it.
   • (b) What is the total surface area of the pyramid? Find it.
   • (c) Compare the area of base and the area of a triangular surface of the pyramid.
6. Q6.

   In the figure, a solid object is formed with the combination of a cylinder and a hemi-sphere having the same base. The diameter of the base of the solid object is 14 cm and its total height is 27 cm.

   • (a) How many total external surfaces are there in the given solid object? Write it.
   • (b) Find the height of the cylindrical part of the solid object.
   • (c) Find the volume of the solid object.
7. Q7.

   The dimension of motor parking place of a house owner is 16 m long and 10 m broad. Square shaped stones having 25 cm long are laid on the parking. The price of each stone is Rs.20.

   • (a) How many total stones are laid on the parking? Find it.
   • (b) To lay down stones on the parking, 3 workers worked for 2 days. Every worker received Rs.1,800 as daily wages. Estimate the total cost of laying stones on the parking.
8. Q8.

   The first term of an arithmetic series is 12 and the sum of its first five terms is 50.

   • (a) What is the sum of first n terms of an arithmetic series having first term a and common difference d? Write it.
   • (b) Find the common difference of the series.
   • (c) Out of first three terms, if 5 and 7 are subtracted from the second and third terms respectively, the terms form a geometric series. Verify with reason.
9. Q9.

   In 2075 B.S. the age of a father was 6 times the age of his son and in 2080 B.S. the numerical product of their ages was 350.

   • (a) Define quadratic equation.
   • (b) Make a quadratic equation according to the given condition.
   • (c) In which year was the son born? Find it.
10. Q10.
    • (a) Simplify: [1/(x-y)] - [(x+y)/(x²-y²)]
    • (b) Solve: 25^x - 6 × 5^(x+1) + 125 = 0
11. Q11.

    In the given figure, PQRS is a quadrilateral whose side QR is produced to the point T and PR // ST.

    • (a) Write the relation of the areas of triangle PRS and triangle PRT.
    • (b) Prove that the areas of triangle PQT and quadrilateral PQRS are equal in area.
    • (c) Prove that: Area of triangle POS = Area of triangle ROT.
12. Q12.

    In the given figure, O is centre of circle and KLMN is a cyclic quadrilateral.

    • (a) Write the relation between angle LOM and angle LNM.
    • (b) If KL // NM, Prove that: KN = LM.
    • (c) Verify experimentally the relation between angle KLM and angle MNK in the given figure. (Two circles with radii at least 3 cm are necessary)
13. Q13.

    In triangle ABC, AB = 4.5 cm, BC = 5.5 cm and angle ABC = 75° are given.

    • (a) Construct a triangle ABC on the basis of the above measurements and construct a parallelogram FCDE equal in area to triangle ABC with angle EFC = 60°.
    • (b) In which condition, the areas of a triangle and a parallelogram between same parallel lines are equal? Write it.
14. Q14.

    A man observes the roof of a house walking 10 m. away from the foot of the house and finds the angle of elevation to be 60°.

    • (a) What is the angle of elevation? Write it.
    • (b) Make a diagram according to the given context.
    • (c) Find the height of the house.
    • (d) What will be the angle of elevation of the roof of the house if it is observed after walking 20 m far away from that place? Find it.
15. Q15.

    In the table below, the ages (in years) of 25 people of a community is given. Ages 20-30: 3, 30-40: 4, 40-50: 6, 50-60: 7, 60-70: 3, 70-80: 2.

    • (a) Write the formula to find the mode of a continuous data.
    • (b) Find the modal value from the above given data.
    • (c) Calculate the median from the above given data.
    • (d) Compare the total number of people whose ages are above and below the median class.
16. Q16.

    In a bag, there are 2 red and 3 white balls having same shape and size. Two balls are drawn randomly one after another without replacement from the bag.

    • (a) Write the multiplication law of probability in independent events.
    • (b) Show the probability of all the possible outcomes in a tree diagram.
    • (c) Find the probability of getting both balls are red.
    • (d) Compare the probability of getting both balls of same color and the different color.

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