The critical value is a useful term that has a unique place in the study of statistics. It is very important in decision making and hypothesis testing as well as confidence intervals which are a few of the analytical and logical areas. The concept of the critical value is very useful for handling data values in data analysis.

In this article, we will elaborate on the important term critical value. We will address its definition and some useful distributions. We will also give some examples to understand this concept easily.

Critical Value

In statistical hypothesis testing, the critical value is a threshold / boundary that assists in determining whether to accept or reject the null hypothesis. In a statistical test, the value distinguishes between the zone of acceptance and the region of rejection.

The desired significance level (α), which denotes the likelihood of making a Type I mistake (wrongly rejecting a valid null hypothesis), is what determines it. The significance level commonly indicated as (alpha), which represents the likelihood of committing a Type I mistake (erroneously rejecting a valid null hypothesis), is used to calculate critical values.

The different distributions that help in categorising critical values depend on the statistical distribution and the desired significance level (α). A hypothesis test is performed by comparing a test statistic against a critical value. If the test statistic is higher than the critical threshold then the null hypothesis will be rejected.

The critical value is a particular value that comes from a test of the sample distribution such as the t-distribution or the normal distribution and it is used to observe whether it is to accept or reject the null hypothesis (H0).

Types of Critical Values

Z-Distribution (Normal Distribution):

For a standard normal distribution, you can find critical values using the z-table or a calculator. The critical value is denoted as zα/2, where α/2 is half of the significance level. For example, if α = 0.05 (a common choice), then the critical value would be z0.025.

T-Distribution:

When working with small sample sizes or when the population standard deviation is unknown, the t-distribution is used. The significance level and degrees of freedom (df) are used to calculate the critical value. Utilising statistical tables or software, you could find the t-critical values.

Chi-Square Distribution:

The number of degrees of freedom and the level of significance are what decide the chi-square test's extremely important value. The formula is written as χ²α which stands for the significance level.

F Distribution:

Critical values are figured out using the F distribution and these are dependent on the degrees of freedom for the numerator and denominator as well as the significance level for analysis of variance (ANOVA) and other F tests.

Importance of Critical Values:

Critical values serve as decision points in hypothesis testing. When conducting a hypothesis test, you compare the test statistic (calculated from your sample data) to the critical value.

The critical value helps determine whether to reject the null hypothesis or fail to reject it. If the test statistic falls in the rejection region (beyond the critical value), you reject the null hypothesis; otherwise, you do not reject it.

·       Statistical Significance: Critical values assist in understanding and demonstrating the statistical significance. They provide a clear concept for examining whether the observed data is unlikely to occur by chance alone.

·       Objective Decision Making: Critical values offer a purpose for the base of making useful decisions in hypothesis testing. They help prevent subjective judgments and biases.

·       Standardization: Critical values provide a precise approach to hypothesis testing and make it possible for researchers and statisticians globally to use the same principles and criteria.

·       Quality Control: The critical values are used to make forbearance and ensure the principles for products meet the required values.

·       Scientific Research: Critical values play an important role in research and enable researchers to draw conclusions and make decisions based on data values.

Calculations

Example 1:

Suppose that a 1 tailed T test is performed on data having:

Sample size = 15

α = 0.025 and find the critical value.

Solution:

Step 1: Given data

n = 15

α = 0.025

Degree of freedom (df) = n - 1

df = 15 - 1

df = 14    

Step 2: Using the T distribution table:

So,

T (0.025, 140) = 2.145 Ans.

Hence:

The critical value for the given 1 tailed T distribution is 2.145

Example 2:

Determine what will be the critical value for a 2 tailed F test carried out on the following samples at a significance level (α) of 95 percent.

Variance = 120 and sample size = 25

Variance = 80 and sample size = 17

Solution:

Step 1: Given data

n1 = 25 and n2 = 17

α = 0.05 (95 percent confidence level)

Step 2:

df1 = n1 – 1 

df1 = 25 – 1

df1 = 24

df2 = n2 – 2

df2 = 17 – 1

df2 = 16

Step 3: We will look at the f distribution table for α = 0.05.

The value at the intersection of the 24^th column and the 16^th row.

So,

F (24, 16) = 2.24

Hence

Critical value = 2.24

The problems of finding critical values can also be solved with the help of using online calculators to get results according to the distribution tables in a matter of second. Below we’ve listed a few calculators for finding critical values that we personally used and found them worthy.

• https://www.criticalvaluecalculator.com/

• https://www.standarddeviationcalculator.io/critical-value-calculator

• https://www.gigacalculator.com/calculators/critical-value-calculator.php

Wrap Up:

We can conclude the whole article as the critical values are necessary to understand the data analysis and offer a useful way for finding hypotheses and making usable decisions. In this article, we have addressed an important term of critical value.

We have elaborated on its definition and explained it with different distributions. We also explained its importance and some examples.

 

Plagiarism is an illegal act that can badly affect the credibility of a student’s work. In this case, if plagiarised text/content is found in a student’s work, it is necessary to remove that. But some students may not know what the correct and ethical methods are to do so.

We have covered this post, to explain the correct and ethical methods for removing plagiarism from student’s work. Let’s delve into it.

4 Correct and Ethical Methods for Removing Plagiarism from Student’s Work

1. Make use of Quoting

During the collection/writing their assignments, there may be some cases when students must make use of others’ work like sayings, pieces of advice, etc. The reason behind this is to maintain the quality of that borrowed text.

In this scenario, their work can get plagiarized. But, if students give credit or authority to that source/author, they can easily remove that plagiarism.

To do this student can apply one of the correct and ethical methods i.e., making use of quotes. There are some important points that you should keep in mind for quoting correctly and ethically.

• For quotes, you should use quotation marks at the start and end of the copied/borrowed text. Let’s take an example,

Albert Einstein said:“Life is like riding a bicycle in which you have to keep running to keep your balance.”

• You should use the exact words of the author to maintain the quality. On the contrary, if you rephrase it in your own words there are chances that it would lose that quality.
• A student can also use “Block Quote”. They are mainly used to directly quote when the text exceeds four lines in the case of prose. However, when using Block Quote there is no need to use quotation marks.
• We would not suggest you make excessive use of quotes. You should only be dependent on your own thoughts and words. So, you should minimize the usage of others’ sayings or quotes in your work.

And so on…

2. Cite the Source

Another correct and ethical way of removing plagiarism is to cite a source. Let us explain what it is. Citing is done to give credit to the original sources of information, from which a student gets words/text. It is a standard method that students can use to acknowledge what resources are used in their work.

If there is found any plagiarism in the student’s work, it can be removed by citing the source with which that piece of text matches. To correctly cite the source students should add the following things.

• For Books: author of the book, title, volume, publisher, and year of publication.
• For Articles: Author, the title of the article, issuance date, permalink of the article.
• For Web Page Resources: Author of the page, title, URL (web address).

3. Paraphrase Text

Paraphrasing is the process of rephrasing/changing the text into a fresh one without altering its meaning/intent. It is the most widely used method by students as well as writers to remove plagiarism from their work.

In the following, we covered important tips that students should consider for paraphrasing, to remove plagiarism.

• You should read the original text (that you want to paraphrase) to understand it better.
• You can paraphrase the text by using the methods like replacing the original words with their synonyms, altering sentence structures, and breaking/merging the sentences.
• After paraphrasing you should revise the fresh text to make sure that its meaning is the same as of the original text. Moreover, you should check for all the synonyms are used correctly according to the context.

4. Use Online Tools

As we know that students must write several assignments during their writing career. In this scenario, removing plagiarism manually can sometimes be a time taking task and a headache for students. This is where online plagiarism remover tools can help students.

Using online plagiarism remover tools can be a valuable suggestion to remove plagiarism from the content whether it is.

• An article
• Research paper
• An essay

Online plagiarism remover tools are based on artificial intelligence. They work like humans but require minimum time and effort. Using online tools students can automatically remove plagiarism from their work. They just must import the plagiarised content/text pieces into the tool, adjust the required settings, and run the tool.

The online tools will automatically rewrite the plagiarised text pieces into fresh/new content that will be plagiarism-free and the same in meaning as the original text.

Conclusion

Plagiarism can badly affect the credibility of student work if it is found in the student’s work. It is necessary to remove it to avoid serious consequences. In this post, we explained the four correct and ethical ways for removing plagiarism from student’s work. You can always rely on these four methods to keep your credibility alive during your academic career.

If you are a student, who has been asked to convert mathematical notes into handwritten notes.  Doing this conversion by manual process (i.e. using pen and paper) can be a headache for you. This is because, sometimes it demands plenty of time and effort.

But, don’t worry we have come up with a solution i.e. using online text converters. They will transform the digital notes into handwritten ones automatically. They work like humans but involve minimum effort.

In this post, our focus will be on the easy steps to convert mathematical digital notes into handwritten notes. Let’s delve deeper into it.

Steps to Convert Mathematical Digital Notes into Handwritten Notes

Step 1. Select the Right Online Converter

The first step in the procedure is to seek the right online converter that can give you the most suitable output. As the internet is overwhelming with a number of converters.

In this scenario making the right decision for you can be a little bit difficult, That’s why, in the following sections we covered some necessary features that you should look for in a converter;

• Providing realistic output: The converter should provide a realistic page design on which the handwritten notes will appear. This feature is important to make your handwritten notes look like they are human-written. Moreover, no one will be able to recognize that the notes are created by online converters.
• Download Results: The online converter should provide multiple download options like PDF files, PNG image form, etc.
• Multiple Handwriting Styles: The online converter should provide you with multiple handwriting styles. So among them, you can choose the most suitable style (that matches your real handwriting style).
• Multiple Page Styles: The text-to-handwriting converter should have multiple page style options like Blank-with-Border”, “A4-Line-Page”, “Light-Blank”, “Dark Blank”, etc.
• Different ink colors: The converters should give different ink colors like Blue, Red, Black, Gel, etc. They are useful to distinguish headings from the normal text.

Additionally, you can check free versions of online converters. You can paste some parts of digital notes to check which one is providing more credible results.

To help you make the right decision, we have come up with a text-to-handwriting converter possessing most of the above-mentioned features i.e. “Editpad”. It’s a free converter to use.

Step 2. Adjust the Setting and Run the Tool

After selecting the right text to handwriting converter it’s time to convert your mathematical notes. But before going to this you should first, adjust the necessary settings. So, you should adjust the following things;

• Pen Ink color.
• Heading size.
• Page Style.
• Font style i.e.bold or Italic.
• Handwriting style that can mimic your actual style.

After that, you should paste/upload digital notes into the tool and run it. The tool will convert it into a handwritten within a matter of seconds. Let’s go practical with an example;

We inputted a sample mathematical text (that was borrowed from a site) into the tool and ran it.

Here’s a demonstration of it;

In the image, you can see what a  clear and accurate the text to handwriting converter gave output. In the same manner, you can convert digital mathematical text into handwriting notes by just putting in minimum effort.

Step 3. Get the Output Done

After creating the handwritten notes, you need to download them in a required form “PDF file” or “PNG”. to share the output with your teachers, friends, or any other person. Moreover, you can print it and get handwritten notes in physical form.

Let’s see these options in the following image;

Conclusion

Whenever you are required to convert mathematical digital notes into handwritten notes. Instead of spending a lot of time on manual writing ( i.e. using pen and paper), you should go for online text-to-handwriting converters to do this task. In the above sections, we step by step explained the whole procedure of conversion i.e. by picking the right converter, adjusting its setting, running the converter, and getting the output done.

FAQs

1. What is the best way to convert digital text into handwriting?

The best way, to do so is using online tools that are Text to handwriting converters. They automatically write text like a human but require minimum effort.

2. What is the working mechanism of text-to-handwriting converters?

Their working mechanism is very simple. To transform digital text into handwriting they use different fonts.

Before delving into antilogarithms, let us quickly recap logarithms. Logarithms are mathematical functions that measure the exponent to which a given base must be raised to obtain a specific number. The logarithm of 128 to the base 2 is 7since 2 raised to the power of 7equals128. They help simplify complex calculations involving large numbers.

In this article, we will discuss the definition of antilogarithm in-depth and its mathematical representation. We will learn how to determine the antilog of the given number by different methods. After this, we will solve some examples of antilog to understand it better.

What is Antilogarithm?

Antilogarithm is the reverse process of the logarithm. It refers to finding the original number given its logarithm value. The logarithms convert numbers into exponents, while antilog reverses the process by converting exponents back into numbers. In other words, the antilog “undoes” the effect of the logarithm.

The antilogarithm function is denoted as “antilog” or “10^x” for common logarithms (base 10) and “antilog _b ^x” for logarithms with different bases, where “x” represented the logarithmic value.

Some Important Properties of Antilog

Here are some important properties of antilog:

• The Antilog of zero is always equal to one.
• The Antilogarithm of a negative number is always a positive number. For example, the antilog of -3 with base 10 is 0.001.
• The antilog of a product of two numbers is the sum of the antilog of the two numbers.
• The antilog of a quotient of two numbers equals the difference of the antilog of two numbers.

How to determine antilog by using an antilog table?

To determine antilog by using an antilog table, follow these steps:

1. Write separate the characteristic (integral part) and mantissa (fractional part) of the given number.
2. Findthe first two digits of the mantissa after the decimal point in the left column and find the third digit of the mantissa in the top row of the antilog table. Write the value where the first two digits and a third digit intersect.
3. Find the fourth digit of mantissa in the top row of the mean difference, and write the value where the first two digits and fourth digits intersect.
4. Add the value obtained from step number 2 and step 3.
5. The number of decimal move-forward steps (from the left) is determined by adding 1 to the given characteristic.

You can also take assistance from an antilog calculator to find antilogarithm with steps.

Determining antilog without using an antilog table:

Determine the base of the given logarithm. If the base is not given, it is assumed to the base 10. The antilog is found by raising the base to the power of the given logarithmic value.

For example, if you have log₁₀², you would calculate the antilog as follows:

Antilog (2) = 10² = 100

If you have log₂³, you would evaluate the antilog as follows:

Antilog (3) = 2³ = 8

Similarly, if you have log₅^1.25, you would calculate the antilog as 5^1.25 = 7.4767

How antilog helps us in the calculation?

Log and antilog are used to simplify mathematical expressions involving multiplication, division, exponents, and roots.

• Assign any name (x, y, z, or any other) to the given number or expression.
• Take a logarithm on both sides of the equation.
• Use logarithmic properties.

Log(x*y) = log x + log y

Log (x / y) = log x – log y

Log x ⁿ = n log x

• Find the log of each number involved in the expression. Combine the log values obtained from the log table into a single number.
• Taking antilog on both sides of the equation. The analog will be the answer to the given number.

Solved examples of finding the antilog

Here are some examples of finding an Antilog by using an antilog table and without using an Antilog table.

Example 1:

Evaluate the antilog of 2.0125 with the help of the Antilog table.

Solution:

Step 1: Write separate the characteristics and mantissa part of the given value. Where,

Characteristic = 2

Mantissa = .0125

Step 2: Find the first two digits of mantissa (0.1) in the left column of the antilog table. Observe the third digit of the mantissa (2) in the top row of the antilog table.

Here, 5 and .01 intersect at 1.

Step 4: Add the obtained values from steps 2 and step 3 i.e. 1028 + 1 = 1029

Step 5: Decimal shift forward 3steps from the right side. (By adding 1 in a given characteristic i.e. 2+1 = 3).

Hence, the antilogarithm of 2.0125 is 102.9

Example 2:

Find the antilog 4 with base 2, without using the antilog table.

Solution:

Antilog₂⁴ =?

Antilog (4) = 2⁴ = 16

Thus, the antilogarithm of 4, with base 2 is 16. 

Conclusion

In this article, we have read the definition of antilog. We discussed some important properties of antilog. We learned how to calculate antilogarithms using an antilog table and without an antilog table. We debated on how antilog helps us to simplify complicated questions. Some solved examples of antilog covered in this article, would help find antilog.

In the realm of academic writing, the ability to articulate thoughts effectively and accurately is paramount. Academic integrity necessitates the avoidance of plagiarism, while a good writing style demands fluency and varied vocabulary. 

In recent years, paraphrasing tools have emerged as valuable aids in meeting these requirements. These tools enable the production of original content, aid in language improvement, and assist in vocabulary expansion.  This article provides an in-depth discussion of how to effectively use the paraphrase tool for academic writing.

How Paraphrasing Tools are Contributing to Academic Writing?

A. Avoiding Plagiarism
One of the primary roles of paraphrasing tools in academic writing is to help avoid plagiarism.  Paraphrasing tools help reword or rephrase existing text into a new, unique version, thereby ensuring the avoidance of plagiarism. They enable the writer to communicate the same idea using different words or sentence structures.

B. Improving Language Fluency and Style

Paraphrasing tools can significantly improve the fluency and style of academic writing. They employ advanced algorithms that understand and mimic human-like writing, thus producing content that is more readable and stylistically improved. 
By offering multiple ways to express the same idea, these tools facilitate the creation of well-structured sentences and coherent paragraphs.

C. Enhancing the Readability of Academic Texts

Complex ideas and concepts often require intricate language, which can affect the readability of academic texts. Paraphrasing tools simplify these complexities, making the text more accessible and easier to comprehend. 
They work by breaking down complicated sentence structures and replacing complex terms with simpler ones, all while preserving the original meaning.

D. Assisting with Vocabulary Expansion

Paraphrasing tools can also help in vocabulary expansion. Suggesting synonyms or alternative phrases for given words, helps writers explore and incorporate a wider range of vocabulary into their work. 
This not only helps to avoid repetitiveness but also enriches the overall quality of the academic writing.

Tips for Effectively Using Paraphrasing Tools

Here are some winning tips to follow:

A. Inserting Only Chunks of Text Instead of Entire Papers
For the best results, it is recommended to use paraphrasing tools for sections of text rather than entire papers. This approach ensures the tool can accurately interpret and rephrase the content without losing the essence or context of the broader narrative.
B. Verifying the Output for Accuracy
Always double-check the output provided by the paraphrasing tool. While these tools are sophisticated, they might not always capture every nuance. It is important to ensure that the rephrased text is accurate, coherent, and aligns with the intended meaning.

C. Adapting the Tool's Output to Match the Overall Tone of Your Paper

Paraphrasing tools may not always match the specific tone of your paper. After using the tool, adapt the rephrased content to ensure it aligns with the overall style, tone, and flow of your paper.

D. Integrating Cited Sources Effectively with the Paraphrased Content

When using paraphrasing tools, ensure that any cited sources are effectively integrated into the paraphrased content. This practice maintains the credibility of your work and prevents any accusations of plagiarism.

E. Ensuring the Paraphrased Content Aligns with the Original Meaning

Maintain the integrity of the original text by ensuring that the paraphrased content does not deviate from its original meaning. Although the words might change, the underlying message should remain intact.

How to Choose the Right Paraphrasing Tool?

1. Considering the Tool's Accuracy

When choosing a paraphrasing tool, the first factor to consider is its accuracy. The tool should accurately capture the essence of the original text while successfully creating a unique version. The sentences produced should be grammatically correct, and the meaning should not be distorted or lost.

2. Assessing the Tool's Capacity to Maintain Context

The ability of a paraphrasing tool to maintain the original context is another crucial consideration.  A good tool will consider the context of the entire text, not just individual sentences, ensuring that the rephrased text aligns with the overall theme and message of the original.

3. Evaluating the Tool's Language Sophistication

A suitable paraphrasing tool for academic writing should possess a sophisticated understanding of language nuances.

It should effectively handle different writing styles, tones, and jargon, depending on the subject matter. It should also be capable of managing various academic writing formats.

4. Checking the Tool's Review and Ratings

User reviews and ratings are an excellent way to assess the reliability and effectiveness of a paraphrasing tool. High ratings and positive reviews typically indicate a tool that is user-friendly and performs well. 

5. Considering the Tool's Cost-effectiveness

Finally, cost-effectiveness is a vital consideration when choosing a paraphrasing tool. While some tools are free, others may require a subscription fee.  Post-Paraphrasing Procedures

• Reviewing and Editing Paraphrased Content
• Proofreading for Grammatical Errors and Syntax Inconsistencies
• Checking for Plagiarism Using a Reliable Plagiarism Checker
• Reading the Paraphrased Content Aloud for a Natural Flow

The Ethical Aspect of Using Paraphrasing Tools

• Understanding Academic Integrity
• Recognizing the Fine Line Between Paraphrasing and Plagiarism
• Emphasizing the Importance of Original Work

Conclusion
Paraphrasing tools have indeed transformed the landscape of academic writing, offering invaluable assistance in maintaining academic integrity, improving language fluency, and expanding vocabulary. 
However, their effective use requires careful selection, thoughtful application, and vigilant review. While these tools offer multiple benefits, it's essential to remember the core purpose of academic writing: to develop and showcase your understanding and critical thinking.

If you are searching for the best solutions of ncert books and you have a lot of doubt in your mind regarding your board exams and also confuse to solve your questions with right answers. This post would be very helpful for you. This is our promise. 

Problems before you during board exams or state borad exams:

• How to prepare this upcoming exams? 
• Where to find best solutions which score highest marks? 
• What to do for doubts? 
• If you do not get satisfactory answers from your coach or teacher? What to do then. 
• Why not join a popular coaching Institute or academy? 
• Are you in trouble due to lengthy answers? 

We will provide all the answers of above questions which is rising in your mind regarding upcoming exams. We are working in education field last 22 years and also provides the best study materials throught ATP Education. Which is 12 years old brand and regularily working day and night for you. 

Datesheeet of CBSE Board Exams 2022-23

The candidates who are going to appear in term 2 cbse board examination 2022-23 for secondary class 10 and senior secondary class 12 the exams date sheet would be release soon. Approximate date of board exams is after February 15, 2023. CBSE has not declare any  such date sheet for term 2 board exams 2023. As per recent reports, CBSE secondary and senior secondary exams  datesheet might be released till November 20, 2022. 

for more information read this articles:

cbse board examination datesheet 2022-23

How to prepare this upcoming exams? 

Completely go through your last term syllabus before the preboard exmas. list your difficulties and doubts. Which chapter is weak for you then have to focus on them? What is your real problems regarding subjects? Do you cover all the concepts regarding chapter's important topics? Remark the most important topics from chapter on which cbse board or other state boards often ask questions? Mind here, If you select 5 topics which are important for your board exams question bank for class 10 and 12.  I as a auther promise you definetly one or two questions must be asked in your exams. This creteria is completely based on our research and experience of our teaching life. Some of the topics are always asked in exams, may be it came in your preboard or other test papers which is organised by your board. Then, there is less possibility to come this question again in next exams. Then you should focus on another topic on which questions can be asked. There is a large possibility for other remain topics or questions. 

Where to find best solutions which score highest marks?

This article is realy complete guide for a student who is going to appear in upcoming any exams what ever it is board or state board exams. The many of students have been taken benifits of our these ideas which is providing you on online plateform. The numbers of students can be thausands. Question is where to find best ncert solutions and ncert question bank which provides latest question and important questions with best and unlengthy solutions. So you can visit ask ncert questions website and other ncert questions banks website which is specially design for students need. You can find here most of the solutions of question bank class 12 cbse and also ncert question bank for class 10. At ask ncert questions website provide you a plateform where you can rise your questions home work  and doubts without any hezitation. First you search your query in search bar of the site. Your query should be a topic which is minimum 3 words. If you find your right question you can find your solutions here, but if that topic or question is not included you can ask your question to go through the given link Ask Your Questions After typing your question you can see your question in Not Answered Question Menu. The first question is your. Try this once. 

Definitely this work will help you much more in your exam preparation. One more thing keep your mind that practicing more and more on topics, don't try to remember as this is not stable for ever so thinks on that topic that you have to learn and just focus on various elements of the topic. What is question and what should be answer? Think on it. 

What to do for doubt? 

Doubts should be clear instantly so you can asked your doubt to your teacher and also analyse yourself according to keep the basic concepts in your mind. Whereever you USA, United Kingdom, Spain, UAE, Canada or India the problem is same. Don't be book worm, just think freely always be positive and and answer positively. One, thing When you are in examination hall you always keep in mind that you (examinee) are teacher and the examiner have no more knowledge on this topic, so you have to explain all basic information to him, in htis ways you have to answer your question's. 

If you do not get satisfactory answers from your coach or teacher? What to do then.

The Answer of this question has been already given to above lines. You must visits this website and can be asked online plateform which is provided by ATP Education no doubt. 

Why not join a popular coaching Institute or academy? 

If you have time then you can do this. But no one minds a special one. There are a group of students who learn their chapters and some of then can be recovered but It depends on you how to tacles this.

Are you in trouble due to lengthy answers? 

However, we face the lengthy answers which are so boaring, Then find the shortest and fine solutions from given site or you can also visit ATP Education NCERT Solutions page where you will see the chapter reviews solutions and the most important and extra questions which often asked in exams. Also you can go through the ask ncert website. 

Tips and final words: 

Identify the ncert exercise questions which are short and valuable in view of exams. This is the question which suites for cbse or boards exam's papers. Don't target a lengthy questions which possibilty is very less. 

In mathematics, the limit is a value that a function (or sequence) "approaches" as the input (or index) "approaches" some value. Limits are important in calculus and analysis in general.

Most of the limits that occur in practice have already been calculated and can be looked up in mathematical tables. In this blog post, we will go over the definition of a limit, the types of limits, how to calculate limits, and finally some examples of calculating limits.

The Definition of a Limit

The definition of a limit is a numerical value that a function approaches as the input gets closer and closer to some value. The limit of the functions is represented in a general expression to evaluate its numerical result. The general expression is:

• “w” is the independent variable of the function.
• “f(w)” is the function whose limit value is to be evaluated.
• “a” is the particular point that a function approaches.
• “L” is the numerical result of the function after applying the limit value.

Types of limits in calculus

There are three types of limits:

1. One-sided limit
2. Two-sided limit
3. Infinite limit

Let us discuss the types of limits in calculus briefly.

One-sided Limits

A one-sided limit is defined as the maximum value that a function can reach when the input is close to but not exactly at that point.

For example, if you have a function that takes an input and returns an output, then its one-sided limit would be infinity (i.e., it can never reach this maximum value).

Two-Sided Limits

A two-sided limit is defined as the minimum and maximum values that a function can reach when the input is close to but not exactly at that point.

For example, if you have a function that takes an input and returns an output, then its two-sided limit would be -1 (i.e., it could theoretically reach this minimum or maximum value). Similarly, if you have a function that takes a float input and returns a floating output, then its two-sided limit would be 0 (i.e., it could theoretically reach this minimum or maximum value).

Infinite Limits

An infinite limit is simply defined as any number beyond which there's no known way to calculate the corresponding limit using standard methods like algebraic manipulation or the Sandwich Theorem.

For example, consider pi – 3 degrees Celsius: there's no known finite amount above which pi will increase by 3 degrees Celsius; instead, it continues on forever towards infinity. So technically speaking, pi has an infinite limit (although we don't know what it actually equals!).

How to calculate limits in calculus?

To calculate a limit, you can use different methods depending on the type of limit you're dealing with. For one-sided limits, you can use substitution or factoring; for two-sided limits, you can use algebraic manipulation or graphing;

and for infinite Limits, you can use L’hopital’s rule.A L’hopital’s rule is a technique for calculating the numerical values of the indeterminate functions by taking the differential of the numerator and denominator and applying the value of the limit.

If the function again formsan indeterminate form, you have to take the second derivative of the function, and so on. 

Let us take a few examples of limit calculus solved with the help of the laws of limit calculus.

Example 1:

Evaluate the limit of the given function if the particular point “w” approaches 3.

f(w) = 6w + 12w⁴ – 2w³ + 12

Solution

Step 1:First of all, apply the notation of limit calculus to the given function along with the value of the specific point.

Lim_w→af(w) = Lim_w→3[6w + 12w⁴ – 2w³ + 12]

Step 2:Now use the sum and difference laws of limit calculus to apply the notation of limit with each term of the function separately and take out the constant coefficients.

Lim_w→3[6w + 12w⁴ – 2w³ + 12] = Lim_w→3[6w] + Lim_w→3[12w⁴] – Lim_w→3[2w³] + Lim_w→3[12]

Lim_w→3[6w + 12w⁴ – 2w³ + 12] = 6Lim_w→3[w] + 12Lim_w→3[w⁴] – 2Lim_w→3[w³] + Lim_w→3[12]

Step 3:Now put the value of the particular point in the place of the independent variable of the above expression.

Lim_w→3[6w + 12w⁴ – 2w³ + 12] = 6[3] + 12[3⁴] – 2[3³] +[12]

= 6[3] + 12[3 x 3 x 3 x 3] – 2[3 x 3 x 3] +[12]

= 6[3] + 12[81] – 2[27] +[12]

= 18 + 972 – 54 +12

= 990 – 54 +12

= 936 +12

= 948

A limit calculator with steps can be used to evaluate the limits to ease up the lengthy and time consuming calculations

Example 2:

Calculate the limit of the given function if the particular point “w” approaches 2.

h(t) = (2t³ – 2t² – 8) / (t² – 2²) 

Solution

Step 1:First of all, apply the notation of limit calculus to the given function along with the value of the specific point.

Lim_t→ah(t) = Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] 

Step 2:Now use the sum and difference laws of limit calculus to apply the notation of limit with each term of the function separately and take out the constant coefficients.

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (Lim_t→2[2t³] – Lim_t→2[2t²]– Lim_t→2[8]) / (Lim_t→2[t²] – Lim_t→2[2²]) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (2Lim_t→2[t³] – 2Lim_t→2[t²]– Lim_t→2[8]) / (Lim_t→2[t²] – Lim_t→2[2²]) 

Step 3:Now put the value of the particular point in the place of the independent variable of the above expression.

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (2[2³] – 2[2²]–[8]) / ([2²] –[2²]) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (2[8] – 2[4]–[8]) / ([4] –[4]) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (16 – 8–8) / (4 –4) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = 0/0

Step 4:Now use L’hopital’s rule of limit calculus as the given function makes an indeterminate form.

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = Lim_t→2[d/dt (2t³ – 2t² – 8) / d/dt (t² – 2²)] 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = Lim_t→2[(6t² – 4t– 0) / (2t – 0)] 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = Lim_t→2[(6t² – 4t) / (2t)] 

Step 5: Now again put the value of the particular point in the place of the independent variable of the above expression.

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (Lim_t→2[6t²] – Lim_t→2[4t]) / (Lim_t→2[2t]) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (6(2)² – 4(2)) / (2(2)) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (6(4) – 4(2)) / (2(2)) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (24 – 8) / (4) 

Lim_t→2[(2t³ – 2t² – 8) / (t² – 2²)] = (16) / (4) = 4 

Example 3:

Find the limit of the given function if the particular point “w” approaches 1.

f(u) = 2u² / 3u * 12u³ / 2u

Solution

Step 1:First of all, take the given function p(r) and apply the limit notation to it.

Lim_u→af(u) = Lim_u→1[2u² / 3u * 12u³ / 2u]

Step 2:Now apply the limit notation to each function separately with the help of product and quotient laws of limit calculus.

Lim_u→1[2u² / 3u * 12u³ / 2u] = Lim_u→1[2u²] / Lim_u→1[3u] * Lim_u→1[12u³] / Lim_u→1[2u]

Lim_u→1[2u² / 3u * 12u³ / 2u] = 2Lim_u→1[u²] / 3Lim_u→1[u] * 12Lim_u→1[u³] / 2Lim_u→1[u]

Step 3:Now substitute r = 1 to the above expression.

Lim_u→1[2u² / 3u * 12u³ / 2u] = 2[1²] / 3[1] * 12[1³] / 2[1]

= 2[1] / 3[1] * 12[1] / 2[1]

= 2 / 3 * 12 / 2

= 0.67 * 12 / 2

= 8 / 2

= 4

Wrap up

Now you can get all the basics of limits in calculus from this post. We have discussed all the basics of limits such as their definition, types, and calculation along with examples. Once you go through this post, you are able to solve any problem of limit.

दक्षिण भारत से वन्दे भारत ट्रेन की शुरुआत - PM मोदी ने दिखाई हरी झंडी

प्रधान मंत्री श्री नरेंद्र मोदी ने आज केएसआर रेलवे स्टेशन, बेंगलुरु में वंदे भारत एक्सप्रेस और भारत गौरव काशी दर्शन ट्रेन को हरी झंडी दिखाई। इन दोनों ट्रेनों के शुरुआत दक्षिण भारत की यात्रा करने वालों के लिए वरदान साबित होगा | बल्कि दक्षिण भारत से उत्तर भारत की यात्रा भी सुलभ और कम समय में होगी | 11 नवम्बर को ही PM मोदी ने ट्विट के माध्यम से देश को बताया | 

देश की पांचवी वन्दे भारत ट्रेन 

प्रधानमंत्री प्लेटफार्म नंबर एक पर झंडी दिखाने वाले क्षेत्र में पहुंचे। क्रांतिवीर संगोली रायन्ना (केएसआर) रेलवे स्टेशन के 7 और चेन्नई-मैसुरु वंदे भारत एक्सप्रेस को हरी झंडी दे दी है। यह देश की पांचवीं वंदे भारत एक्सप्रेस ट्रेन होगी और दक्षिण भारत में इस तरह की पहली ट्रेन होगी। यह चेन्नई के औद्योगिक केंद्र, बेंगलुरु के टेक और स्टार्टअप हब और प्रसिद्ध पर्यटन शहर मैसूर के बीच संपर्क को बढ़ाएगा। इसके बाद प्रधानमंत्री प्लेटफॉर्म नंबर 8 पर झंडी दिखाने वाले क्षेत्र में पहुंचे। प्रधानमंत्री के भारत गौरव काशी यात्रा ट्रेन को हरी झंडी देते ही कर्नाटक भारत गौरव योजना के तहत इस ट्रेन को चलाने वाला पहला राज्य बन गया है जिसमें कर्नाटक सरकार और रेल मंत्रालय मिलकर कर्नाटक से तीर्थयात्रियों को काशी भेजने के लिए काम कर रहे हैं। तीर्थयात्रियों को काशी, अयोध्या और प्रयागराज जाने के लिए आराम से यात्रा और मार्गदर्शन प्रदान किया जाएगा।

वंदे भारत एक्सप्रेस की विशेषताएँ - क्यों अलग है अन्य ट्रेनों से 

वंदे भारत एक्सप्रेस : यह ट्रेन (वंदे भारत एक्सप्रेस 2.0) कई बेहतरीन, आधुनिक सुविधाओं के साथ-साथ विमान में यात्रा करने जैसा अनुभव देगी। यह उन्नत अत्याधुनिक सुरक्षा सुविधाओं से लैस है जिसमें स्वदेशी रूप से विकसित ट्रेन टक्कर बचाव प्रणाली-कवच शामिल है। इसकी प्वंरमुख विशेषताएँ निम्नलिखित है - 

• वन्दे भारत 2.0 अधिक प्रगति और बेहतर सुविधाओं से लैस होगा जैसे कि 0 से 100 किलोमीटर प्रति घंटे की गति केवल 52 सेकंड में और अधिकतम गति 180 किलोमीटर प्रति घंटे तक पहुंचना है।
• इसका वजन भी कम किया गया है यह 430 टन के पिछले संस्करण की तुलना में बेहतर वंदे भारत एक्सप्रेस का वजन 392 टन होगा।
• इसमें वाई-फाई कंटेंट ऑन डिमांड की सुविधा भी होगी। प्रत्येक कोच पिछले संस्करण में 24 की तुलना में यात्री सूचना और सूचना प्रदान करने वाली 32” स्क्रीन से लैस है।
• वंदे भारत एक्सप्रेस भी पर्यावरण के अनुकूल होने जा रही है क्योंकि एसी 15 प्रतिशत अधिक ऊर्जा कुशल होंगे। ट्रैक्शन मोटर की धूल रहित स्वच्छ वायु शीतलन से यात्रा अधिक आरामदायक हो जाएगी।
• साइड रिक्लाइनर सीट की सुविधा जो पहले केवल एक्जीक्यूटिव क्लास के यात्रियों को प्रदान की जाती थी, अब सभी वर्गों के लिए उपलब्ध कराई जाएगी।
• कार्यकारी कोच में 180 डिग्री घूमने वाली सीटों की अतिरिक्त सुविधा है। वंदे भारत एक्सप्रेस के नए डिजाइन में, वायु शोधन के लिए रूफ-माउंटेड पैकेज यूनिट (आरएमपीयू) में एक फोटो-कैटेलिटिक पराबैंगनी वायु शोधन प्रणाली स्थापित की गई है।
• सेंट्रल साइंटिफिक इंस्ट्रूमेंट्स ऑर्गनाइजेशन (सीएसआईओ), चंडीगढ़ की सिफारिश के अनुसार, इस सिस्टम को आरएमपीयू के दोनों सिरों पर डिजाइन और स्थापित किया गया है ताकि ताजी हवा और वापसी हवा के माध्यम से आने वाले कीटाणुओं, बैक्टीरिया, वायरस आदि से मुक्त हवा को फिल्टर और साफ किया जा सके।

जन-सुविधाओं को बढ़ाने के साथ-साथ इस थीम का उद्देश्य भारत गौरव ट्रेनों के माध्यम से भारत और दुनिया के लोगों को भारत की समृद्ध सांस्कृतिक विरासत और शानदार ऐतिहासिक स्थानों का प्रदर्शन करना है। इस योजना का उद्देश्य भारत की विशाल पर्यटन क्षमता का दोहन करने के लिए थीम-आधारित ट्रेनें चलाने के लिए पर्यटन क्षेत्र के पेशेवरों की मुख्य ताकत का लाभ उठाना भी है, ताकि टूरिज्म को बढाया जा सके और उन सभी टूरिस्ट क्षेत्रों को दुनिया के सामने एक उभरती हुई स्थल के रूप में पेश किया जा सके | 

Getting a scholarship for advanced studies is the desire of every student. Most students want to complete their studies with minimum investment as well as explore the world with such opportunities. 

According to research, 1.7 million scholarships are awarded to students all over the world through different channels and universities. The number of scholarships is far less than the number of students or applicants. 

Then the question is how to achieve a scholarship in your concerned field. The most important thing in this regard is the scholarship application that will open doors for you. 

Some students take it as a formality and don’t pay focus while writing this application. As a result, they are unable to secure their spot on that scholarship. If you want to increase your chances of achieving a scholarship, you should write a good application. 

This blog will help you in learning how to write an impressive application for scholarships. 

How to Write a Good Scholarship Application?

When it comes to writing a good scholarship application, the most important thing is to be unique. Many students try to copy the writing style of their predecessors who have been selected for the same scholarship. 

It is because they think that it will help them in winning that scholarship. No doubt, it is an effective technique but it can also lead you to commit duplication. In simple words, the professors can put an allegation of cheating on you if they have found this. 

After reading the above, you probably won’t be inclined to copy someone else’s work. However, the thing with plagiarism is that it can occur even unintentionally. In other words, your content could match with an existing template or a scholarship essay stored within the institute’s database.

A free plagiarism checker can be a great solution for avoiding this issue. You simply use it to see if there is any duplication in your content or not.

We talk about using a free plagiarism checker in particular because it is not worth spending money on a premium one if you only have to check a scholarship essay using it. It’s a different thing for people who have to regularly use such software. For them, investing in a paid one is a viable option. 

Now that we’re done with this point, let’s move on to actually discuss some tips that you can keep in mind to write a good scholarship application.

5 Tips to Write a Scholarship Application

1.Plan Before Writing 

Do you know what the biggest mistake students made while writing a scholarship writing? It is writing without having a specific plan. Many students write this letter just before the deadline. 

In such a case, they may not be able to understand and follow the instructions while writing. If you want to keep yourself away from such conditions, you should make a plan before writing. 

You should have to make sure that you have understood all the instructions given by the university or scholarship authorities. Along with this, you should keep the deadline date in your mind and try to submit your application before it. 

By doing this, you will be able to find a penalty of time to write, revise, and edit your scholarship application. Moreover, you will not need to worry about the late submission of your essay to acquire the opportunity. 

2.Describe Yourself To-The-Point 

Many students, especially those who are applying for the first time, make a mistake like over-selling themselves. No doubt, it is important to describe yourself in this application. But, it is not a wise act to fill pages with your introduction and other details. 

You should describe yourself shortly and to the point. It is good to show yourself in a few lines or a few paragraphs. But you should also describe yourself enough to make the authorities comfortable while selecting you. 

To accomplish this task, we recommend you keep the following questions in your mind and discuss them briefly. 

• Who are you?
• What is your previous experience?
• Why are you applying for a scholarship?
• How are you different from other applicants?
• What have you achieved in the field till now?

These questions will help you in describing yourself properly in a maintained flow. Along with this, you should discuss them shortly in a few lines instead of taking a page for every question mentioned above. 

3.Don’t Add Fluff Text 

As mentioned above, you shouldn’t describe yourself on multiple pages. Similarly, you shouldn’t try to drag the simplest thing to multiple pages or paragraphs. It is common to use unnecessary words even when there is no need for such words. 

It is good to avoid fluff text in your application and try to keep it as simple as possible. The best thing is to use a single word when you can do so instead of using a long phrase for the same purpose. 

This activity will automatically reduce the detection of fluff text and allow the reader to understand quickly what you want to say in your letter. 

4.Keep Your Application Readable 

It is common to think that academic writing can’t be readable because of the involvement of complex words. No doubt, you should use subject-specific words in your scholarship application. 

But it doesn’t mean that you shouldn’t consider the readability of your text. You can use simple and easy-to-understand terms in other sections of your application. And even if you don’t do this in the first draft, you can always paraphrase difficult parts of your letter during the editing phase.

It will help the readers in reading your application with comfort and understand what you want to say. If you think it is hard for you to paraphrase manually, you can also rephrase online. 

If you opt to paraphrase online, you can easily replace the original terms and words with readable related words. Also, it can help you in avoiding duplication from your given text. 

Whether you have copied text from others accidentally or repeated your words, again and again, online paraphrasing will help you in removing such problems. 

1.Show Your Passion 

It is one of the most important tips that you should keep in your mind while writing a scholarship application. If we say that it is the part of your letter that decides whether you will get a spot or not, it will be right. 

The reason is authorities mostly look for pitching sentences to understand what your passion is. So, you should describe to them why you need a scholarship, what is your previous experience in the field, and how passionate you are to get awarded this scholarship. 

You have to write this section carefully. The best way is to write this part of your application in a unique way and by the involvement of engaging words. 

Summarizing Up

By reading the above guide, you must have got an idea about scholarship application. We recommend you follow the above-mentioned five tips when writing one. 

These tips can help you in raising your chances of being awarded any scholarship. Lastly, we suggest you ask someone to read your application to get a better idea of whether it is readable and engaging or needs improvements. 

कोरोना वायरस क्या है ? भारत में यह कितना प्रभावी हुआ?

कोरोना वायरस के लक्षण

कोरोना के लक्षण बुखार जैसे ही है इसके शुरुवाती लक्षणों में सूखी खासी, बुखार, मांसपेशियों में खिचाव आदि है इसके लक्षणों में आगे 8 वे दिन सास लेने में तकलीफ आदि है |

बचाव

1. हाथो को बार बार साफ़ करे |
2. आंख, मुह, कान को बबर न छुए |
3. अगर किसी को खासी बुखार हो तो उससे कम से कम 1 मीटर की दूरी बने रखे |
4. खासते समय मुह पर रुमाल रक्खे |

CBSE Board Exams Date sheet 2022-23 for Class 10 and 12 releasing date:

The candidates who are going to appear in term 2 cbse board examination 2022-23 for secondary class 10 and senior secondary class 12 the exams date sheet would be release soon. Approximate date of board exams is after February 15, 2023. CBSE has not declare any  such date sheet for term 2 board exams 2023. As per recent reports, CBSE secondary and senior secondary exams  datesheet might be released till November 20, 2022. Students can see the date sheet on cbse official website "cbse.gov.in". 

As soon as after announcing the exam date sheet cbse also would provide date sheet in PDF on it's official website downloadable format for class 10 and 12. There is no any tentative date sheet released by CBSE board. Board exams 2023 are expected to begin from February 20, 2023 for both classes for 10 and 12 and end till mid of April for Class 12. As previously we has seen the board exams pattern. 

The school affilated  by CBSE board would also be announce the date sheet if any released although students and paraent also can be check it from official website cbse.gov.in. Student must prepare for their exams by cbse exams patterns which can be seen by cbse sample papers 2022-23. These latest sample papers has also been released on it's wensite or you can download it from our website download section and also from cbse sample papers section. 

How to prepare for Board Exams? 

It is very important for the students appearing in the board exam that how is their exam preparation? What do they think to get good marks in the upcoming exam? And what is their plan for the exam? At such a time, they should not worry but think for the exam. First of all, they should have complete control over all their subjects before coming to their preboard and have to practice them again and again in the subject in which they are less proficient.

Many students face problem regarding hall ticket and admit card at the time of examination, they should check all their papers responsibly. If the students who prepare for Preboard completely, then they will have to face less problem at the time of board examination. The latest sample papers are very important for the preparation, as the latest sample papers helps in understanding the pattern that will be asked in the exam.

Children, who are called the future of the country, are getting trapped in the quagmire of wages even in this modern era. Childhood is that moment of a man's life, remembering that he passes the whole life, this is the beautiful moment when a person is seen playing, reading, writing and playing, regardless of all the sorrows, worries and responsibilities of the world. When he reaches the stage of maturity and when he comes to know about other realities of life. When troubles, troubles come, he says, better than this were the days of my childhood when there was no worry, it was only reading and playing with friends. What fun it was in my childhood, but not everyone's childhood is like this.

Today, more than half of the country's children are under the age of 14 who work seven days a week. This situation is frightening in India as compared to the world. This child labour has become a curse for our country. Despite the efforts of the government, we have not been able to stop child labour. This malpractice is equally distributed in both the urban and rural areas of the country. Children who should have copy-book, pen-pencil in their hands, today utensils, broom-wipes and burdens have been placed in those hands. Children whose age is less than 14 years and they work for livelihood, then it is called child labour or child labour.

Due to poverty, helplessness, hunger and oppression of parents, today these children are getting trapped in the team of child labour. Poverty is the biggest cause of child labour in India. Many times, due to poverty, many parents get caught in the clutches of people doing child labour. Many times they even lose their hands from the lives of their grandparents. Today our society is passing through inequality. On the one hand the children behind whom their parents are spending thousands of thousands on their future and food, on the other those children who are living a life of hunger, malnutrition and contempt. Many children are poor, orphans or victims of exploitation by some evil person. They do not get enough food, and work is taken from them like an adult person.

There is a need for a lot of improvement in this subject in our society today. The government made a law for child labour, declared it illegal but there has been no visible change in the mindset that should be expected today. This effort of the government has definitely helped in arresting those who illegally employ children below 14 years of age or keep them imprisoned. In this fight to stop child labour, first of all we have to educate our society and make proper arrangements for poverty.

Subject:

Child labour, child labour, child labour a curse, child labour problem.

महेंद्र सिंह धोनी 

महेंद्र सिंह धोनी एक ऐसा नाम जो देश और दुनिया में हर क्रिकेट प्रेमी के दिल में बस्ता है | जीवन में कामयाबी की बुलंदियों पर पहुचने वाला एक ऐसा सितारा जिसके जैसा न पहले कोई हुआ न ही होगा |

धोनी के इंटरनेशनल क्रिकेट से रिटायर होने की घोषणा के साथ ही एक बेहद ही शानदार युग का अंत हो गया | धोनी का जन्म झारखण्ड के राची में एक मध्यम वर्गीय परिवार मे हुआ | उनके पिता का नाम पान सिंह व माता का नाम देवकी है |

धोनी भारतीय टीम के पूर्व कप्तान और सबसे सफल एक दिवसीय अंतर्राष्ट्रीय कप्तान रह चुके है | अपनी आक्रामक बल्लेबाजी और चपल विकेटकीपिंग के दम पर भारतीय टीम में जगह बनाने वाले धोनी ने अपनी कप्तानी में भारत को ICC विश्वकप 20-20 (2007), ICC विश्वकप (2011) और ICC चैंपियंस ट्रोफी (2013) में जीत दिलाई | ICC के तीनो प्रारूपो मे ऐसा करने वाले वो एक लोते कप्तान है |

धोनी को पद्म भूषण, पदमश्री और राजीव गाँधी खेल रतन पुरुस्कार से भी सम्मानित किया जा चूका है | अपने लम्बे बालो और शांत स्वभाव के कारण उन्हें माही और कैप्टेन कूल जैसे नामो से भी जाना जाता है |

यदि आपको यह आर्टिकल पसंद आया हो तो कमेंट में जाकर अपनी राय जरुर से और अपना सुझाव भी दे | 

डसॉल्ट राफेल या राफेल एक फ्रेंच दोहरे इंजन वाला, कैनर्ड डेल्टा विंग, मल्टीरोल डेसॉल्ट एविएशन द्वारा डिजाइन और निर्मित लड़ाकू विमान है। हथियार की एक विस्तृत श्रृंखला के साथ सुसज्जित, राफेल का उद्देश्य वायु वर्चस्व, हस्तक्षेप, हवाई पुनर्मिलन, जमीन समर्थन, गहराई से मार, विरोधी जहाज हड़ताल और परमाणु प्रतिरोध मिशन करने का है। राफेल को डेसॉल्ट द्वारा "ओमनीरोले" विमान के रूप में जाना जाता है।

1970 के दशक के अंत में, फ्रांसीसी वायुसेना और नौसेना अपने मौजूदा बेड़े को प्रतिस्थापित करने और समेकित करने की मांग कर रहे थे। विकास लागत को कम करने और संभावित बिक्री को बढ़ावा देने के लिए, फ्रांस ने यूके, जर्मनी, इटली और स्पेन के साथ एक चुस्त बहुउद्देश्यीय लड़ाकू, यूरोफाइटर टाइफून का उत्पादन करने के लिए एक व्यवस्था में प्रवेश किया। कार्यशालाओं और अलग-अलग आवश्यकताओं के बाद के असहमति ने फ्रांस के अपने विकास कार्यक्रम की खोज की। डैसॉल्ट ने एक तकनीकी प्रदर्शक बनाया जो पहली बार जुलाई 1986 में आठ साल के फ्लाइट-टेस्ट प्रोग्राम के हिस्से के रूप में उड़ान भर गया, जिससे परियोजना के आगे बढ़ने का मार्ग प्रशस्त हो गया। राफेल अपने युग के अन्य यूरोपीय सेनानियों से अलग है कि यह लगभग पूरी तरह से एक देश द्वारा बनाया गया है, जिसमें फ्रांस के प्रमुख रक्षा ठेकेदारों जैसे डेसॉल्ट, थाल्सैंड सफ्रान शामिल हैं।

एक जरूरी है, ताकि एयर-टू-ग्राउंड और एयर-टू-सी संचालन सुरक्षित और कुशलता से संचालित किया जा सके। विषम और आतंकवाद विरोधी संघर्षों के दौरान, वायु सेना भी सैन्य प्रयास में सबसे आगे रहती है, इसकी लचीलेपन और फायरिंग शक्ति की मदद से यह सुनिश्चित होता है कि संबद्ध सेना प्रबल हो। 11 सितंबर की घटनाओं से पता चला है कि, मयूर में, आसानी से तैनात नियंत्रण और वायु रक्षा परिसंपत्तियों के साथ राष्ट्रीय हवाई क्षेत्र को सुरक्षित करना आवश्यक है। आधुनिक युद्ध में वायु घटक का निर्णायक स्थान उन राष्ट्रों द्वारा तय की गई रक्षा रणनीतियों द्वारा प्रदर्शित किया जाता है जो विश्व मंच पर एक अग्रणी भूमिका रखना चाहते हैं। 

राफेल फ्रांसीसी वायु सेना और फ्रेंच नौसेना में वाहक-आधारित संचालन दोनों के लिए बनाया जा रहा है। राफेल को कई देशों में निर्यात के लिए विपणन किया गया है, और भारतीय वायुसेना, मिस्र वायुसेना और कतर वायुसेना द्वारा खरीद के लिए चुना गया था। अफगानिस्तान, लीबिया, माली, इराक और सीरिया में राफेल का इस्तेमाल किया गया है।

राफेल, अपनी "ओमनीरोले" क्षमताओं के साथ, बढ़ती सरकारों द्वारा चुनी गई क्षमता दृष्टिकोण का सही उत्तर है। यह पूरी तरह से विमान की सबसे छोटी संख्या के साथ भूमिकाओं की सबसे विस्तृत श्रृंखला को पूरा करने की आवश्यकता का अनुपालन करता है। राफेल स्थायी "क्विक रिएक्शन अलर्ट" (क्यूआरए) / वायु-रक्षा / वायु संप्रभुता मिशन, बाहरी मिशनों के लिए शक्ति प्रक्षेपण और तैनाती, गहरी हड़ताल मिशन, जमीनी बलों के लिए हवाई समर्थन, टोही मिशन, पायलट प्रशिक्षण सॉर्ट और परमाणु निवारक कर्तव्यों में भाग लेता है । वायु सेना एकल सीट राफेल सी, वायु सेना दो सीट राफेल बी, और नौसेना एकल सीट राफेल एम में अधिकतम एयरफ्रेम और उपकरण समानता, और बहुत ही समान मिशन क्षमताओं की सुविधा है।नवीनतम संघर्षों से सीखा सबक जहां वायु शक्ति का उपयोग किया गया था, राजनीतिक निर्माताओं द्वारा हथियार प्रणालियों के बारे में चार अतिशयोक्तिपूर्ण उम्मीदों में संक्षेपित किया जा सकता है: बहुमुखी प्रतिभा, वह क्षमता, एक ही प्रणाली के साथ, विभिन्न अभियानों को करने के लिए, इंटरऑपरेबिलिटी, या सहयोगियों के साथ गठबंधन में लड़ने की क्षमता, सामान्य प्रक्रियाओं और मानकों के समझौतों का उपयोग करना, और अन्य प्रणालियों के साथ वास्तविक समय में सहयोग करना और संचार करना, लचीलापन, जिसे एक ही सॉर्टी के दौरान कई अलग-अलग मिशनों को संचालित करने की क्षमता द्वारा चित्रित किया जा सकता है ("ओमनीरोले" क्षमता)। इस क्षमता के साथ, राजनीतिक निर्णय लेने वाले की मांग पर, एक जबरदस्ती मिशन ("स्ट्राइक फोर्स") से एक निवारक मिशन (एक निराशाजनक कम-ऊंचाई, उच्च गति "बल का प्रदर्शन") पर तुरंत स्विच करना संभव है। या अंतिम सेकंड (प्रतिक्षेपकता) तक एक मिशन को रद्द करने के लिए भी, उत्तरजीविता, जो कि घने खतरे के माहौल में जीवित रहने की क्षमता है, जो कि चोरी और / या उन्नत इलेक्ट्रॉनिक युद्ध प्रणालियों के लिए धन्यवाद है। चार्ल्स डी गॉल विमान वाहक। राफेल एम। चार्ल्स डी गॉल विमान वाहक। राफेल एम। "ओमनीरोले" राफेल इन सभी लाभों को जोड़ती है: यह पारंपरिक और विषम दोनों खतरों के खिलाफ प्रासंगिक है, यह बदलते भूराजनीतिक संदर्भ में सशस्त्र बलों की उभरती जरूरतों को संबोधित करता है, और यह तकनीकी नवाचार में सबसे आगे रहता है। इसकी बहुमुखी प्रतिभा, इसकी अनुकूलनशीलता और सभी हवाई मिशन आवश्यकताओं को पूरा करने की क्षमता के लिए धन्यवाद, राफेल "पोस्टर चाइल्ड" परिवर्तनकारी सेनानी है जो वायु सेनाओं को "कम", "कम" के साथ "अधिक" करने की आवश्यकता का सामना करने का एक तरीका प्रदान करता है। कभी बदलते सामरिक और आर्थिक परिवेश में। मध्यम आकार का, फिर भी बेहद शक्तिशाली, शानदार फुर्तीला और बहुत असतत, डसॉल्ट एविएशन से नवीनतम प्रकार का लड़ाकू विमान न केवल सेंसर की सबसे बड़ी और सबसे आधुनिक रेंज को एकीकृत करता है, यह एक तकनीकी सफलता के साथ उनकी दक्षता को भी गुणा करता है, "मल्टी सेंसर डेटा फ्यूजन ”। उड़ान में राफेल। उड़ान में राफेल। खोज करना

राफेल स्टील्थ टेक्नोलॉजी से लैस है. यानी यह दुश्मन के रडार को चकमा देने के ताकत रखता है| साथ ही इसे इस हिसाब से डिजाइन किया गया है कि यह हिमालय के उपर भी उड़ान भर सकता है. बता दें कि हिमालय के उपर उड़ान भरने की काबिलियत अच्छे-अच्छे लड़ाकू विमानों में नहीं होती है.

फ्रांस ने अबतक कुल 10 राफेल विमान बना लिए हैं भारत के लिए. लेकिन अभी सिर्फ 5 राफेल विमानों को कल भारतीय वायुसेना के हवाले किया गया है. अन्य 5 राफेल विमानों को फ्रांस में ही रखा गया है ताकि वायुसेना के पायलटों व क्रू को फ्रांस में ट्रेनिंग दी जा सके. वहीं पिछले साल 1 राफेल विमान भारत को सौंपा गया था ताकि भारतीय पायलट भारत में राफेल की ट्रेनिंग अच्छे तरीके से ले सके.

अगर हथियारों की बात करें तो राफेल में सबसे खतरनाक मिसालइल Meteo beyond Visual Range AIR to Air Missile है. यह मिसाइल हवा से हवा में मार करने की क्षमता से लैस है. साथ ही बीते दिनों भारतीय वायुसेना ने राफेल में हैमर मिसाइलों को भी लैस करने की बात कही थी. इन मिसाइलों की खासियत है कि नो स्केप जोन में अगर कोई भी लड़ाकू विमान हो तो राफेल उसे मार गिराएगा. यह अचूक है. बता दें कि कुल 36 राफेल विमान भारत फ्रांस से खरीद रहा है. इसमें अन्य एयरक्राफ्ट को दो सालों में भारत को सौंप दिया जाएगा.

भारत के 11वे राष्ट्रपति डा. एपीजे अब्दुल कलाम को जब भी कोई भी देशवासी याद करता है तो उनके लिए सम्मान का भाव मन में भर जाता है | एक ऐसा व्यक्ति जिसने अपना पूरा जीवन देश को समर्पित कर दिया | उनका हेयर स्टाइल युवाओ में बोहोत ही लोकप्रिय था |

भारत के ‘मिसाइल मैन’ के नाम से लोकप्रिय डा. एपीजे अब्दुल 27 जुलाई 2015 को दुनिया को अलविदा कह दिया | वे बेहद ही साधारण परिवार से ताल्लुक रखते थे | उनके पिता जैनुलब्दीन एक मछुआरे थे | इनकी माता अशिअम्मा एक गृहणी थी |

अब्दुल कलाम का पूरा नाम अवुल पाकिर जैनुलब्दीन अब्दुल कलाम था | इनका जन्म 15 अक्टूबर 1931 को रामेश्वरम में एक तमिल मुस्लिम परिवार में हुआ था | इनके 3 बड़े भाई व एक बहन परिवार में थी |

बेहद ही गरीब परिवार से होने के कारण अब्दुल कलाम को अपनी आरंभिक शिक्षा जारी रखने के लिए अख़बार बाटने का काम किया | कलाम ने 1950 में मद्रास इंस्टीट्यूट ऑफ़ टेक्नोलॉजी से अन्तिरिक्ष विज्ञान में स्नातक किया |

1992 से 1999 तक कलाम रक्षा मंत्री के रक्षा सलाहकार भी रहे, इस दौरान वाजपेयी सरकार ने पोखरण में दूसरी बार न्यूक्लियर टेस्ट भी किए और भारत परमाणु हथियार बनाने वाले देशों में शामिल हो गया. कलाम ने विजन 2020 दिया. इसके तहत कलाम ने भारत को विज्ञान के क्षेत्र में तरक्की के जरिए 2020 तक अत्याधुनिक करने की खास सोच दी गई. कलाम भारत सरकार के मुख्य वैज्ञानिक सलाहकार भी रहे.

कलाम को 1981 में भारत सरकार ने पद्म भूषण और फिर, 1990 में पद्म विभूषण और 1997 में देश के सर्वोच्च नागरिक सम्मान भारत रत्न प्रदान किया. भारत के सर्वोच्च पद पर नियुक्ति से पहले भारत रत्न पाने वाले कलाम देश के केवल तीसरे राष्ट्रपति हैं. उनसे पहले यह मुकाम सर्वपल्ली राधाकृष्णन और जाकिर हुसैन ने हासिल किया था.