Important Uses of Binomial Theorem

A mathematical expression with two terms is known as “Binomial”. When the binomials are multiplied by itself, the calculations get longer and longer, and a pattern gets developed. The pattern is summed up by using the “Binomial Theorem”. This theorem describes the algebraic expressions of the powers of a binomial. It expands the binomial expressions. Hence, this theorem is also known as binomial expansion. It uses Pascal’s triangle to determine the coefficients. This theorem is applied to the powers of any binomial.

The binomial theorem has enormous applications and uses in the real world. Some of the uses are:

IP Address Distribution

In computing areas, the binomial theorem is used for the distribution of IP address. With the help of this theorem, the distribution of the virtual IP address is also possible apart from the automatic distribution of the IP address. The theorem is used when the IP address of the fixed host and the number of hosts are more than the total round off.

Economic Prediction

This theorem plays an important role in predicting the nation’s economy. To predict the behaviour of the economy in the future years, it helps us to count the probabilities which depend on numerous distributed variables. Realistic economic forecastings are feasible only with the help of binomial theorem.


In the field of architecture, this theorem is widely used to design the infrastructure. To deliver the accurate estimates like cost, the time required to complete the project and to find the other magnitudes of the project, the binomial distribution is used. It helps to ensure the project cost to deliver them with enough profit. To obtain the exponential growth in the architecture which is an inverse function of the logarithm, the expansion of binomial is really helpful.

Weather Forecasting

In weather forecasting and disaster forecasting, the binomial theorem is widely used. It is impossible to do the weather forecasting without the binomial distribution.

Candidates Ranking system

To rank the candidates in many competitive examinations, the binomial distribution is widely used. The probability will be difficult without binomial distribution. Since this theorem is used in higher calculations and mathematics, it helps to solve many scientific works with a higher degree of equations.

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Tips To Get Better At Mathematics

Mathematics is not an inherently difficult subject. It just depends on how that subject is perceived. But for many students, they actually do find it difficult as they end up failing in the subject. Even worse, students may start hating mathematics and this might make their learning experience more difficult. But learning maths doesn’t always have to be difficult. With some unique tips and techniques, we can turn around the experience into a pleasant one.

Catch Up With The Basics

The first thing that students need to do is to brush up on their basics. Often, weak fundamentals will result in students losing their confidence in mathematics. They take more time to solve problems and are prone to making mistakes. Having a strong foundation is not only beneficial for academics, but also everyday life. Intellectual acuity and mathematical prowess improve considerably. Another added advantage is, the basics will help the student prepare for future competitive exams like JEE. For this, students can start with Class 11 maths ncert solutions and gradually move on to class 12 before jumping into more advanced topics.

Practice Faithfully

Mathematics is like a sport, or a musical instrument – to get good at it, you need to practice. So, the more you invest time to understand a concept, the more easily you can solve problems. So, ensure that you devote enough time to practice mathematics. And furthermore, practicing can help you increase the speed at which you can solve problems, and reduce the likelihood of going wrong. With enough practice, various concepts in mathematics will come naturally – like how a person can learn to ride a bike.

Right Resources

We have various choices when it comes to education. From YouTube videos to self-help blogs, students have a range of options to learn mathematics. And each medium is tailored to meet specific needs and requirements. For instance, some mathematical concepts are better explained through an illustrative video, which helps students visualize concepts. While other concepts are better explained through a content on a blog. To practice, students may opt for class 10, 11 or even Class 12 maths ncert solutions. In conclusion, the best resources are the ones that offer the best learning experience.

To explore the various mathematical concepts in detail, visit MY NCERT SOLUTIONS.

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Best Reference Books for CBSE Board Exams

Exams are the turning point of every student’s career as it plays an important role in shaping the student’s future. Scoring the best marks is the greatest aspiration of every student and therefore, it needs true dedication and hard work.

As we all know, the CBSE 10th and 12th board examinations are one of the toughest exams and so, choosing the correct books for preparation is a major matter of concern. Before starting with the preparations, it is important to know which books have the most relevant information and are best for the board exams. From an exam point of view, NCERT books and solutions, RS Aggarwal solutions and RD Sharma solutions are a few best study materials to start with the preparations.

Class 10 and 12 are considered as the stepping stone both for the competitive exams and other higher studies. Since all the basic concepts are taught in these grades, every student should be regular in their classes and stay focused towards their studies. During their exam preparation time, most of the students will be in a dilemma or confused to select which books are best among the vast study materials. To help students with their preparations, here is a list of the few reference books which can be quite helpful for the students in their exam preparations.

NCERT textbooks

It is well known that NCERT textbooks are the best and abundant for CBSE exam preparation. Therefore, prepare your own notes by collecting all the important points from the respective NCERT textbooks. Students can also refer to NCERT Solutions and NCERT exemplar, as there are more possibilities that questions are directly selected from these NCERT Books.

Other reference books

Students can also refer to these following books for Biology, Chemistry, Physics and Maths subject and practice more examples, questions, diagrams, sample questions, important questions and other objective types of questions. These books include:

  • Chand’s Biology for Class XII.
  • Concepts of Physics by HC Verma.
  • 15 Sample Question Papers by Arihant.

Along with these books, students should also refer to their class notes and solve more questions from their textbooks. Those students who find difficulties in finding solutions or understanding the concepts can refer to the solutions which are available in both NCERT and RD Sharma solutions for class 10 and for class 12. In these solutions, students can understand the topic easily as all the answers are explained by the subject experts in a best and lucid manner to help students with their preparations.

These were some important and the best reference study materials for the students preparing for their CBSE exams. For more information regarding the tips, tricks, guidance and other study materials for the CBSE board exams, students can visit our website at BYJU’s and also learn by watching interactive video lessons on various topics by subscribing to the BYJU’S YouTube Channel.

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Skills That An Online Education Will Develop In You

Be it online or offline, getting an education is the best for us to learn more about our world and the facts that govern it. Since the advent of smartphone technology and massive reforms that came along with it, a large range of opportunities has opened up for the people. Giving people unprecedented flexibility with several other advantages.

Let us thus look at some of the various skills which can be developed in you with the help of an online education.

  • Digital literacy- In our current day and age, technology is advancing at a dynamic rate. With newer and better adaptations coming out every day, having the competence to work with them is a mandatory skill. In our current scenario, teachers use WhatsApp, Skype, and even Twitter as discussion platforms. Studying about the nomenclature of organic compounds isn’t just enough, digital literacy also matters.
  • Communication- Having good communication skills is mandatory for any application. An online learning platform creates a scenario wherein students need to communicate, share information and have discussions.. This brings students from all sectors of our planet speaking different languages with the same goal of learning.
  • Problem-solving and Decision Making- Decision making and problem-solving skills are developed with proper practice and experience. An online education offers students with multiple ways by which students can work on their skills like games and quiz sections. Online education offers a much more efficient approach to acquiring skills.

Thus, we have discussed some of the many skills which can be developed with the help of an online education. For more information and to get a chance to learn how an online education offers better content to learn topics like chemical equilibrium and more, check out our YouTube channel –

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Perks Of Having A Beverly Hills Virtual Office

Founding a startup in Southern California sounds glamorous. Forgoing entry-level jobs and cutting straight to making money and impressing people is this generation’s American dream.  Unless you are a trust fund baby, though, renting an office in Beverly Hills is beyond your budget, even if your business is doing well.  When you are trying to get your business started, you probably do most of your work from a public library or a coffee shop with free Wi-Fi.  Your clients don’t have to know that.  You can rent LA virtual office space, complete with a Beverly Hills live answering service.

Make an Executive Impression at Gig Economy Prices

When you rent virtual office space in Beverly Hills, you get an address and phone number that belong to an actual office there.  The receptionists at the office will receive your business mail and take phone calls for your company.  Of course, they also do this for all of the other virtual office clients.  Therefore, renting a virtual office costs a lot less than you would pay if you hired a receptionist full time.  Needless to say, you are also saving money by not renting an office out of which you physically operate your business every day.

What About Meeting Clients?

The public library is a great place to write work emails, but you would not want to meet clients there.  Virtual offices also have conference rooms that their clients can rent.  These conference rooms are as elegant as hotel conference rooms.  You can rent them only for the day or parts of days when you need them.  Therefore, you can eliminate a lot of overhead costs.

With a virtual office from Global Business Centers, you can cut the costs associated with running an office, while still looking professional and successful.

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Are Point of Sale Systems Necessary For Your Business?

Are the point of sale (POS) systems necessary for your business? In the short answer; yes. There are no successful businesses out there that do not have some sort of POS system. A cash register is a POS. Granted it is a very antiquated system, but one nonetheless. So the question really is if you need an upgraded POS system, and if you do which one should you choose. The Clover point of sale terminal is considered one of the best in the business, and that is because they incorporate all of what you need and everything that you want.

The Best Systems

The best POS solutions will offer your customers multiple ways to pay for your products or services. The reason the newer POS systems are elevating so many businesses is that they are removing the limitations of what people can do and how they spend their money. The customer wants to feel empowered and when they are not limited, they are more inclined to spend their money in that space. It is widely used in medical billing industries as well. See this best medical billing company new york for more details.

Another attribute of the best solutions is the merchant services. You should be able to have real-time access to your business information. You should know what your profit is for the day, how much inventory is available, and how much you may have lost without mauling over receipts and reports.

…On the Contrary

If you determine that you are not ready, or do not need a POS system that streamlines your business and makes it easier for your customers to do business with you, then there may be a question of how long you are going to have that business, or how successful it may ultimately be. That is not because you do not have something amazing to offer your customers, but you will not have the technology to satisfy your customer’s needs.

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Central Teacher Eligibility Test is what you have to face, if you are aspiring to become a teacher. CTET sets the benchmark of teacher’s quality in selection process and inducing teacher’s education.

It is of immense importance that our coming generation is provided with quality education and that is completely in the hands of teachers. So, it becomes a very important task for us to choose those teachers very carefully. Keeping this thought in mind, CTET is organized by CBSE, for the recruitment of teachers to the Central and State Government schools for classes I to VIII.

CTET Exam is conducted in two stages i.e. Paper I for Primary Stage (Classes I-V) and Paper II for Elementary Stage (Classes VI-VII). Percentage of candidate qualifying the exam is very low. Last year, only 60,000 candidates qualified the exam, out of 5 lac candidates who appeared for the exam.

The result for CTET Exam is valid for seven years, from the date of its declaration. CBSE CTET Merit list is prepared after the announcement of CTET result on the basis of marks secured in the exam. If you manage to qualify the test, you are provided with a CTET Certificate.


You have to make sure that you fulfill certain eligibility conditions, which are set by CBSE, before appearing in CTET Exam. The eligibility conditions for Primary Stage and Secondary Stage are listed here. The candidates belonging to reserved categories (SC/ST/OBC/PwD) are allowed a relaxation up to 5% in the qualifying marks in the academic eligibility for the exam.

For Primary Stage

The candidates applying for recruitment of classes’ I-V are required to have at least one of the following eligibility:

  • Cleared senior secondary with minimum 50% marks and completed/appearing in the final year of a 2 year diploma, in elementary education
  • Secured at least 45% marks in senior secondary and completed/appearing in final year of a 2 year diploma in Elementary education, by following the norms of NCTE (National Council for Teacher Education)
  • Cleared senior secondary with minimum 50% marks and passed or appearing in final year of a 4 year Bachelor of Elementary Education (B.El.Ed)
  • Secured at least 50% marks in senior secondary and completed or appearing in final year of 2 year diploma in Education (Special Education).
  • Graduation and completed/appearing for the final year of 2 year Diploma in Elementary Education

 For Elementary Stage

The candidates applying for classes VI-VIII, needs to satisfy any one of the following CTET Eligibility criteria:

  • You must have a degree of 2 year diploma in elementary education. If you are still in the final year of your graduation, then also you can apply
  • Graduation with minimum 50% marks and Bachelor of Education program (B.Ed.)
  • Graduation with at least 45% marks and must have cleared or appearing in 1 year B.Ed. program, following the NCTE Regulations
  • Passed senior secondary with at least 50% marks and must have passed/appearing in final year of 4 year degree program in Bachelor in Elementary Education (B.El.Ed)
  • Obtained at least 50% marks in senior secondary and must have passed/appearing in final year of the 4 year B.A/ B.Sc.Ed. Or B.A.Ed./B.Sc.Ed.
  • Graduation with at least 50% marks and must have passed/appearing in B.Ed. (Special Education)

Exam Pattern

Getting over with Eligibility, next thing you have to focus on is the exam pattern. CTET Exam consists of 150 objective type questions for both paper I and paper II. Remember that this exam is conducted in offline mode.

For Primary teachers, you have to attempt Paper I and for Elementary Teachers, you have to go for Paper II. In case, you wish to apply for both stages than you need to attempt both the CTET papers. To understand it more clearly, CTET Exam Pattern for both the papers is tabulated here:

CTET Exam Pattern
Features Paper I Paper II


Written Test Written Test


English and Hindi English and Hindi


2 and a half hours 2 and a half hours
Marking scheme +1 for Correct answer +1 for Correct answer
Negative Marking No No
Sections Child Development and Pedagogy (30 questions) Child Development and Pedagogy (30 questions)
Language I (30 questions) Language I (30 questions)
Language II (30 questions) Language II (30 questions)
Mathematics (30 questions) Mathematics and Science (60 questions)
Environmental Studies (30 questions) Social Studies/Social Science (60 questions)
Type of Questions Multiple Choice Questions (MCQ) Multiple Choice Questions (MCQ)
Total number of Questions 150 150
Total Marks


150 150


Once you are done with all these things and appeared in CTET Exam, all you wait for is CTET Results. Make sure that you score at least 60% in CTET exam or you won’t get the CTET Award Certificate. You have check the results online, don’t wait for any offline announcement to be made regarding your results.

Keep yourself updated by checking the official webpage of CTET from time to time. It is not difficult at all to check your result online, you just have to enter your Roll No. to get hold of it. The result window looks similar to this:


So keep your Roll No. safe, so that when the time comes, you can check your result without facing any problem.

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Reasonable Online Shopping on Limeroad

While there are online shopping malls, there are also online stores dedicated to a particular category of shopping. One of the most popular among them is online apparel and accessories stores. Online stores like Myntra, Craftsvilla, Jabong, Limeroad, and Voonik are ruling the online fashion shopping stores. These online portals provide the customers with a wide range of fashion products and accessories.


Let us see how Online Shopping is beneficial.

  1. Coupons, Offers and shopping festivals

Every now and then you must have seen television advertisements stating things like, ‘Flipkart Big Billion Days’ or ‘Amazon’s Grand so and so sale’ etc. These are like shopping festivals where prices of commodities are reduced and people can buy products at discounted rates.

Similarly, many online shopping portals have coupons and discount offers which the customer can use to buy products at lower prices. There can apparel discount offers like Myntra discount offers, Limeroad Coupons, Jabong Cashback or can be Flipkart discount, Amazon coupons etc.

These coupons and Cashback are usually available on Online Recharge Web portals or websites that only deal with coupons. These coupons, Cashback and Discounts make shopping even more interesting and joyful.

  1. Reasonable Prices for all

The reasonability of price for one commodity differs from person to person. But online shopping stores have something for everyone at the price which the customer finds reasonable. While searching for product online, the customer can filter their search according to prices from lower to higher or higher to lower. When done so, the categories which fit into that price window will be displayed and the customer can choose from those products. Also, applying Limeroad Couponsgives you great discounts!

Hence, your budget and your willingness to spend will help you decide on a product you want to buy.

  1. No salesman breathing down your neck

This is the biggest advantage of shopping online. Often the shopping experience is ruined when either the shopkeeper is not interested in selling the products the way you want or they keep giving you suggestions on what to shop. We are sure you would often think this when the salesman is giving you advise that you don’t want, ‘seriously, nobody asked for your opinion whether this looks good on us or not!’

On the online shops there are no salesmen. If you have a query regarding the product you can connect yourself to one on the live chat or ask the customer care. Often there are reviews about the product by both experts and people who have been using or have used that product. All of these let you shop peacefully!

  1. Shop anytime, anywhere

Honestly, if you have access to internet or have the online application of the online stores, you can shop at anytime of the day and anywhere. Even at the oddest hour at the oddest place, you can browse through the products and quickly buy yourself a new product. This is because the online stores are never closed and are open 24×7.

No more worrying about a shop getting closed by a particular time or being closed on national and other holidays. Just open the internet and shop away!

  1. Sadly, no bargaining

So the biggest disadvantage and a bad news for many is that, online shopping does not let you bargain on commodities. That can happen only if you shop for products in a real market!

To conclude, with the internet ruling our world, shopping for electronics, apparel, accessories, electronics etc has become easy and efficient. There are all types price window available for all commodities and the price which a customer finds reasonable they can buy that without any interference from the salesman. You can shop sitting or travelling anywhere and at any time. So keep calm and shop on!

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