Capital gain utilisation

As per section 54 of the Income tax act , exemption is available for only Long term capital gains ,( holding period more than 24 months) ,
In your case holding period is less than 24 months ( 11.11.20 to 4-4-22 = 1year ,5 months) So it's short term capital gains , therefore you can not claim any exemption . Capital gain tax payable .

A new apartment was purchased on 11.11.20. Another property was sold for 40l on 04.04.22. This property was purchased on 10.01.2010. There he made a long term capital gain of 20l. Can this 20L be adjusted against the purchase of new apartment bought on 11.11.20

No this LTCG cannot be set off against the purchase of new property. Cost of purchase of new apartment can be deducted when you sale that new apartment.

The new property can be purchase 1 year before or 2 years after the date of sale of the old property inorder to claim LTCG exemptions.
Since the date of sale is 04.04.2022, inorder to claim the exemption the property was needed to be purchased after 05.04.2021 (i.e. 1 year before date of sale) inorder to claim exemption. Since, the property was purchased on 11.11.20 i e. more than 1 year before the sale of the 40lacs property, LTCG exemption cannot be taken.

Have you paid or your bank ( if there was a home loan ) disbursed any amount directly to the seller in April 2021 or thereafter towards the flat purchased in Nov 2020 ??? If yes, there might be a possibility of claiming the exemption.

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Although you can not claim the benefit of exemption of property purchased on 11.11.2020 but still you can buy a one more residential house on or before 03.04.2024 or can construct a house on or before 03/04/2025.

till that you can deposit the capital gain into bank on or before the return file date u/ s 139  (1) into capital gain deposit account scheme.  

Sir CA Raj Doshi no home loan

You cannot claim the capital gain exemption against the property purchased in 2020. 

However, you can transfer the proceeds of Rs. 40 Lacs to the capital gains accounts scheme to make an eligible investment in the period 1 yr or 2 yr as applicable.