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DNA molecule is a double stranded structure with two polynucleotide strands attached to each other by hydrogen bonding. According to the base pair rule, a pyrimidine joins a purine. Adenine and guanine are purines, while cytosine, thymine, and uracil are pyrimidines.

In a DNA, adenine base pairs with thymine, and guanine base pairs with cytosine. In RNA, adenine base pairs with uracil instead of thymine, while guanine base pairs with cytosine. 5鈥� to 3鈥� is the leading strand, while 3鈥� to 5鈥� is the lagging strand.

While drawing a DNA double helix using the given sequence, 5鈥�-AGCT-3鈥� with 5鈥�-TCGA-3鈥�, it looks like the following:

\(\begin{aligned}{l}5\prime - AGCT - 3\prime \\\,\,\,\,\,\,\,\,\,\, \downarrow \downarrow \downarrow \downarrow \\3' - \,AGCT\, - \,5'\end{aligned}\)

The purine cannot make a base pair with purines. Similarly, the pyrimidines cannot base pair with pyrimidines.

Thus, A cannot base-pair with A, G cannot base-pair with G, C cannot base-pair with C, and T cannot base-pair with T.

Therefore, the given statement is false.

If you try to match the two sequences 5鈥�-GCGC-3鈥� with 5鈥�-TATA-3鈥�, we will get the following:

\(\begin{aligned}{l}5\prime - GCGC - 3\prime {\rm{ }}\\\,\,\,\,\,\,\,\,\,\, \downarrow \downarrow \downarrow \downarrow \\3' - \,ATAT - 5'\end{aligned}\)

Here, G pairs with A and C pairs with T, which is incorrect according to the base-pairing rule. The base pairing occurs between A and T, G and C.

Thus, the sequence 5鈥�-GCGC-3鈥� with 5鈥�-TATA-3鈥�, could not form a short stretch of DNA double helix.

Therefore, the given statement is false.

Arranging the given sequence5鈥�-ATGC-3鈥� with 5鈥�-GCAT-3鈥� according to the DNA double helix, we get the following:

\(\begin{aligned}{l}5\prime - ATGC - 3\prime \\\,\,\,\,\,\,\,\,\,\, \downarrow \downarrow \downarrow \downarrow \\{\rm{ }}3' - TACG - 5'\end{aligned}\)

Here, A pairs with T, T pairs with A, G pairs with C, and C pairs with G. The base-pairing rule is correctly followed by this sequence where purines base pair with pyrimidines and vice versa.

Thus, the given sequence 5鈥�-ATGC-3鈥� with 5鈥�-GCAT-3鈥� could form a short stretch of DNA double helix.

Therefore, the given option is true.

The sequences given in options A and B cannot form DNA, while option C can be a DNA sequence.

Thus, all are not correct statements.

Therefore, the given statement is false.