# Ten easy topics to be prepared in maths for competitive exams in India

Mathematics is a vast topic. This subject covers all the concepts of numbers, equations, calculations, etc. It helps us in our day-to-day life as well as in competitive exams. There are several competitive exams in India where students have to take a sectional test for Maths. The topics which are most frequently asked in these exams are given below:

## 1. Arithmetic Mean

Mean is a fundamental concept in Maths. The mean of a data set can be calculated by adding the values of all the data points in the set and dividing the total by the number of data points. The mean is used to describe the center of a distribution. It can be applied to any data set size and discrete and continuous distributions. It is also known as an average or arithmetic mean for its simplicity. Still, it has other names, too, such as arithmetic average, mean value, average value, or simply average, depending on how exactly it applies to your case. In statistics, it's referred to as "a measure of central tendency."

The mean is the average of all the data points in a set. It can be calculated by adding the values of all the data points in the set and dividing that total by the number of data points.

## 2. Geometric Mean

The geometric mean of a set of numbers is the nth root of the product of the numbers — that is, it's equal to the product when you take its logarithm and raise it to a specific power. For example, if you take the geometric mean of 2, 3, and 4 (which are 1/2 x 3/4 x 5/6), you get [1/2]^(1/3) = 1/6 — which is their product. So if you know how to find these products and powers efficiently, you'll be able to compute a geometric mean without too much trouble!

Geometrically speaking, think about how adding up two sides where one side has been multiplied by itself will give you a number closer than either original side was all on its own — this allows us to come up with formulas for calculating these things. Quickly by hand or calculator! Practice makes perfect here, so try out some practice problems before diving head first into the exam itself.

The geometric mean of two numbers is the nth root of the product of these numbers, where n is called the common multiple. For example:

Let us consider a few examples to understand this concept better.

In the case of A and B, we have to find their geometric mean: A = 7 and B = 12.

Hence, Their Geometric Mean would be √(7 × 12) ≈ 20.

Hence, Their Geometric Mean would be √(10 × eight × 6) ≈ 30.

In case of A , B and C , we have to find out their Geometric Mean : A = 10 ; B = 8 ; C = 6 .

## 3. Harmonic Mean

The harmonic mean is the average of the reciprocals of numbers. The harmonic mean is also known as root mean square (RMS) and quadratic mean. It is calculated by finding the arithmetic average of two quantities and then taking a reciprocal.

Harmonic Mean = Arithmetic Mean/Reciprocal

For example, if you want to find a harmonic mean between 1 and 6, you first have to find their arithmetic average of 3.5 (add them together, get 7). Then take the reciprocal of 3.5, which will be 1/3.5= 0.2364103569

You can also use other methods like formulas or using a calculator, but using this method will help you understand how it works in real-life situations so that when any question comes in future exams, you won't have any problem answering them

## 4. Profit and loss

Profit and loss are the difference between the sales revenue and cost. To calculate profit and loss, you first need to know what profit is and how you can figure it out.

Profit = Sales - Cost

In this formula, sales mean selling price, which is the purchase or production cost. If your company has sold an item for $50 and bought it for $40, then your profit will be $10; if your company has sold an item at $42 but bought it at $28, then your overall loss would be ($8).

Your Profit & Loss Formula: Profit = Sales - Cost

To calculate the selling price from cost and profit, use the formula: Profit = Selling Price - Cost (SP – C), which is rearranged to SP = C + Profit. To calculate cost from selling price and profit, use the formula: Profit = Selling Price - Cost (SP – C), which is rearranged to C = SP – Profit.

Let's take an example to understand calculating P&L in percentage better. Suppose you have bought an item

## 5. Percentage

Whenever we see any number with a percentage sign (%), the first number is multiplied by 100 and then divided by the second. In other words, it represents a part of the whole component or total. For example, if you want to calculate 20% of 50, you need to divide 50 by 100 and multiply it by 20. The answer would be ten because 10 is 20% of 50.

In maths for competitive exams in India, there are many questions on percentage calculation that can be solved in multiple ways, including direct, indirect, and shortcut methods such as PCT. Let’s learn all these methods one by one:

## 6. Time and Work

Time and work problems are the most common math questions on competitive exams. These questions require you to solve for time, distance, or speed using given formulas. This section will discuss solving these problems using the procedure and its real-life applications.

How to Solve Time and Work Problems?

The first step is to identify which variable is being asked: time or work. The second step is knowing what formula should be used (or if there is a formula). If there's no formula given as an option, then you'll need to figure out what unit system they're using (minutes/hours or seconds/meters) to use those units throughout your calculations. Finally, once all that has been done correctly and there are no other variables left over from previous steps - it's time to solve! Start by determining how much work was done by dividing both sides by t(time) or w(career). This will give us our answer as an equation with one variable left over; this means we can plug in any number for t(time) into each side of our equation until it becomes true again after substitutions have been made into each side of our equation until both sides match up with each other perfectly again

## 7. Numbers

Numerical series: A collection of numbers in which the difference between two consecutive terms is constant.

Numerical sequences: A set of numbers arranged in a definite order, where no two consecutive terms are alike, and the first and last terms are equal.

Sum of numerical series: The sum is obtained by adding all the members in a given finite number sequence or infinite number sequence like 1+2+3+4+5=15 or 1/2 + 1/4 + 1/8 + etc. =1

## 8. Ratio and Proportion

This section will deal with the concept of ratio, proportion, quotient, and calculation of both direct and inverse proportions. The idea is quite simple: you need to convert a word problem into a mathematical equation that you can then solve. Here are some examples:

A cleaner earns $800 per month. If she works for three months at half her usual rate, how much will she make then?

Using your calculator, divide 800 by 2 (since she is working at half her usual rate) to get 400. Then multiply 400 by 3 (she has performed three months) to get 1200 which is her new total income for those three months. In other words, if someone works at half their regular pay rate, they would make 25% less than they usually do!

## 9. Simple and Compound Interest

Simple and compound interest are two types of money earned on an investment. The amount of interest earned will depend on the time since the initial investment. Simple interest means that the amount is calculated only once at the end of a specific period. However, compound interest allows you to earn more money over time by calculating it periodically during this same period.

The formula for simple interest is I = Prt, where I stands for interest, P stands for the principal (initial investment), r stands for rate or rate of return (expressed as a decimal) per annum, and t represents time (in years). The formula for compound interest is: C = Pe^{rt} Where C denotes cumulative cash flow over r periods at an annual rate of i

## 10. Probability

Probability is the likelihood of an event. It can be defined as a number between 0 and 1, where 0 means that the event will certainly not happen and one means it will happen. Probability is a measure of how likely something is to occur. In other words, given certain events, what are the chances of them happening?

If you were asked what probability it would take for you to win a lottery (where there are millions of tickets sold), your answer would be pretty different from another person's if their answer was based on their experience with playing lotteries and buying tickets in general. They could tell you there's no way they'd ever win even if they bought 100 tickets every week because their chances are slim. But if both answers were based on previous experience with lotteries (or similar games), then both solutions would probably be close!

These are the topics most frequently asked in competitive exams for math sections.

These topics are straightforward to understand and remember. Also, they can be easily solved by applying the basic concepts of algebra or geometry. Some of these topics are also useful in daily life as well as competitive exams like banking exams, any entrance exams, etc., but make sure that you practice regularly to master this skill quickly so that you don’t miss out on any question asked in an exam.

## Conclusion

Maths is a significant subject in competitive exams in India, and it is also the main reason we have to do a lot of practice to prepare for competitive exams. But it’s not just about exercise; we should also know about the topics and formulas frequently asked in exams to easily score good marks by practicing them. This blog post lists ten easy topics that every aspirant should be prepared with. These topics will help you score good marks in the Maths section on your exam day without any difficulty.