Correct Option
Assertion (A) is true. Dara Shikoh, the eldest son of Emperor Shahjahan, was indeed appointed to lead military expeditions to Balkh, Badakhshan, and Qandahar. These campaigns were undertaken by Shahjahan between 1647 and 1652 CE as part of his policy to reclaim ancestral Mughal territories in Central Asia and to secure the northwestern frontier against the Safavids.
Reason (R) is false. The expeditions sent by Shahjahan to these regions were not a "marvelous success."
- The Mughal attempts to recapture Qandahar from the Safavids, despite significant efforts and resources, were unsuccessful, leading to its permanent loss to the Safavids in 1649.
- The campaigns in Balkh and Badakhshan were militarily and financially burdensome, resulting in heavy casualties and an eventual retreat without achieving lasting territorial or strategic gains.
Therefore, Assertion (A) is true, but Reason (R) is false.
Incorrect Options
Options 1, 2, and 4 are incorrect because Reason (R) is factually false. The expeditions to Balkh, Badakhshan, and Qandahar during Shahjahan's reign are historically documented as failures, marked by substantial expenditure, military setbacks, and the permanent loss of Qandahar. Consequently, any option that states R is true or that R provides a correct explanation for A cannot be correct.