SEE 2081 (2025) - Mathematics Questions:
Group 'A'
Answer all the questions
1. In a survey of a group of 360 students, 100 students like basketball only, 60 like cricket game only and 100 do not like any of the two games.
(a) If 'B' and 'C' denote the set of students who like basketball and cricket game respectively, then what is the value of n(B∪C)? Write it. (1)
(b) Present the above information in a Venn-diagram. (1)
(c) Find the number of students who like both games. (3)
(d) If everyone who is not interested in any game liked cricket game in the second survey and found others to be same then, what would be the number of students who like at least one game? Find it. (1)
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 sum for same time and same rate of interest compounded annually to Shyam.
(a) According to the given context, which interest is more among simple interest and compound interest for 2 years? Write it. (1)
(b) How much profit did Rajan get during the transaction of 2 years? Find it. (2)
(c) How much more interest should Shyam need to pay to Rajan if Rajan had lent the amount at semi-annual compound interest? Find it. (2)
3. The population of a village is 20,000. The population increases by 2% annually in the village.
(a) If the initial population is P, growth rate is R per annum and population after T years is Pt then write the formula to find Pt. (1)
(b) After how many years the population of the village will be 20,808? Find it. (2)
(c) 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. (1)
4. According to the currency exchange rate, the buying rate of 1 American dollar was NRs. 136.13 and selling rate was NRs. 137.25 on a certain day.
(a) Which rate buying or selling is used when you exchange American dollar into Nepali rupees? Write it. (1)
(b) How many Nepali rupees can American tourist get by exchanging 1000 dollars? Find it. (1)
(c) The American tourist spent NRs. 1,01,817.50 while staying in Nepal, how many American dollars can he/she exchange from remaining Nepalese rupees, while returning back to own country? Find it. (2)
5. A group of students constructed a square-based pyramid-shaped tent having length of base side 24 meter and vertical height 5 meter.
(a) How many triangular surfaces are there in the square-based pyramid? Write it. (1)
(b) Find the slant height of the above square-based tent. (1)
(c) If cost of cloth required for triangular surfaces is Rs.125 per square meter, find total cost. (2)
6. In the given figure, wooden cylinder and cone having equal base are shown.
(a) Write the formula to find the volume of a cone. (1)
(b) Find the volume of the cone in the given objects. (2)
(c) If given wooden cylinder is drilled out in the given conical shape, what will be the volume of remaining wood in cylinder? Find it. (2)
[Figure: Cylinder height 24m, radius 10m; Cone height 10m, radius 10m]
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, 1/10 part of the wall is occupied by clay joints.
(a) How many bricks are required to construct the wall? (3)
(b) Estimate the cost of bricks used at the rate of Rs. 14500 per 1000 bricks. (1)
8. Ramesh deposits an amount in a co-operative for 7 days by increasing the amount every day double than previous day. He deposited Rs.10 on first day, Rs.20 on second day, Rs.40 on third day and so on till 7th day.
(a) What type of series is formed from the deposit amount according to above context? Write it. (1)
(b) How much amount will Ramesh deposit by the end of 7 days? Find it using formula. (2)
(c) If Ramesh withdraws the amount deposited by 4 days, how much will he receive at the end of 7th day? Find it. (2)
9. A rectangular field has longer side 40 m more than shorter side and diagonal 40 m more than longer side.
(a) Write the relation among length (l), breadth (b) and diagonal (d). (1)
(b) Find length of shorter and longer sides. (2)
(c) How many maximum plots of 30 m × 20 m can be made? (2)
10. (a) Simplify: (p+q)/pq – (q+r)/qr + (r+p)/rp (3)
(b) Solve: 3^x + 3^(x+2) = 9^(1/9) (1)
11. Given △ABC and △BCD on same base BC between parallel AD, BC. BP⊥AC.
(a) Name triangle equal in area to ABAD. (1)
(b) If AC=9cm, BP=6cm, find area △BCD. (2)
12. In △PQR, ∠POR=60°, QR=x, PQ=6cm, OR=8cm, PO⊥QR.
(a) Construct △PQR, rectangle RITA equal in area. (3)
(b) Why areas are equal? Reason? (1)
13. PAQ and PBQ are angles on same arc PQ, O center.
(a) Relation between circumference angles PAQ, PBQ? (1)
(b) If ∠POQ=12x+4°, ∠PAQ=3x-20°, find x. (2)
(c) Verify experimentally central angle double inscribed angle. (2)
14. Height tower AB 24.5m, house CD 4.5m. BC distance.
(a) Angle of elevation define. (1)
(b) Find AE, value AT. (1)
(c) If ∠ADE=30°, find BC. (1)
(d) Angle elevation comparison AE, ED equal. (1)
15. Marks of 75 students in math exam:
(a) Model class illustrate. (1)
(b) Median. (2)
(c) Mean. (2)
(d) % students below model class. (1)
16. Box with 6 white, 10 black balls, two balls drawn with replacement.
(a) Multiplication law independent events. (1)
(b) Probability tree diagram. (2)
(c) Probability same color balls. (1)
(d) Probability comparison different vs white balls. (1)
