Statements (B), (C) and (D) are the accepted figures — option 2 — while (A) and (E) each state the opposite of the truth.

(A) is false, and the reason is instructive. Single-mode fibre is the less lossy of the two, reaching about 0.2 dB/km at 1550 nm against 2 to 3 dB/km for multimode. Its very small core carries the light almost entirely in the purest central region of the glass, and it suffers none of the mode-coupling and mode-dependent losses that a multimode core does. The common intuition — that a bigger core must be better — is exactly backwards.

(D) — the numerical aperture of step-index fibre.

\(NA=\sqrt{n_{1}^{2}-n_{2}^{2}}\)

For a multimode step-index fibre with a comparatively large index contrast this lies in the range 0.2 to 0.5, which is what allows an inexpensive LED to be coupled into it. The quoted band is the standard one.

(E) is false because the numbers are far too high. A graded-index fibre's NA is smaller than a step-index fibre's, typically about 0.2, and it varies across the core because the index does. A value approaching 0.99 would need an index contrast no glass fibre possesses — and since NA is a sine, values close to 1 imply an acceptance angle approaching 90°, which is physically absurd for a guided structure.

(C) — the "infinite bandwidth" claim, properly understood. Grading the index equalises the transit times of the different modes: rays taking the longer off-axis paths spend that extra distance in lower-index glass where they travel faster. For an ideal parabolic profile the compensation is exact to first order, so intermodal dispersion vanishes altogether and the theoretical bandwidth is unlimited. In practice profile errors and material dispersion cap it near 1 GHz·km — but the statement is about the theoretical limit, and in that sense it stands.

(B) — the 50 MHz figure is the conventional textbook value for the bandwidth-distance product of multimode step-index fibre, whose large intermodal dispersion of tens of nanoseconds per kilometre restricts it severely. It is the contrast with (C) that the question is drawing.

Hence, the correct statements are (B), (C) and (D).