SEE Mathematics Question Paper 2080 - Gandaki Province

A survey was conducted among 20 students of a Secondary School of class X, where 14 students participated in football and 12 students in volleyball games. Every student has participated in at least one game.

1. Assuming the set of students who participated in football as F and volleyball as V, write the cardinality of the set of students who participated in volleyball or football.
2. Present the above information in the Venn diagram.
3. Find the number of students participating in exactly one game by using Venn diagram.
4. If two students who respond only to football are unable to play the game due to health problems, the cardinality of which set is changed? Give reason.

Dolma is 16 years old now. Her grandfather wants to deposit Rs. 50,000 in a bank so that she will withdraw the whole sum at the age of 18 years. While going to the bank there are two options as follows.

1. Write the formula for finding semi-annual compound interest.
2. If Dolma's grandfather deposits the sum in the bank according to the second option, how much amount will she get? Find it.
3. Which option will you suggest to Dolma's grandfather? Give reason with calculation.

In 2077 B.S. there were 1000 students in a school. A rule that a group of 100 students should bring 10 new students for enrolment was imposed to increase the number of students.

1. What is the rate of annual growth of students to increase the number of students?
2. What was the number of students in the school in 2079 B.S.? Find it.
3. Will the total number of students of the school be 1600 in 2082 B.S.? Justify with calculation.

A man exchanged some Canadian dollars of NRS. 9,72,000 at the exchange rate of 1 CAD ($) = NRS. 97.20 to visit Canada. He canceled his tour due to his health problem, so he exchanged his dollars to Nepali rupees after a week. On that day Nepali currency was devaluated by 2%. 

1. How manyh Canadian dollars did he exchange in the beginning? Find it.
2. Find the new exchange rate after devaluation of Nepalese currency.
3. How much amount did he gain during these transactions? Find it.

A group of tourists planned to fix a pyramid-shaped tent at the Everest Base Camp as shown in the figure. The length of a side of its base is 12 ft and the area of triangular surfaces is 240 sq. ft.

1. Write the formula to find the area of triangular surfaces of a square-based pyramid.
2. Find the slant height of the tent.
3. If 64 cu. ft. of air is required for a tourist, how many tourists can be accommodated easily in the tent? Find it.

In the figure, a conical object with slant height 25 cm and a hemispherical object with radius of 7 cm is composed to make a solid object.

1. What type of triangle is formed when the vertical height of the cone is drawn in the given figure? Write it.
2. What will be the total cost to paint the solid at the rate of 25 paisa per square centimeter? Find it.
3. What is the volume of the solid object? Find it.

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Tiles of length 25 cm, breadth 20 cm and height 5 mm are paved on the floor of the room.

1. How much cost of carpeting is required in the room at the rate of Rs. 250 per sq.m? Find it.
2. How many maximum numbers of tiles can be paved on the floor? Find it.

A student bought a Nepali dictionary from the Sajha Pustak Bhandar. He decided to learn new words in arithmetic sequence every day. On the first day he learned 20 new words and on the fifth day 40 new words.

1. How many terms are there in an arithmetic sequence having five means?
2. How many new words did he learn in the succeeding day? Find it.
3. How many new words will he learn till tenth day? Find it.

The present age of father is 50 years and the age of his daughter is 13 years.

1. What were the ages of father and his daughter before x years? Write it.
2. How many years before, the numerical product of their ages was 360? Calculate it by forming quadratic equation.
3. Does the product of their ages after 12 years, a perfect square? Give reason. 

Simplify: $\rm \frac {1}{x - y} - \frac {y}{xy + y^2}$

If $\rm x = 2^{\frac {1}{3}} - 2^{\frac {-1}{3}}$, prove that: $\rm 2x^3 + 6x - 3 = 0$

Triangle PQT and parallelogram PQRS are standing on the same base PQ and between the same parallel lines PQ and ST.

1. Write the relationship between the area of parallelogram and area of triangle standing on the same base and between the same parallel lines.
2. If the length of base of parallelogram PQRS is 12 cm with height 8 cm, find the area of $\triangle$PQT.

In a $\rm \triangle $ABC, $\rm \angle $ABC=60°, BC=4.4 cm and AB = 5.2 cm are given.

1. Construct a $\rm \triangle$ABC according to above measurements, then construct a rectangle MNOC equal in area to the triangle.
2. Why the areas of triangle and rectangle so formed are equal? Write reason. 

In the figure, two circles are intersected at the points P and Q. Two lines AB and CD pass through the point Q.

1. What is the relation between the inscribed angles made by the same arc? Write it. 
2. If $\rm \angle$ QAP =  25$^{\circ}$ and $\rm \angle$ QCP =  (2x - 15)$^{\circ}$, find the value of x.
3. Prove that: $\rm \angle $CPA = $\rm \angle $BPD.
4. Verify experimentally that the central angle is double of the inscribed angle standing on the same arc by making two circles having at least 3 cm radii. 

A tree is broken by wind. The top of the broken part without detaching makes an angle of 30$\circ$ with the ground. The distance from the foot of the tree to the point on the ground where the top of the tree touches the ground is $\rm 9\sqrt 3$ m.

1. Define angle of elevation.
2. Sketch the figure from the above context.
3. Find the length of the broken part of the tree.
4. If the length of the remaining part of the tree after broken is also $9\sqrt 3$ meter, what angle will the top of the tree make with the ground? Write reason.

The weight of 20 students is presented here in the table.

1. In a continuous series, what does m represent in the formula ($\rm\overline X$)=$\rm \frac {\sum fm}{N}$ to calculate mean? Write it. 
2. Find the median class of the given data.
3. Calculate the average weight from the given data.
4. Is the class of measure of central tendencies of the given data same? Justify it. 

There are 1 red, 1 black and 1 white ball of the same shape and size in a bag. Two balls are drawn randomly one after another without replacement.

1. If A and B are two independent events, write the formula of P(A $\rm \cap$ B).
2. Show the probability of all the possible outcomes in a probability tree diagram. 
3. Find the probability of getting a red ball and a black ball. 
4. Is there any possibility of getting both balls of the same color? Give reason.