A mixture of three DNA fragments, X (large), Y (medium) and Z (small)…

The correct answer is Option (3) → Z lies farthest from the well, towards the anode.

Two facts settle this question. First, DNA fragments are negatively charged, so they all move away from the well towards the anode (the positive electrode). Second, the agarose gel works as a sieve, so the smaller the fragment, the farther it moves. The small fragment Z therefore travels farthest towards the anode, and the large fragment X stays nearest the well.

Option (1) X lies farthest from the well, towards the anode. — Incorrect. X is the largest fragment. The gel holds it back the most, so it stays closest to the well, not farthest.

Option (2) Z lies farthest from the well, towards the cathode. — Incorrect. Z does move farthest, but DNA moves towards the anode. Being negatively charged, it cannot move towards the cathode.

Option (3) Z lies farthest from the well, towards the anode. — Correct. The smallest fragment, Z, moves the farthest from the well, towards the anode.

Option (4) X, Y and Z stay together, as all of them carry a negative charge. — Incorrect. The same charge is what makes all three move in one direction, but the sieving effect of the gel makes them move at different speeds, so they separate.

NCERT Extract:
Restriction Enzymes – “… Since DNA fragments are negatively charged molecules they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. Nowadays the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel. Hence, the smaller the fragment size, the farther it moves.”

Figure 9.3 A typical agarose gel electrophoresis showing migration of undigested (lane 1) and digested set of DNA fragments (lane 2 to 4)