Step 1: Recall the working definition of a chute spillway: it is a spillway that carries the discharge down a steep slope through an open, lined channel (a chute or trough), instead of letting the water fall freely off a vertical or near vertical face as in an ordinary overfall (free-fall) spillway. Statement (I) restates this definition correctly, so (I) is correct.
Step 2: Now examine statement (II), which compares chutes with a series of drop structures on steep terrain. A chute spillway is essentially one continuous lined channel, so it needs only one set of energy dissipation works, typically a stilling basin at the toe. A series of drop structures instead needs a separate structure, foundation and stilling arrangement at every drop, which multiplies construction and maintenance cost on a steep slope. So chutes genuinely work out more economical in that situation, making (II) correct as well.
Step 3: Since both the physical description in (I) and the economic comparison in (II) match accepted hydraulic structures theory, both statements are correct together, matching option 1.