I need to send mails from our centos server, what are tools required ?

server
CentOS release 6.5 (Final)

How to check if sendmail is installed and configured?

I even tried mutt, I could install but not able to send mails. Is there any configuration required ?

Even mutt (which is an email CLIENT, though a nice one) requires an MTA or email SERVER.
Sendmail is not the only one, just the grandaddy. Exim and others also complete and compete for that space.

Make sure that you have an MTA installed, then read the docs about how to configure it. (Sendmail may be configured using WEBMIN, editing the sendmail.mc file and compiling it with m4 (under control of make in recent packages, makes it easy) or by direct editing of sendmail.cf - not recommended) but different packages can use different configuration files, or the same files differently.

From your site do you require a SMARTHOST or parent SMTP server for relay? If so, that relay must be set to allow your host to forward: setting the client machine properly may or may not suffice.

I hope that this helps.

I did not understand the SMARTHOST part, though I added the exchange server address as SMARTHOST in sendmail.mc

BTW, we have multiple domains. My CentOS server is in one domain and exchange server is in different domain. My sendmail seems working. If I see the logs in maillog, it says connection timeout after 60 seconds.

All the mails I sent are present in /var/spool/mail/user. But I want those mails to be delivered to my outlook

Any help ?

I am not sure I will be able to resolve this with you, but let us get some detail so someone else has the right information to work with.

You have two mail servers, different mail domains, one exchange and one linux.
You are sending from the Linux machine using mutt, mail, mailx, or other mail client.
You are sending TO an account served by your Exchange mail server.

If the Exchange server is NOT forwarding email for the Linux mail server to the outside world, you do NOT need the SMARTHOST setting. If it DOES relay mail for the linux mail server, then you do.

BOTH mail servers should have MX records in DNS for their domains. If they lack these, there are settings that need to be adjusted to allow each to send mail to the others without that security check and setting them as the mail target for that domain. I do not manage Exchange, so I cannot discuss those settings in any detail.
If your MX records are present and use external addresses, you may need host table entries with the internal addresses on each host. (most routers have trouble routing the same packet in and out on the same interface)

Between linux machines it is easier, you can use email names with the that use the FQDN of the target server. (john@node1.mynet.local instead of john@mynet.local) and they will direct send. Exchange does not by default, though it has a LOT of settings and might be capable.

Considering these things, please describe what you try and how it changes the behavior or log entries.