Mathematics

If F and V are the sets of students who like to play football and volleyball respectively, write the set of students who like to play both games in cardinality natation.

Present the given information in a Venn-diagram.

Find the number of students who like to play football.

By what percentage the number of students who like to play volleyball is more or less than the number of students who like to play football? Compare it.

Find the sum.

By how much the quarterly compound interest is more than the semi-annual compound interest of the same sum in one year? Find it.

Define compound depreciation.

How much price of the machine is depreciated in first year? Find it.

Will it be possible to buy that machine at half of its current price after 3 years? Give logic with calculation.

Among the buying rate and selling rate, which one is used while exchanging US dollar into Neplease rupees? Write it.

How many Nepalese rupees can an American tourist get while exchanging 3,000 dollars? Find it.

Compare the buying rate and selling rate after 0.5% devaluation in Nepali currency.

How much will the tourist gain while exchanging the 3,000 American dollars into Nepalese rupees after devaluation? Find it.

What does $a$ denote in the formula $V = \frac{1}{3}a^2h$, to find the volume of the square based pyramid? Write it.

What is the total surface area of the pyramid? Find it.

Compare the area of base and the area of a triangular surface of the pyramid.

How many total external surfaces are there in the given solid object? Write it.

Find the height of the cylindrical part of the solid object.

Find the volume of the solid object.

How many total stones are laid on the parking? Find it.

To lay down stones on the parking, 3 workers worked for 2 days. Every worker received Rs.1,800 as daily wages. Estimate the total cost of laying stones on the parking.

What is the sum of first $n$ terms of an arithmetic series having first term $a$ and common difference $d$? Write it.

Find the common difference of the series.

Out of first three terms of the series, if 5 and 7 are subtracted from the second and third terms respectively, the terms form a geometric series. Verify with reason.

Define quadratic equation.

Make a quadratic equation according to the given condition.

In which year the son was born? Find it.

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

Solve: $25^x - 6 \times 5^{x+1} + 125 = 0$

Write the relation of the areas of $\Delta PRS$ and $\Delta PRT$.

Prove that the areas of $\Delta PQT$ and quadrilateral PQRS are equal in area.

Prove that: Area of $\Delta POS$ = Area of $\Delta ROT$.

Write the relation between $\angle LOM$ and $\angle LNM$.

If KL // NM, Prove that: KN = LM.

Verify experimentally the relation between $\angle KLM$ and $\angle MNK$ in the given figure. (Two circles with radii at least 3 cm are necessary)

Construct a $\Delta ABC$ on the basis of the above measurements and construct a parallelogram FCDE equal in area to $\Delta ABC$ with $\angle EFC = 60^\circ$.

In which condition, the areas of a triangle and a parallelogram between same parallel lines are equal? Write it.

What is the angle of elevation? Write it.

Make a diagram according to the given context.

Find the height of the house.

What will be the angle of elevation of the roof of the house if it is observed after walking 20 m far away from that place? Find it.

Write the formula to find the mode of a continuous data.

Find the modal value from the above given data.

Calculate the median from the above given data.

Compare the total number of people whose ages are above and below than the median class.

Write the multiplication law of probability in independent events.

Show the probability of all the possible outcomes in a tree diagram.

Find the probability of getting both balls are red.

Compare the probability of getting both balls of same color and the different color.