The Kakatiya dynasty rose to prominence after the decline of:

Chalukyas of Kalyani
Satavahanas
Cholas
Yadavas

The correct answer is: A) Chalukyas of Kalyani.

The Kakatiya dynasty was a Telugu-speaking Indian dynasty that ruled the Deccan region of India from the 11th to the 14th centuries. The dynasty was founded by Prola I in 1076 CE, and its capital was at Warangal. The Kakatiyas reached their peak under the rule of Ganapatideva (1199-1261 CE), who expanded the dynasty’s territory and built many temples and other monuments. The Kakatiya dynasty declined after the death of Ganapatideva, and it was overthrown by the Delhi Sultanate in 1323 CE.

The Chalukyas of Kalyani were a Kannada-speaking Indian dynasty that ruled the Deccan region of India from the 10th to the 13th centuries. The dynasty was founded by Tailapa II in 973 CE, and its capital was at Kalyani. The Chalukyas of Kalyani reached their peak under the rule of Vikramaditya VI (1076-1126 CE), who expanded the dynasty’s territory and built many temples and other monuments. The Chalukyas of Kalyani declined after the death of Vikramaditya VI, and it was overthrown by the Hoysala dynasty in 1196 CE.

The Satavahanas were a Telugu-speaking Indian dynasty that ruled the Deccan region of India from the 2nd century BCE to the 3rd century CE. The dynasty was founded by Simuka in 230 BCE, and its capital was at Pratishthana (modern-day Paithan). The Satavahanas reached their peak under the rule of Gautamiputra Satakarni (106-130 CE), who expanded the dynasty’s territory and defeated the Sakas. The Satavahanas declined after the death of Gautamiputra Satakarni, and it was overthrown by the Western Kshatrapas in the 3rd century CE.

The Cholas were a Tamil-speaking Indian dynasty that ruled the Chola Nadu region of India from the 9th to the 13th centuries. The dynasty was founded by Vijayalaya Chola in 850 CE, and its capital was at Thanjavur. The Cholas reached their peak under the rule of Rajaraja I (985-1014 CE) and Rajendra Chola I (1014-1044 CE), who expanded the dynasty’s territory and built many temples and other monuments. The Cholas declined after the death of Rajendra Chola I, and it was overthrown by the Pandyas in the 13th century CE.

The Yadavas were a Marathi-speaking Indian dynasty that ruled the Deccan region of India from the 12th to the 14th centuries. The dynasty was founded by Seunachandra Yadava in 1189 CE, and its capital was at Devagiri (modern-day Daulatabad). The Yadavas reached their peak under the rule of Ramachandra Devaraya (1271-1309 CE), who expanded the dynasty’s territory and built many temples and other monuments. The Yadavas declined after the death of Ramachandra Devaraya, and it was overthrown by the Delhi Sultanate in 1318 CE.