Mathematics

If I and A denote the sets of youths who liked iPhone and Android Phone respectively, write the value of $n(I \cap A)$.

Show the above information in a Venn-diagram.

Find the number of youths who liked iPhone only.

By what percentage more or less is the number of youths who liked iPhone only than the number of youths who liked only Android Phone? Compare it.

How many times is compound interest calculated semiannually in 2 years? Write it.

The farmer paid Rs.3,00,000 at the end of the first year, including some principal and interest. How much does he need to pay to clear the debt in the next year? Find it.

If the farmer had paid the loan in a lump sum at the end of two years, how much less or more interest would he have paid than before? Find it.

What does $P_T$ represent in the formula $P_T=P_0\left(1+\frac{R}{100}\right)^T$? Write it.

What was the purchasing price of the land in 2080 B.S.? Find it.

If the price of land depreciates by 10% per annum, what will be the price of the land after two years from now? Find it.

How much Nepali currency can be exchanged for 5,000 Australian dollars? Find it.

If the Nepalese currency is devalued by 1.5%, what will be the new exchange rates? Find them.

How much profit or loss will there be when exchanging 5,000 Australian dollars into Nepalese rupees after devaluation? Find it.

Write the relation among the triangular surfaces of a square-based pyramid.

Find the length of the base side of the pyramid.

Find the ratio of the total surface area to the area of the triangular surfaces of the pyramid.

Write the formula for the volume of a cone.

Find the volume of the solid object.

Find the total surface area of the solid object.

How much does it cost to carpet the room at the rate of Rs.250 per sq. ft? Find it.

If plastering the four walls and ceiling, excluding doors and windows, costs Rs.1,18,200, find the plastering rate per square foot.

If $a$, $m$, and $b$ are in an arithmetic sequence, what is the arithmetic mean $m$? Write it.

How much does the officer earn in 7 years? Find it.

In how many years can the officer earn Rs.1,02,24,000? Is it possible? Give logic with calculation.

Write the roots of the quadratic equation $ax^2+bx+c=0; a\neq0$.

Find the length of the field by forming a quadratic equation.

What is the maximum number of rectangular pieces measuring 4 m × 4 m that can be made in the field? Present it with a diagram.

Simplify: $\frac{p}{x-y}-\frac{p}{x+y}$

Solve: $2^x+2^{-x}-1=\frac{3}{2}$

Write the relation between the areas of a parallelogram and a triangle standing on the same base and between the same parallel lines.

Prove that: $\Delta PQR=\Delta QRT$ (in area).

What is the sum of the opposite angles of a cyclic quadrilateral? Write it.

Find the value of $x$ from the given figure.

Verify experimentally that the circumference angle $WXY$ is half of the central angle $WOY$. Two circles having radii of at least 3 cm are required.

Prove that $\angle OWZ+\angle OYZ=135^\circ$.

Construct parallelogram PQRS according to the given measurements. Also construct $\Delta QTU$ having side QT = 5 cm and equal in area to the parallelogram.

Why are the areas of parallelogram PQRS and triangle QTU equal? Give a reason.

What angle is formed when observing the top of the view tower from the roof of the house? Write it.

Find the height of part AE of the tower.

Find the height of the house.

How far must the observer descend from the top of the view tower so that the angle of depression to the roof is $45^\circ$? Find it.

What is the median class interval? Write it.

Find the value of $m$ from the given data.

Find the mean.

Are the modal class and the first-quartile class the same? If so, justify it.

If A and B are two independent events, write the multiplication law of probability.

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

Find the probability of getting two blue balls.

Find the ratio of the probability of getting balls of the same colour to that of getting balls of different colours.