Step 1: Understanding the Question.
This question specifically says growth "in Indian Rupees", which means we need the actual rupee amount by which each commodity's export value rose from 2004-05 to 2005-06, not the percentage rate of growth. A commodity with a small base can show a huge percentage jump while adding very little in rupee terms, so we must compute rupee values directly.
Step 2: Convert weight percentages to rupee values.
Total Exports were Rs. 375339.53 crore in 2004-05 and Rs. 454799.97 crore in 2005-06.
Petroleum products: \(8.57\% \times 375339.53 = 32166.6\) crore in 2004-05, and \(11.21\% \times 454799.97 = 50983.1\) crore in 2005-06. Increase \(= 50983.1 - 32166.6 = 18816.5\) crore.
Project goods: \(0.06\% \times 375339.53 = 225.2\) crore in 2004-05, and \(0.13\% \times 454799.97 = 591.2\) crore in 2005-06. Increase \(= 366.0\) crore.
Ores and minerals: \(5.29\% \times 375339.53 = 19855.5\) crore in 2004-05, and \(6.02\% \times 454799.97 = 27379.0\) crore in 2005-06. Increase \(= 7523.5\) crore.
Sports goods: \(0.12\% \times 375339.53 = 450.4\) crore in 2004-05, and \(0.13\% \times 454799.97 = 591.2\) crore in 2005-06. Increase \(= 140.8\) crore.
Step 3: Compare the increases.
Petroleum products added about Rs. 18816.5 crore, far ahead of ores and minerals (about Rs. 7523.5 crore), project goods (about Rs. 366.0 crore) and sports goods (about Rs. 140.8 crore). If we also check the other commodities in the table, none comes close to petroleum products in absolute rupee increase, even commodities like textiles and engineering goods, whose bigger base still gives them a smaller jump than petroleum products' near-doubling weight share. So the answer is not "None of the above"; petroleum products genuinely has the largest rupee increase among all commodities.
Step 4: Why the other options fail.
Project goods and sports goods have tiny weight shares, so even a large percentage jump adds only a small rupee amount. Ores and minerals grew fast in percentage terms too but from a smaller base than petroleum products, so its rupee increase is less than half of petroleum products' increase.
Final Answer:
Petroleum products witnessed the maximum growth in exports, in Indian Rupees, in 2005-06 over 2004-05.
\[ \boxed{\text{petroleum products}} \]