A word has been given in the question and used in the sentences below. Identify the statements where the word has been used in a contextually and grammatically correct manner.

BORNE OUT

(A) His claims were borne out by the evidence presented during the investigation.

(B) The heavy weight was too much to be borne out by the fragile wooden shelf.

(C) Her success was borne out of years of hard work and consistent effort.

To determine the correct usage of the phrasal verb "borne out", let us analyze its meaning and look at each sentence individually.

The phrasal verb "bear out" (past participle: "borne out") means to support, confirm, or verify a statement, claim, or theory.

Analysis of Statement (A):
"His claims were borne out by the evidence presented during the investigation."
Here, "borne out" is used to mean that the evidence confirmed or supported his claims. This is grammatically and contextually correct.

Analysis of Statement (B):
"The heavy weight was too much to be borne out by the fragile wooden shelf."
In this context, the sentence refers to carrying or supporting physical weight. The correct verb to use here is simply the passive form of bear, which is "borne" (e.g., "borne by the fragile wooden shelf"). Adding the particle "out" is incorrect in this physical weight context.

Analysis of Statement (C):
"Her success was borne out of years of hard work and consistent effort."
This sentence refers to something originating from or being a result of something else. The correct expression for origin or birth is "born of" or "born out of" (spelled without the 'e' at the end of born). Thus, "borne out of" is grammatically incorrect in this context.

Therefore, only statement (A) uses the phrase correctly.