Concept:
Phenolphthalein is one of the most widely used acid–base indicators in titrations. To answer this, you simply need to recall the pH range over which it changes colour, which is a standard value worth memorising.
Step 1: An indicator changes colour over a particular range of pH. For phenolphthalein, this transition range is about pH 8.3 to 10.0. Below this range it is colourless (in acidic solution) and above it turns pink/magenta (in basic solution).
Step 2: Because it changes colour on the slightly basic side, phenolphthalein is ideal for titrating a weak acid with a strong base, where the endpoint falls in the basic region.
Step 3: The other ranges given belong to different indicators — for example, methyl orange changes around pH 3.1–4.4 and works in the acidic region. So the correct range for phenolphthalein is 8.3–10.0.
Answer: Option (4) — 8.3–10.0.