SEE Mathematics Model Question Paper 2080 with Solutions - Set 1
Answer all the questions:
In a survey of 300 people, it was found that 150 people like iPhones and 200 people like Android phones. But 25 people did not like any of these two phones.
- If I and A denote the sets of people who like iPhone and Android Phones respectively, write the cardinality of $\rm n \overline {( I \cup A ) }$.
- Present the above information in a Venn diagram.
- Find the number of people who like iPhones only.
- Compare the number of people who like both iPhone and Android phones and who do not like any of these two phones.
A retired teacher deposited Rs. 80,000 in own account at the development bank for two years to get half-yearly compound interest at the rate of 10% per annum.
- How many times the interest is calculated according to the semi-annual compound interest in 2 years? Write it.
- According to the half-yearly compound interest, what would be the compound interest received by the teacher at the end of 2 years? Find it.
- According to the same rate of yearly compound interest, in how many years will the compound amount of Rs. 80,000 be Rs. 1,06,480? Find it.
A minibus is purchased for Rs. 40,00,000. After using the bus for three years, Rs. 15,00,000 is earned. The value of the bus depreciates at the rate of 15% per annum and the minibus is sold after three years.
- If the purchasing price of the bus is Rs. $\rm V_{o}$, the annual rate of compound depreciation is $\rm R$%, and price of the bus after T years is Rs. $\rm v_{t}$, the express $\rm V_{t}$ in terms of $\rm V_{o}, R, \ and \ T$.
- Find the selling price of the bus after three years.
- FInd the total profit or loss in percent through the total transaction of that minibus.
A man went to the Bank to exchange American dollars to visit abroad. On that day, according to the money exchange rate, the buying rate of the American Dollar is Rs.132 and the selling rate is Rs.133.
- How many dollars does the man receive while exchanging American dollars with Rs. 332500? Find it.
- How much Nepali rupees does his friend receive while exchanging American dollars 2800 on the same day? Find it.
- After 10 days, the selling rate for American dollar 1 becomes Rs.138.32 then by what percent the Nepali currency was devaluated? Find it.
A metallic solid made up of a cone and a cylinder is given in the figure. The radii of the base of the cone and cylinder are equal. The height of the cylinder is 40cm, the height of the cone is 24cm and the radius of the base of the cone is 7cm.
- If the radius of the base and the slant height of the cone are given then write the formula for finding the curved surface area of the cone.
- Find the volume of the solid object.
- Compare the volume of the cylindrical part and the volume of the conical part.
The height of a square-based pyramid is 21 cm and the length of the base is 20 cm.
- How many triangular surfaces are there in a square-based pyramid? Write it.
- Find the slant height of the pyramid.
- What is the total cost of painting the total surface area of the pyramid at the rate of Rs. 5 per square cm? Find it.
The length, breadth, and height of a rectangular room are 14 ft, 13 ft, and 10 ft respectively. There are two square windows with 3 feet edges and two doors of size 6ft × 3ft in the room.
- How much does it cost to paint four walls and ceiling of the room excluding doors and windows at the rate of Rs. 36 per square foot? Find it.
- How much the total cost will increase to paint on the same part if the cost of painting per square meter is increased by one-third of what it was before due to the increase in the market price? Find it.
There are 3 geometric means between 3 and 243.
- First term 'a', last term 'b', and the number of geometric means 'n' are given. Write the formula for the calculation of the common ratio in the given condition.
- What is the third mean of the given series? Find it.
- In arithmetic mean and geometric mean between 3 and 243, which one is greater and by how much? Compare it.
Atith Adhikari
·
1 year ago
Solution
Let the first and the last numbers be denoted by a and b. Then, their geometric means are denoted by \( \rm m_{i} \).
If there are n geometric means, then the formula for the calculation of the common ratio (r) is
\( \rm r = \left ( \frac{b}{a} \right )^{\frac{1}{n+1}} \).
Given
\( \rm a = 3; b = 243; n = 3\)
\( \rm r = \left ( \frac{243}{3} \right )^{\frac{1}{3 + 1}} \)
\( \rm \therefore r = 3 \)
The nth mean of the series is given by the formula \( m_{n} = a r^{n} \).
The 3rd mean of the series is given by \( m_{3} = 3 \cdot 3^{3} \).
\( \rm \therefore m_{3} = 81 \).
Geometric mean between 3 and 243 is \( \rm GM = \sqrt{3 \cdot 243} = 27 \).
Arithmetic mean between 3 and 243 is \( \rm AM = \frac{3 + 243}{2} = 123 \).
Hence, AM > GM. The difference is \( \rm AM - GM = 123 - 27 = 96 \).
The perimeter and area of a rectangular ground are 66 m and 260 sq.m. respectively.
- Illustrate the roots of x in the quadratic equation $\rm ax^{2} + bx + c = 0$, $\rm a \neq 0$.
- Find the length and breadth of the given ground.
- How many pieces of land can be made with dimension (13×4) square meter from that rectangular field? Calculate it.
Simplify: $\rm \frac{x + y}{x - y} - \frac{x - y}{x + y}$.
Atith Adhikari
·
1 year ago
Solution
Given,
$\rm \frac{x + y}{x - y} - \frac{x - y}{x + y}$
Multiplying and dividing the first term by $\rm (x + y) $and the second term by $\rm (x - y)$, we get,
$\rm = \frac{x + y}{x - y} \cdot \frac{x + y}{x + y} - \frac{x - y}{x + y} \cdot \frac{x - y}{x - y}$
Taking LCM and simplifying the expression, we get,
$\rm = \frac{ (x + y)(x + y) - (x - y)(x - y)}{ (x - y)(x + y)}$
$\rm = \frac{ (x + y)^{2} - (x - y)^{2} }{ (x - y)(x + y)}$
Using the expansion formula for each of the terms in the above expression, we get,
$\rm = \frac{ (x^{2} + 2xy + y^{2}) - ( x^{2} - 2xy + y^{2} ) }{ x^{2} - y^{2}}$
$\rm = \frac{ x^{2} + 2xy + y^{2} - x^{2} + 2xy - y^{2} }{x^{2} - y^{2}}$
$\rm = \frac{ 4xy}{x^{2} - y^{2}}$
$\rm \therefore \frac{x + y}{x - y} - \frac{x - y}{x + y} = \frac{ 4xy}{x^{2} - y^{2}}$
Solve: $\rm 4^{x} + \frac{1}{4^{x}} = 16 \frac{1}{16}$.