Consider the following dynasties:

1. Hoysala
2. Gahadavala
3. Kakatiya
4. Yadava
   
   

How many of the above dynasties established their kingdoms in the early eighth century AD?

Explanation:

Hoysala

• The Hoysalas came into the limelight from the beginning of the 11th century. In the Kaliyur (near Talakad) inscription of about 990 A.D., a Hoysala chief is mentioned in the Ganga confederacy fighting against Aprameya, a Chola general, and this chief is identified as Nripakama, the earliest known member of the Hoysala dynasty. His son and successor Vinayaditya is first referred to in a record of 1047 A.D. So, option 1 is not correct.
  
  

Gahadwala

• With the break-up of the Pratihara empire, a number of Rajput states came into existence in north India. 
• The most important of these were the Gahadavalas of Kanauj, the Paramaras of Malwa, and the Chauhans of Ajmer. There were other smaller dynasties in different parts of the country, such as the Kalachuris in the area around modern Jabalpur, the Chandellas in Bundelkhand, the Chalukyas of Gujarat, the Tomars of Delhi, etc Bengal remained under the control of the Palas and, later, under the Senas. The Gahadavalas of Kanauj gradually squeezed the Palas out of Bihar.
• Chandradeva (1089–1103 CE), also known as Chandraditya, was an Indian king from the Gahadavala dynasty. He ruled the Antarvedi country in present-day Uttar Pradesh, including Kanyakubja and Varanasi.
• At its height, the Gahadval kingdom extended from Mongyr in Bihar to Delhi. The greatest ruler in the dynasty was Govind Chandra who ruled in the first half of the twelfth century. He made Kanauj his capital, with Banaras remaining a second capital. Persian sources of the time call Govind Chandra the greatest ruler of Hindustan.
• The Gahadvars are reputed to be the biggest defenders against the continued Ghaznavid raids into the doab. Govind Chandra was succeeded by Jai Chandra who had to contend with the rising power of the Chauhans. So, option 2 is not correct.
  
  

Kakatiya

• The sub-feudatories of the Rashtrakutas emerged themselves as independent kings and founded the Kakatiya dynasty around 950 AD and this kingdom became a strong and united whole of Telugu-speaking lands and lasted for more than three centuries and a half. The kingdom saw powerful kings like Ganapatideva, Rudradeva and Prataparudra as well as the first-ever woman ruler in the subcontinent, Rudramadevi. The Kakatiyas ruled from Hanumakonda in the beginning and shifted their capital to Warangal later. So, option 3 is not correct.
  
  

Yadava

• In the last quarter of the 12th century AD the Yadavas of Devagiri came into prominence. They had previously been ruling over Seunadesha (Khandesh) as feudatories of the Chalukyas of Kalyani. The founder of the family was Dridhaprahara, the son of Subahu. So, option 4 is not correct.
  
  

Therefore, option (d) is the correct answer.