In the context of the IS LM model Suppose an economy in which economic authorities they carry out a contractive fiscal policy

The correct answer is third one .i.e. Every Options.

REASON :

Fiscal policy is the means by which a government adjusts its spending levels and tax rates to monitor and influence a nation's economy.

As the GDP is declined, and there is a decrease in investment.  

If GDP is slowing down, or is negative, it can lead to fears of a recession which means layoffs and unemployment and declining business revenues and consumer spending. Without investment, an economy could enjoy high levels of consumption, but this creates an unbalanced economy. There will tend to be a current account deficit and little investment in future growth prospects

When monetary policy becomes ineffective because, despite zero/very low-interest rates, people want to hold cash rather than spend or buy illiquid assets.

A liquidity trap is characterised by

• Very low-interest rates
• Low inflation
• Slow/negative economic growth
• Preference for saving rather than spending and investment
• Monetary policy becomes ineffective in boosting demand

Faced with contractionary fiscal policy the central bank simultaneously bought bonds to the open market , to improve the economy .

The central bank does not have interest rate target due to decline in GDP.

The economy is in the liquidity trap due to decrease in investment.

Therefore , all the statements are correct,