Step 1: Understanding the question.
The question asks us to identify the correctly matched pair of a national park and the state in which it is located. National parks are protected areas created for the conservation of wildlife, forests, biodiversity, and natural habitats.
Step 2: Checking Option (A).
Periyar National Park is not located in Madhya Pradesh. It is located in Kerala, in the Western Ghats. It is famous for elephants, tigers, and the Periyar Lake. Therefore, Option (A) is incorrect.
Step 3: Checking Option (B).
Manas National Park is located in Assam. It is a UNESCO World Heritage Site and is famous for its rich biodiversity, including tigers, elephants, rhinoceros, golden langur, and many species of birds. Therefore, Option (B) is correctly matched.
Step 4: Checking Option (C).
Bandhavgarh National Park is not located in Rajasthan. It is located in Madhya Pradesh. It is especially famous for its high tiger population and is one of India's important tiger reserves. Therefore, Option (C) is incorrect.
Step 5: Checking Option (D).
Corbett National Park is not located in Uttar Pradesh. It is located in Uttarakhand. It is India's first national park and was earlier known as Hailey National Park. It is also famous for tiger conservation under Project Tiger. Therefore, Option (D) is incorrect.
Step 6: Conclusion.
Among the given options, only Manas -- Assam is correctly matched. Hence, the correct answer is Option (B).