Mathematics

If 'I' and 'A' denote the sets of youth who like iPhone and android phone respectively, write the cardinality notation of the set of youth who liked iPhone.

Present the given information in a Venn-diagram by supposing $x$ as the number of youth who like both type of phone.

Find the number of youths who liked exactly one type of phone.

By what percentage the number of youth who liked android phone only is more or less than the number of youth who liked iPhone only? Compare it.

If principal 'P', Time 'T' and rate of interest 'R%' per year, write the formula to find annual compound interest.

Find the compound interest received by Pemba in 2 years.

Compare the simple interest and compound interest of 2 years.

Define compound depreciation.

Find the selling price of the electric scooter after 2 years.

How much the total amount of price of scooter is depreciated in two years? Find it.

How much Nepali rupees is needed to exchange 500 dollars? Find it.

If the Nepalese currency is devaluated by 0.5%, what will be the new buying rate? Find it.

How much less or more Nepalese rupees is required to exchange 500 dollars after devaluation than before? Find it.

How many surfaces are there in square based pyramid? Write it.

Find the volume of the pyramid.

Find the area of a triangular surface of the pyramid.

Write the relation among $l, h$ and $r$ of a cone.

How many maximum liters of water can be stored in the tank? Find it.

Compare between the curved surface area of cone and base area.

How many turfs of 4 square feet are required to lay down in the land? Find it.

Is Rs.40,000 sufficient to lay the turf in the land at the rate of Rs.150 per turf? Calculate it.

In which sequence new students are being increased every day? Write it.

How many total new students will view the video till $10^{\text{th}}$ day? Find it.

The ratio of students who viewed the video up to the $3^{\text{rd}}$ day and up to other any day is 7:255, which day is that day? Find it.

Write the standard form of a quadratic equation.

Make a quadratic equation from the given verbal problem.

Find the natural number.

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

Solve: $2^{2x} - 3 \cdot 2^{x+1} + 8 = 0$

Write the ratio of areas of triangle QRS and parallelogram PRSY.

Prove that the areas of parallelogram PRSY and parallelogram XRSQ are equal.

Construct a triangle ABC in which sides BC = 6 cm, AC = 7 cm and $\angle ABC = 75^\circ$. Also construct parallelogram CDEF whose one side ED = 6.5 cm and equal in area to the given triangle.

Write the relation between $\angle AEC$ and $\angle ADC$.

If $\angle AEC = (5x - 9)^\circ$ and $\angle ABC = (3x + 5)^\circ$, find the value of x.

Verify experimentally that the inscribed angle is half of the central angle standing on same arc by making two circles having at least 3 cm radii.

Prove that the area of $\Delta QRU$ and area of parallelogram PQRS are equal.

Prove that: $\Delta QTR = \Delta PQT + \Delta RST$.

Define angle of elevation.

Draw a figure according to the given context.

Find the distance between boy and tower.

If the angle of elevation is $45^\circ$, what would be the difference between the previous distance and current distance of the boy and tower? Compare it.

What does 'L' represent in the formula finding median $(M_d) = L + \frac{(N/2 - c.f.)}{f} \times i$ of a continuous data.

Find the median.

Find the average age of the players.

If two player having ages before (50 - 60) year are added to the above data, what will be the new average? Find it.

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

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

Find the probability of getting both marbles of same colour.

Compare between the probability of getting both marbles of same colour and different colour.