Questions

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.

1. 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.
2. Find the volume of the solid object.
3. Compare the volume of the cylindrical part and the volume of the conical part.

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.

1. How many dollars does the man receive while exchanging American dollars with Rs. 332500? Find it.
2. How much Nepali rupees does his friend receive while exchanging American dollars 2800 on the same day? Find it.
3. 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.

40 tourists are coming from Switzerland to visit Mt. Everest. They planned to stay at Everest base camp for 4 days. For this purpose, they ordered some squared base pyramid tents in Nepal. A tent can hold 8 people and each person has 6 ft×3ft space on the ground with 48 cu.ft. of air to breathe. Find the total cost of all tents at the rate of Rs.560 per ft².

A queen of heart is absent in a well-shuffled pack of playing cards.

1. Draw a tree diagram to show all the possible outcomes.
2. What is the probability of getting both the kings if two cards are drawn at random?
3. Find the probability of getting both are other than king.
4. Find the probability of getting king in the first time and non-king in the second time.

Three children are born in a family.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write down the sample space of the experiment.
3. Find the probability of being all three sons
4. Find the probability of being all three daughters
5. Find the probability of being at least one son.
6. Find the probability of being two sons and one daughter.
7. Find the probability of being one son and two daughters.

A coin is tossed two times.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write the sample space.
3. Find the probability that both are heads.
4. Find the probability that both are tails.
5. Find the probability of getting the same kind of events.
6. Find the probability of getting at least one head.

There is one red, one white, and one yellow sweet in a pot. A sweet is taken out randomly and not replaced. Then another sweet is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Write the sample space of the experiment.
3. Find the probability of getting red and white sweet.
4. Find the probability of getting at least one red sweet.

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random and not replaced. Then another ball is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Find the probability that both balls are blue.
3. Find the probability that both balls are red.
4. Find the probability of getting both are of same colour.
5. Find the probability of getting both are of different colour.
6. Find the probability of getting at least one red.
7. Find the probability of getting at most one blue.

X and Y are two mutually exclusive events. If $\rm P(X) = \frac {1}{8}$ and $\rm P(Y) = \frac {5}{24}$.

1. Find $\rm P(X \cup Y)$.
2. Find $\rm P \overline{ (X \cup Y)}$. 

There is a coin and a dice. A coin is tossed and a die is rolled simultaneously. Find the probability of getting the following events.

1. Tail and 4.
2. Head and 5.
3. Tail and even numbers
4. Head and odd numbers.
5. Head or prime numbers.
6. Tail or even numbers