Is it a better or worse plan to : Instead of purchasing a house and
paying the price in cash with no financing, is it a better idea to buy
the property and get a mortgage and invest the difference in good
mutual funds?

It depends.  Here are a couple of articles discussing the pros and
cons that will help you make a decision.  If you pay cash, you lose
liquidity and the mortgage interest deduction.  Historically, stocks
have also had higher returns over long periods.  However, there are
circumstances where paying cash is better, such as when interest rates
are high or if you feel pessimistic about stock returns.

Sincerely,

Wonko

"Pay off the mortgage or invest?  It depends..." USA Today
http://biz.yahoo.com/usat/051212/13269487.html

"Is it smart to pay cash for a home?" by Steve McLinden, Bankrate
http://64.233.179.104/search?q=cache:s0zY4TE_H1gJ:biz.yahoo.com/brn/050528/14743.html%3F.v%3D1+%22is+it+smart+to+pay+cash+for+a+home%22&hl=en&gl=us&ct=clnk&cd=1

I'd have to say that borrowing and investing is almost always the
right way to go.  An example:
You have $100,000 to buy a $100,000 house...

Option A: Pay $10,000 down and borrow $90,000
We'll assume a high interest rate of 10% (way above the market average
today) to be on the conservative side.  The total interest on this 30
year loan is $194,000.  This is tax deductible (assuming you're in in
the US).  Again to be conservative, we'll assume a 15% tax rate...
which brings your tax savings to $194,000 X .15 = $29,000
So the total cost of buying the house is:
$100,000 + $194,000 - $29,000 = $265,000
In the meantime, that $90,000 is invested in the market.  The market
has averaged 11% over the long run, but we'll assume an 8% return
(again to be on the really conservative side).  The total interest
(compounded of course) over 30 years is about $800,000.
So in the end you have $800,000 - $265,000 = $535,000 and a house from
your $100,000 investment.

Option B: Pay cash
The math on this one is easy... all you have to show for your money in
30 years is a house.

Even with my very conservative estimates for interest rates, taxes,
and investment returns, Borrowing money to buy the house is the better
option (better by $535,000 after 30 years).

**note that any money after 30 years will be worth less due to
inflation, however with Option B there is no money... Money that has
lost some value is always more valuable than no money at all.

This is reall a tax question and one you should run by a CPA to get
the correct answer for you. Many factors come into play and only a CPA
who reviewe your entire profile should be consulted.

But, for extensive real estate information, I would recommend you visit:
http://www.brokerforyou.com