The correct answer is (d).
The first passenger train ran between Liverpool and Manchester on September 15, 1830. The train was operated by the Liverpool and Manchester Railway, and it was pulled by the locomotive Rocket. The Rocket was designed by George Stephenson, and it was the first locomotive to be built specifically for passenger service. The Liverpool and Manchester Railway was the first public railway in the world, and it was a major engineering feat. The railway was built to connect the two cities of Liverpool and Manchester, and it was a major factor in the Industrial Revolution.
The other options are incorrect.
(a) 1820: This is the year that the Stockton and Darlington Railway opened. The Stockton and Darlington Railway was the first public railway in the world, but it was a horse-drawn railway.
(b) 1825: This is the year that the Liverpool and Manchester Railway was chartered. However, the railway did not open until 1830.
(c) 1830: This is the year that the Liverpool and Manchester Railway opened. However, the first passenger train did not run on the railway until September 15, 1830.