The correct answer is 4 because statement 4 is factually incorrect in the context of The Lyrical Ballads. Here's an explanation for each statement:
It carried only one ballad proper, which was Coleridge’s ‘The Rime of the Ancient Mariner’:
This is true. Coleridge's The Rime of the Ancient Mariner was the only ballad proper in the first edition of Lyrical Ballads (1798). Though the title suggests "ballads," the collection primarily contained other forms of poetry.
It also carried pastoral and other poems:
This is true. In addition to the ballad, Lyrical Ballads included a variety of other poetic forms, including pastoral poems and meditations on rural life, like Wordsworth’s Lines Composed a Few Miles Above Tintern Abbey.
It carried a ‘Preface’ which Wordsworth added in 1800:
This is true. Wordsworth added the famous Preface to the second edition of Lyrical Ballads in 1800. This preface is considered one of the most important documents in English literary criticism, outlining the principles of Romantic poetry.
It also printed from Gray’s ‘Elegy Written in a Country Churchyard’:
This is false, making it the correct choice. Thomas Gray's Elegy Written in a Country Churchyard (1751) was not included in Lyrical Ballads. Gray was a pre-Romantic poet, but his Elegy was not part of Wordsworth and Coleridge’s collection. This makes statement 4 incorrect.
Thus, statement 4 is the one that is not true, and that's why it is the correct answer.