The question asks for operations that induce a shuffle and return a new DataFrame with updated partitions.

• A. coalesce(): Reduces partitions without a shuffle (merges existing partitions), so it does not induce a shuffle.
• B. rdd.getNumPartitions(): Retrieves the partition count but does not modify the DataFrame or trigger a shuffle.
• C. repartition(): Always induces a shuffle to redistribute data and creates a new DataFrame with the specified number of partitions.
• D. union(): Combines DataFrames by appending rows, which does not require a shuffle (partitions are concatenated).
• E. intersect(): Requires a shuffle to compare rows across all partitions and find common elements, resulting in a new partitioned DataFrame.

Thus, C and E are correct as they involve shuffling and produce new partitions.