Sub. code 1031
NEB — GRADE X
2082 SP
Old Question
Compulsory Mathematics Question Paper 2082 SP (Old Question)
The candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Pass Marks : 32
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
This old question question paper is for Class 10 Compulsory Mathematics, 2082 SP (subject code 1031), carrying full marks of 75 with a pass mark of 32, to be completed within 3 Hours. Answers with step-by-step solutions are available for every question below.
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.
If I and A denote the sets of youths who liked iPhone and Android phone, respectively, write the value of .
Show the above information in a Venn diagram.
Find the number of youths who liked iPhone only.
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.
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 per annum. Bank calculated the interest compounded semiannually.
How many times is the compound interest semiannually calculated in 2 years? Write it.
The farmer paid Rs. 3,00,000 at the end of the first year with some principal and interest. How much does he need to clear the debt next year? Find it.
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.
The price of land purchased in the year 2080 B.S. increased at an annual rate of , and by the year 2082 B.S., the price became Rs. 1,44,00,000.
What does represent in the formula ? Write it.
What was the purchasing price of the land in 2080 B.S.? Find it.
If the price of the land is depreciated by per annum, then what will be the cost of land after two years from now? Find it.
According to Nepal Rastra Bank's exchange rate, the buying rate and selling rate of 1 Australian dollar were NRs. 93.20 and NRs. 93.59, respectively on a certain day.
How much can Nepali currency be exchanged with Australian dollars 5,000? Find it.
If the Nepalese currency is devalued by 1.5%, what will be the new exchange rate? Find it.
How much profit or loss will be there by exchanging Australian dollars 5,000 into Nepalese rupees after devaluation? Find it.
The diagram alongside is a square-based pyramid. Its slant height is 20 cm. The area of the triangular surfaces of the pyramid is 1280 square cm.
Write the relation among triangular surfaces of square-based pyramid.
Find the length of base side of the pyramid.
Find the ratio of total surface area and area of triangular surfaces of that pyramid.
The provided illustration depicts a composite solid formed by joining a cylinder and a cone, where the base diameter measures , the height of the conical portion is , and the overall height of the complete figure reaches .
Write down the formula to find the volume of the cone.
Find the volume of that solid object.
Find the total surface area of the solid object.
A rectangular room has length , breadth and height . There are two square windows of dimension and one door of dimension .
How much does it cost for carpeting the room at the rate of Rs. 250 per sq. ft? Find it.
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.
The monthly salary of an officer employed at an institution is Rs. 60,000, with an annual increment of Rs. 2,000 extending up to 10 years.
If 'a', 'm', and 'b' form an arithmetic sequence, what is the expression for the arithmetic mean 'm'? Write it.
How much total income does the officer accumulate over 7 years? Find it.
In how many years can the officer accumulate Rs. 1,02,24,000? Is it achievable? Provide reasoning alongside the calculation.
The length of a rectangular field is measured to be 3 meters less than twice its breadth, and the total area of this field is 135 square meters.
Write down the roots of the quadratic equation , where .
Determine the length of the field by formulating and solving a quadratic equation.
Calculate the maximum number of square plots of dimensions that can be carved out of this field, and illustrate this with a diagram.
Solve:
Simplify:
In the given figure, and .
Write the relation between the areas of parallelogram and triangle standing on the same base and between the same parallel lines.
Prove that:
In the given figure; O is the centre of the circle, where and are given.
What is the sum of the opposite angles of a cyclic quadrilateral? Write it.
Find the value of x from the given figure.
Verify experimentally that the circumference angle WXY is half of the central angle WOY. (Two circles having at least 3 cm radii are necessary.)
Prove that:
is a parallelogram in which , and .
Construct the parallelogram according to the given measurements. Also construct having side and equal in area to the parallelogram.
Why are the areas of parallelogram and triangle equal? Give reason.
In the figure alongside, from the top of the 45 meter high view tower (AB), an angle of is formed when looking at the roof of a house (CD) at a distance of 15 meter to the east of the tower.
What is the angle formed when observed from the roof of the house to the top of the view tower? Write it.
What is the height of the part AE of the tower? Find it.
What is the height of the house? Find it.
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 ? Find it.
Median of the data given below is 24.
Class Interval | 0−10 | 10−20 | 20−30 | 30−40 | 40−50 |
Frequency | 4 | 10 | 9 | 5 |
What is the class interval of median? Write it.
Find the value of 'm' from the given data.
Find the mean.
Are the modal class and the first quartile class in the given data same? If it is, then justify it.
A box contains 5 green and 7 blue balls of identical shape and size, where two balls are drawn successively with replacement.
State the formula for the multiplication law of probability for two independent events and .
Illustrate all possible outcomes using a tree diagram.
Find the probability of drawing two blue balls.
Determine the ratio of the probability of selecting balls of the same color to those of different colors.
Paper Overview & Analysis
2082 SP
Year
Old Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
49
Question Items
Question Type Breakdown