Mathematics

'A' represents the set of people who like apple and 'O' represents the set of people who like orange then write the cardinality notation of the number of people who don't like any of these fruits.

Present the above information in a Venn diagram.

Find the number of people who like apple.

Compare the number of people who like apple and who like orange.

Write the relation among principal P, annual compound interest rate R, time T and compound interest CI.

Find the compound interest of the first year.

How much total interest was paid by Niraj in two years? Find it.

By how much does the price of machine depreciate in first year? Find it.

After how many years was the machine sold? Find it.

Find the profit or loss percentage from selling the machine if she earns Rs. 4,900 from the rent of machine.

Which exchange rate is used when Ramesh exchange American dollar with Nepali rupees? Write it.

Find the American dollar obtained from NRs. 2,07,345.

By what percent Nepali currency is devaluated when the selling rate of 1 US dollar is Rs. 140.2183? Find it.

How many plane surfaces area are counted to find the total surface area of a square based pyramid? Write it.

Find the vertical height of the pyramid.

Find the total surface area of the pyramid.

How many curved surfaces are there in a combined solid made of a cylinder and a hemisphere? Write it.

Find the volume of the tank.

How much maximum liters of water is contained in the tank? Find it.

How much does it cost for carpeting the room at the rate of Rs. 300 per sq. ft.? Find it.

If the cost of coloring four walls and ceiling excluding doors and windows of the room is Rs. 19,560, find the rate of coloring per square feet.

Define mean in arithmetic series.

How much total money is deposited upto 10th birthday? Find it.

Is Rs. 66,000 deposited on Aashish account by 11th birthday? Give reasons.

In how many years, will Rs. 1,05,000 be deposited in the account of Aashish? Find it.

Write down the standard form of quadratic equation.

How much the length of wire is required to fence the field once with wire? Find it.

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

Solve: $2^x + \frac{16}{2^x} = 10$

Write the relation between the areas of parallelograms PQRS and PQUT.

Prove that area of $\Delta PQT$ is half of the area of parallelogram PQRS.

Are the areas of $\Delta APD$ and $\Delta BPQ$ equal in the given figure? Write with reason.

Define the inscribed angle.

If the central angle LOP = $(9x + 2)^\circ$ and inscribed angle LMP = $(4x + 5)^\circ$, find the value of $x$.

Verify experimentally that inscribed angles LMP and LNP are equal. (Two circles having at least 3cm radii are necessary.)

Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 5.6 cm, RS = 5.4 cm, SP = 6.8 cm and $\angle PQR = 75^\circ$. Then construct a triangle PSM equal in area to the quadrilateral PQRS.

In the given adjoining parallelogram ABCD, AE = BE. What percentage of area of parallelogram ABCD is occupied by the triangle BEC? Find it.

Write the name of angle of elevation of top of tower as observed from the roof of the house.

Find the value of TR.

Find the distance between the house and the tower.

Is the angle of depression of $30^\circ$ formed when the roof of the house is observed from a point 28 meter below the top of the tower? Give reason.

Write the median class.

Find the value of $x$.

Find the mean mark of the given data.

Find the ratio of students obtaining marks less than 20 and 20 or more than 20.

If B and R be two independent events then write the formula of $P(B \cap R)$.

Show the probabilities all the possible outcomes in a tree diagram.

Find the probability of getting both black balls.

By how much the probability of getting both red balls is more or less than the probability of getting both black balls? Find it.