Odd function & Even Functions

Even Functions

for video classes.: - https://www.youtube.com/watch?v=O178h_HkQss&t=111s

A function is "even" when:

f(x) = f(−x) for all x

This is the curve f(x) = x²+1

They got called "even" functions because the functions x², x⁴, x⁶, x⁸, etc behave like that, but there are other functions that behave like that too, such as cos(x):

Cosine function: f(x) = cos(x)
It is an even function

But an even exponent does not always make an even function, for example (x+1)² is not an even function.

https://www.youtube.com/channel/UCnSzn6hUZk-M7juvSAK2Eqw/videos

Odd Functions

A function is "odd" when:

−f(x) = f(−x) for all x

Note the minus in front of f(x): −f(x).

And we get 

This is the curve f(x) = x³−x

They got called "odd" because the functions x, x³, x⁵, x⁷, etc behave like that, but there are other functions that behave like that, too, such as sin(x):

Sine function: f(x) = sin(x)
It is an odd function

But an odd exponent does not always make an odd function, for example x³+1 is not an odd function.

Neither Odd nor Even

Don't be misled by the names "odd" and "even" ... they are just names ... and a function does not have to be even or odd.

In fact most functions are neither odd nor even. For example, just adding 1 to the curve above gets this:

This is the curve f(x) = x³−x+1

It is not an odd function, and it is not an even function either.
It is neither odd nor even

Even or Odd?

Example: is f(x) = x/(x²−1) Even or Odd or neither?

Let's see what happens when we substitute −x:

f(−x) =(−x)/((−x)²−1)

=−x/(x²−1)

=−f(x)

So f(−x) = −f(x) , which makes it an Odd Function

Even and Odd

The only function that is even and odd is f(x) = 0

Special Properties

Adding:

• The sum of two even functions is even
• The sum of two odd functions is odd
• The sum of an even and odd function is neither even nor odd (unless one function is zero).

For more videos.

https://www.youtube.com/channel/UCnSzn6hUZk-M7juvSAK2Eqw/videos

Tata Steel Recruitment 2019 for Assistant Engineer Trainee | Last Date: 17 February 2019

Tata Steel Recruitment 2019 scheduled to hire Assistant Engineer Trainee (AET) for Fresher Engineering graduates. The detailed eligibility and application process are given below.

Tata Steel Recruitment 2019:

Job Role	Assistant Engineer Trainee
Qualification	B.E/B.Tech/B.Sc(Engg)
Total Vacancies	Not disclosed
Experience	Freshers
Salary	1st year: Rs.28,000/Month 2nd year: Rs.30,000/Month
Job Location	Across India
Last Date	17 February 2019

Detailed Eligibility:

• B.E. / B. Tech. / B.Sc. (Engg) in the relevant disciplines only (Candidates with 0 years of experience post completing their engineering are also eligible to apply)
• Must have attended Full time AICTE/UGC approved Campus Program.
• Must have scored minimum of 6.5 (where the scoring pattern is CGPA) or 65% (where the scoring pattern is in percentage) in B.E. / B. Tech. / B.Sc. (Engg) Examination.

Eligible Streams:

For TSK Locations:

• Electrical / Electronics / Instrumentation
• Mechanical
• Metallurgy
• Chemical

For Tata Steel & Associated Group Companies:

• Civil & Structural
• Ceramic
• Chemical
• Electrical / Electronics / Instrumentation
• Mechanical
• Metallurgy
• Mineral Processing
• Production Engineering
• Any other domain of Engineering

Age limit (As on 17th February 2019): Below 30 years. (Candidates born on or after 17th February 1989)

Selection Procedure:

Over 400 active jobs every month for B.E/B.Tech Graduates:- Register Now

Only shortlisted candidates would be invited for selection process. All selected candidate will undergo Background Verification as per company’s standard, before their appointment.

How to apply for Tata Steel Recruitment 2019 for AET?

All interested and eligible candidates can apply for AET vacancies through online latest by 17 February 2019.

For More details: Click here

To Apply: Click here

Steps to apply for Tata Steel Recruitment:

• Visit careers.tatasteelindia.com
• Click on “Careers”
• Click “Apply Now”
• Select “Tata Steel India” (scroll down)
• Select “Apply for jobs/internship”
• Select “Application tab”

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Leave Policy in India

Numbers of leaves entitlement in a company depends upon state you are in. Every state has different leave entitlement and leave policies which should be seen before one defines leave policy of your company. Leave policy of a company cannot be less than that mentioned by the State’s shop and establishment act.

Earned Leave

This is a paid leave earned by employees during a year and availed in the subsequent year. If the number of earned leave is over, the day is considered as an unpaid leave and the day’s pay is cut from the salary. These leaves can also be en-cashed while leaving the company. The following are number of earned leaves according to laws:

Factory workers need to work minimum 240 days in the organization in a year to be eligible for earned leave. Adults get 1 day for every 20 days, and children, below the age of 15, get 1 day for every 15 days work in the previous year.Mine workers below the ground can avail 1 day for every 15 days work; and those working above the ground can avail 1 day for every 20 days work.Workers in a Bidi or Cigar factory get 1 day leave for every 20 days work in the previous year. If the worker is a child of below age 15, he gets 1 day off for every 15 days of work.People working in sales, and newspaper running company (which includes journalists) can avail one month earned leave for every 11 months of work.Domestic workers are also eligible for 15 days earned leave in a year.Casual Leave

This is another paid leave that although not earned, is entitled to employees only if prior permission is granted by the organization. If the employer does not grant permission and the employee nevertheless takes a leave, the day’s pay is cut from the salary. Usually every organization allows a certain number of casual leaves in a year, which is fixed by the company’s administration. Although, there is laws for certain types of workers:

Sales and newspaper employees (including journalists) are entitled 15 days of casual leave in a yearApprentices are entitled annually 12 days casual leaveSick/Medical Leave

Employers provide sick leaves to employees when they are ailing. Some organizations ask for a medical certificate to grant sick leave. Others don’t deem in necessary. If the employee has used up all his sick leaves, the company uses his earned leaves. Sick leaves can also be carried forward to the next year. The specifications are although determined by the company’s administration. Laws governing sick leaves for different types of employees are:

Apprentices are entitled for 15 days of sick leave in a year. This can be accumulated to a maximum of 40 days.Journalists and Newspaper employees can avail medical leave of one month for every 18 months of work. During the medical leave, the employees are paid half the day’s pay.Sales employees are entitled to medical leave similar to that of newspaper employees. They although mandatorily need to show a medical certificate for their absence.Maternity Leave

Female employees, as per law, are entitled to 3 months or 12 weeks of leave when she is pregnant. During this time, employers will have to pay their female employees normally.

Paternity Leave

Male employees who are soon to become fathers can avail upto 15 days of leave within 6 months of their wife’s date of delivery.
Apart from these, there are others paid, unpaid or half-paid leaves like Study Leave, Bereavement Leave and Leave for Voting. These although are left at the organization’s discretion.

Lost PAN Card – Reapplication Procedure

Lost PAN card or damaged PAN card is a common occurrence for many taxpayers in India. The Income Tax Department has provided a hassle-free and easy way for taxpayers to apply for a new PAN card in case of lost PAN card. In this article, we look at the procedure to apply for a new PAN card, in lieu of a lost PAN Card.

Lost PAN Card Application

​If a PAN card is lost an application for duplicate PAN card can be submitted using the Form for “Request for New PAN Card or/ and Changes or Correction in PAN Data” and a copy of FIR may be submitted along with the form. Submission of FIR is not mandatory, its optional only.

Follow the steps below to submit the lost PAN card application:

Step 1: You can reapply for a lost PAN card through the NSDL or UTI PAN Facilitation Centres or online through the website of NSDL or UTI.

• NSDL Lost PAN Application

Step 2: In case of lost PAN card, complete the form with the old PAN provided at the beginning of the application. Do not submit application for new PAN card. It is illegal for a person to possess more than one PAN. Hence, submission of the application without the old PAN mentioned at the beginning of the form could lead to a new PAN being generated.Step 3: In case of any changes to the PAN, select the box on the left hand side of the form and update the information. In case of no changes, complete the form completely but do not select any box on left margin.

Step 4: Submit the documents required along with the application. For lost PAN card, proof of PAN must be submitted. Proof of PAN can be one of the following only:

• Copy of PAN card; or
• Copy of intimation letter issued by the Income Tax Department in lieu of PAN card intimating PAN.
• In case one of the above proofs are not available, a copy of FIR (stating loss of PAN card) can be submitted.

If proof of PAN (as stated above) is not submitted, the application will be processed on a ‘good effort’ basis even without a copy of FIR. However if it is found that there are differences between the PAN or the data provided in the application with the Icome Tax Department database, the application may not be processed and the processing fee will be forfeited.

Step 5: Pay the PAN card processing fee. If the communication address of the taxpayer is within India, then the fee for processing new PAN application will be Rs.110. If the communication address of the taxpayer is outside of India, then the fee for processing PAN application will be Rs.1020.

Step 6: On confirmation of successful payment, a 15 digit unique acknowledgment will be generated. The applicant must save and print the acknowledgement.

Step 7: Sign the application and place a photo of the applicant along with signature or thumb impression in the place provided. Attach a copy of the old PAN card or intimation letter issued by IT Department or FIR.

Step 8: Send the completed application to NSDL or UTI. The address for NSDL is as follows:

• Income Tax PAN Services Unit,
  NSDL e-Governance Infrastructure Limited,
  5th Floor, Mantri Sterling, Plot No. 341,
  Survey No. 997/8,Model Colony,
  Near Deep Bungalow Chowk, Pune – 411 016.

Forgot PAN

If the PAN card is lost and you do not remember your PAN, then before filing the lost PAN card application, use the “Know Your PAN” facility on the Income Tax Department website. Using “Know Your PAN”, by entering details like Name, Father’s Name and Date of Birth, you can find your PAN. 

How to Link Aadhaar Number, Mobile Phone Using IVR for Re-Verification

The ongoing Aadhaar-mobile SIM card re-verification process has just become a little easier for people across the country. Consumers can now simply dial a central number, regardless the network, to link their mobile number with Aadhaar number. This will bring a sigh of relief for consumers across the country, who only had the option to visit offline stores run by their operators to link the two till now. Now, they can use the IVR (Interactive voice response) service from their homes instead, cutting out the hassle involved in going to physical outlets. Consumers have till February 6 to link their mobile number with Aadhaar.

How to link Aadhaar with mobile phone number

If you want to re-verify your phone number by linking it to Aadhaar, the process is rather simple. You just need to keep your Aadhaar number at hand. Whether you are on Airtel, Idea, Jio and Vodafone or any other operator, you simply need to call the toll-free number 14546 from the phone number. Follow these steps, as directed by the IVR, to complete the re-verification process.

1. When you call 14546, you will be asked to select whether you are an Indian national or an NRI by selecting the respective option
2. Next, you will have to give consent to link Aadhaar with your phone number by pressing 1
3. After that, you need to provide your Aadhaar number and press 1 to confirm
4. This step generates the OTP, which you will receive on your mobile phone
5. Now, you need to enter your phone number
6. Here, you are asked to give consent to your operator to pick your name, photo and date of birth from UIDAI data base
7. The IVR now mentions the last four digits of your number to confirm that you have keyed in the right number
8. If the number is correct, you can enter the OTP you received on SMS
9. You must press 1 to complete the Aadhaar-mobile number re-verification process
10. If you hold another phone number, you can link that too by pressing 2 and following the steps provided by the IVR system. Keep your other mobile phone handy as you will receive the OTP on this number

The OTP you receive for Aadhaar-mobile phone re-verification is valid for 30 minutes, so you can use it even there is some network glitch and the call terminates prematurely. Subscribers who are on corporate plans do not need to need to undergo the re-verification process. So far, Airtel, Idea, and Vodafone have activated the service. Since Jio takes Aadhaar number to activate the SIM card, subscribers do not need to re-verify on the network.

As Aadhaar is a central number, Airtel and Vodafone say users can link their mobile numbers to Aadhaar irrespective of the state it is issued in and the circle the number belongs to. However, Idea Cellular in a tweet said the Aadhaar number should belong to the same circle as the mobile number. Aircel has not started the IVR process, and is still asking users to go to offline stores even after the new centralised number has been deployed.

In late November, telecom operators had also been directed to set up a website so that subscribers can link Aadhaar and mobile number online. However, there is no such website so far. Going by the image in a tweet by the Digital India Twitter account, it seems users will be able to link the two using the mAadhaar app, which is available only for Android so far, as well in some time.

Check your EPF Account Balance in 6 Easy Steps

Check your EPF Account Balance in 6 Easy Steps

Do you know the total accumulated balance in your employees provident fund (EPF)? In case you are keen to know the balance and are unable to do so, it is an easy process if you have been allotted an Universal Account Number (UAN) by the EPFO.

 In case you do not have your 12-digit UAN, you can get it activated through your employer to know the summary of PF deducted through EPFO portal. All employees need to have only one UAN throughout their working life irrespective of the number of companies they change. It is a universal account number (UAN) which facilitates in linking of multiple EPF accounts of a member.

To see your EPFO account and view your provident fund passbook online, you need to follow these simple steps:

Step 1

Employees need to login the member portal by visiting the EPFO website (unifiedportalmem.epfindia.gov.in/memberinterface/). You need to enter your 12 digit Activated UAN number and the password to view your account details. If you have not activated your UAN, you can also activate it by clicking on the tab below. Once you have entered the right credentials, it takes four days to activate your UAN.

Step 2

Once you have entered into the portal, you can find all kind of online services that are available on the EPFO website. From there you can track your queries related to claim status, transferring request, which is required in case your current employer has created another UAN number to track your PF account.

Step 3

You can see various tabs present on the dark green ribbon above. Clicking on the ‘view’ tab will take you to visit your profile, service history, UAN card and your passbook address. This passbook address is a separate website link where you can view your PF account.

Step 4

To view your PF passbook, you need to visit epfindia.gov.in website. This is a different website where you can view various other details related to EPFO. You need to go to the ‘our service’ tab and under our service tab, you need to click on the ‘for employees’ link. To view the EPF contributions done by your employer every month you need to then click on the ‘member passbook’ link.

Step 5

After clicking on the member passbook link, you will be redirected to a separate tab, where you need to re-enter your activated UAN and the same EPFO passwords which you used it for the EPFO member login portal.

Step 6

Once you have entered your credentials, you can visit your EPF passbook and view your PF contribution made by the company.

The government has come up with various other benefits where they are giving special benefits to employees who had to leave their current job due to some physical incapacitation. If you want visit the office, you may even locate the nearest EPFO office through this EPFO website, you can also view the eligibility for making online claims and obtain lots more service facilities through this online portal.

One should also know that the accumulated amount is payable on retirement, resignation or death. You can also make partial withdrawals for financing life insurance policies, acquiring a house, wedding of self or dependents, child’s education planning or any treatment of illness etc.