Mathematics

If M and S denote the set of students who take extra class of Maths and Science respectively, write the set of students who did not take extra class in any of these two subjects in cardinality notation.

Illustrate the above given information in a Venn-diagram.

Find the number of students who take extra class of Maths subject.

Compare the number of students who take extra class of at least one subject and who take extra class of at most one subject in ratio.

What should be the rate of compound interest? Find it.

Find the principal.

Compare the simple interest and quarterly compound interest for 1 year at the same rate of interest on the same principal.

Write the formula to find compound depreciation.

Find the selling price of the truck after 3 years.

Find the profit or loss percent to the businessman while selling the truck after 3 years.

Define currency exchange rate.

How many American dollar will Pemba get to exchange NRs.2,15,160? Find it.

Due to different circumstances, Pemba can't go abroad. Then how many Nepali rupees will he get back after exchanging American dollars on the same day? Find it.

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

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

What is the volume of the pyramid? Find it.

Write the formula to find the radius of base of cone when slant height ($l$) and vertical height ($h$) of cone are given.

Find the volume of that solid object.

If it is melted to form a cylindrical wire of radius 3.5 mm, what is the length of the wire? Find it.

What is the cost of plastering the floor and 4 walls of the tank at the rate of Rs.1,500 per square meter? Find it.

What will be the cost to fill water in the tank at the rate of 25 paisa per litre? Find it.

What is the arithmetic mean between two numbers $a$ and $b$? Write it.

Find the common difference and first term of the given arithmetic sequence.

Find the sum of the first 10 terms of the sequence.

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

Find the length and breadth of the field.

How many maximum numbers of pieces of land can be made with size 4 meter × 4 meter in that rectangular field? Also present it in a diagram.

Simplify: $\frac{1}{a+2b} - \frac{1}{a-2b} + \frac{2a}{4b^2 - a^2}$

Solve: $4^{x-2} = 0.5$

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

Prove that the area of $\Delta BCD$ and $\Delta ABC$ are equal.

Write the relation between the opposite angles of a cyclic quadrilateral.

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

Verify experimentally that the central angle POR is twice the circumference angle PSR. (Two circles with at least 3 cm radii are necessary.)

Prove that: $\angle QPO + \angle QRO = 120^\circ$

Construct a rectangle MNOP according to the given measurements. Also, construct a triangle NQR having one angle $60^\circ$ and equal in area to the rectangle.

Why are the area of $\Delta NQR$ and rectangle MNOP equal? Give reason.

Give an example of angle of depression.

Draw a figure according to given context.

What is the height of the kite from the ground level? Find it.

If the angle formed by string with horizon decreases from $60^\circ$ to $45^\circ$ then what is the height of the kite from the ground level now? Find it.

Write the formula to calculate mode of the continuous series.

Find the mode from the given data.

Calculate upper quartile from the given data.

Find the average height of the students above model class.

Two events G and B are not mutually exclusive events, then write the formula of $P(G \cup B)$.

Show the probability of all possible outcomes obtained from the above information in a tree diagram.

Find the probability of selecting same gender student.

By how much is the probability of selecting both girls less than the total probability? Find it.