For the purpose of Fifth Schedule, the expression 'State' includes which one of the following States?

No, for the purpose of the 5th Schedule, the expression "State" does not include Sikkim. The 5th Schedule applies to the administration and control of Scheduled Areas and Scheduled Tribes in states other than Assam, Meghalaya, Tripura, and Mizoram. The 6th Schedule, on the other hand, deals with the administration of tribal areas in the four northeastern states mentioned. Don't show wrong information

Assam, Meghalaya, Tripura, Mizoram are exempted from the Fifth Schedule of the Indian Constitution. (That means the expression "states" under the 5th schedule does not include Assam,Meghalaya, Tripura, Mizoram,they are dealt in 6th schedule. Although option (D) sikkim is not technically correct because sikkim used to come under 10th schedule under 35th schedule which gave it "associate statehood" later on sikkim got "full statehood" with the 36th amendment and omitted the previous 10th schedule and then a new 10th schedule which related to "anti defection law" (amendment limiting the ability of politicians to switch parties in parliament) was added by the 52nd Amendment. So technically sikkim doesn't come in any schedule but the considering the options ,option d is correct because for other 3 5th schedule expressly bars them.
Article 244 (1) of the Indian Constitution defines Scheduled Areas as the areas defined so by the President of India and are mentioned in the fifth schedule of the Constitution.
In India, there are 10 states which come under scheduled areas.
Article 244 deals with the Scheduled and Tribal Areas.
The provisions regarding the administration and control of Scheduled and Tribal Areas of any state except the four states are mentioned under the fifth schedule.

The Sixth Schedule of the Constitution provides for the administration of tribal areas in Assam, Meghalaya, Tripura, and Mizoram to safeguard the rights of the tribal population in these states. This special provision is provided under Article 244(2) and Article 275(1) of the Constitution.