Concept:
The earliest dated standing image of the Buddha belongs to the Kushan period and was dedicated by the monk Bhikshu Bala. It is an outstanding example of the Mathura School of Art, which flourished under the Kushan rulers.
The sculpture is carved from the characteristic red spotted sandstone of Mathura and represents one of the earliest anthropomorphic images of the Buddha. Today, this important sculpture is preserved in the Government Museum (Museum of Archaeology), Mathura.
Step 1: Recall the location of the earliest standing Buddha image dedicated by Bhikshu Bala.
The sculpture is housed in the
\[
\boxed{\text{Museum of Archaeology, Mathura}}
\]
Step 2: Examine the given options.
• Madras Museum -- Houses important South Indian sculptures but not this image.
• Indian Museum, Calcutta -- Contains important Gandhara and Mathura sculptures but not the Bhikshu Bala standing Buddha.
• Museum of Archaeology, Mathura -- Correct; preserves the earliest standing Buddha image dedicated by Bhikshu Bala.
• Archaeological Museum, Sarnath -- Famous for Gupta-period Buddha images and the Lion Capital.
Hence,
\[
\boxed{\text{(C) Museum of Archaeology, Mathura}}
\]