SEE 2082 Sudurpashchim Province — Maths Past Paper
- Q1.
In a survey among 80 youths of a community, it is found that the ratio of the number of youths who liked iPhone and Android phone was 3:2. Among them 10 liked both types and 10 liked other types of phone.
- (a) If I and A denote the sets of youths who liked iPhone and Android Phone respectively, write the value of n(I ∩ A).
- (b) Show the above information in a Venn-diagram.
- (c) Find the number of youths who liked iPhone only.
- (d) By what percentage more or less is the number of youths who liked iPhone only than the number of youths who liked only Android Phone? Compare it.
- Q2.
A farmer has taken Rs.5,00,000 loan from Agriculture development bank for his poultry farm. He aimed to pay back the loan in 2 years at the rate of 8% per annum. Bank calculated the interest compounded semiannually.
- (a) How many times the compound interest semiannually is calculated in 2 years? Write it.
- (b) The farmer paid Rs.3,00,000 at the end of first year with some principal and interest. How much does he need to clear the debt in next year? Find it.
- (c) If the farmer had paid the loan at the end of two years, how much less or more interest should he have to pay than before? Find it.
- Q3.
The price of land purchased in the year of 2080 B.S. increased at an annual rate of 20%, and by the year 2082 B.S. the price became Rs.1,44,00,000.
- (a) What does Pₜ represent in the formula Pₜ = P₀(1 + R/100)ᵀ? Write it.
- (b) What was the purchasing price of land in 2080 B.S.? Find it.
- (c) If the price of land is depreciated by 10% per annum then what will be the cost of land after two year from now? Find it.
- Q4.
According to Nepal Rastra Bank's exchange rate, the buying and selling rate of 1 Australian dollar were NRs.93.20 and NRs.93.59 respectively in a certain day.
- (a) How much Nepali currency can be exchanged with Australian dollars 5,000? Find it.
- (b) If the Nepalese currency is devaluated by 1.5%, what will be the new exchange rate? Find it.
- (c) How much profit or loss will be there by exchanging Australian dollars 5000 into Nepalese rupees after devaluation? Find it.
- Q5.
The diagram along side is a square based pyramid. Its slant height is 20 cm. The area of the triangular surfaces of the pyramid is 1280 square cm.
- (a) Write the relation among triangular surfaces of square based pyramid.
- (b) Find the length of base side of the pyramid.
- (c) Find the ratio of total surface area and area of triangular surfaces of that pyramid.
- Q6.
The given figure is a combined solid made up of a cylinder and cone. Diameter of base is 14 cm, height of cone is 24 cm and total height of solid object is 54 cm.
- (a) Write down the formula to find the volume of the cone.
- (b) Find the volume of that solid object.
- (c) Find the total surface area of the solid object.
- Q7.
A rectangular room has length 16 ft., breadth 14 ft. and height 10 ft. There are two square windows of dimension 3.5 ft. and one door of dimension 3 ft. x 6 ft.
- (a) How much does it cost for carpeting the room at the rate of Rs.250 per sq. ft? Find it.
- (b) If the cost of plastering four walls and ceiling excluding doors and windows of the room is Rs.1,18,200, find the rate of plastering per square feet.
- Q8.
The monthly salary of an officer working in an institution is Rs.60,000. His/her monthly salary increases by Rs.2,000 in every year as a grade up to 10 years.
- (a) If a, m and b are in arithmetic sequence, what is the value of arithmetic mean m? Write it.
- (b) How much amount does he/she earn up to 7 years? Find it.
- (c) In how many years he/she can earn Rs.1,02,24,000? Is it possible? Give logic with calculation.
- Q9.
The length of a rectangular field is 3 meter less than twice of its breadth. The area of that field is 135 square meter.
- (a) Write the roots of quadratic equation ax² + bx + c = 0; a ≠ 0.
- (b) Find the length of that field by making quadratic equation.
- (c) How many maximum number of rectangular pieces having dimension 4 meter x 4 meter can be prepared in that field? Also present it in diagram.
- Q10.
- (a) Solve: p/(x−y) − p/(x+y)
- (b) Simplify: 2ˣ + 2⁻ˣ − 1 = 3/2
- Q11.
In the given figure PT // QR and PQ // SR.
- (a) Write the relation between the area of parallelogram and triangle standing on the same base and between the same parallel lines.
- (b) Prove that: triangle PQR = triangle QRT.
- Q12.
In the given figure, O is the centre of the circle. Where angle WXY = x° and angle WZY = 3x° are given.
- (a) What is the sum of the opposite angles of a cyclic quadrilateral? Write it.
- (b) Find the value of x from the given figure.
- (c) Verify experimentally that the circumference angle WXY is half of the central angle WOY. (Two circles having at least 3 cm radii are necessary.)
- (d) Prove that: angle OWZ + angle OYZ = 135°.
- Q13.
PQRS is a parallelogram. In which PQ = 4 cm, QR = 6 cm and angle PQR = 60°.
- (a) Construct the parallelogram PQRS according to the given measurements. Also construct triangle QTU having side QT = 5 cm and equal in area to the parallelogram.
- (b) Why are the area of parallelogram PQRS and triangle QTU equal? Give reason.
- Q14.
In the figure along side, from the top of the 45 meter high view tower (AB) an angle of 60° is formed when looking at the roof of a house at a distance of 15 meter to the east of the tower.
- (a) What is the angle formed when observed from the roof of the house to the top of the view tower? Write it.
- (b) What is the height of the part AE of the tower? Find it.
- (c) What is the height of the house? Find it.
- (d) What distance does the observer have to come down from the top of the view tower to observe the roof of the house such that the angle of depression is 45°? Find it.
- Q15.
Median of the data given below is 24:
- (a) What is the class interval of median? Write it.
- (b) Find the value of m from the given data.
- (c) Find the mean.
- (d) Is the model class and the first quartile class in the given data same? If it is, then justify it.
- Q16.
A box contains 5 green and 7 blue balls of same shape and size. Two balls are drawn randomly one after another with replacement from the box.
- (a) If A and B are two independent events, write the formula of the multiplication law of probability.
- (b) Show the probability of all the possible outcomes in a tree diagram.
- (c) Find the probability of getting both blue balls.
- (d) Find the ratio of the probability of getting balls of the same colour to the different colour.
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