A clock is so placed that at 12 noon its minute hand points towards…

To determine the direction of the hour hand at 1:30 p.m., we must first calculate the rotation applied to the clock face.

Step-by-Step Analysis
Determine the Clock's Rotation:

Normally, at 12:00 noon, the minute hand points North.

In this scenario, the minute hand points North-East.

North-East is a 45-degree clockwise rotation from North. Therefore, the entire clock has been rotated 45 degrees clockwise.

Determine the Hour Hand's Position at 1:30 p.m.:

On a standard clock, the hour hand at 1:30 is halfway between the 1 and 2 marks.

Each hour mark represents 30 degrees (360 degrees / 12 hours).

At 1:00, the hour hand is at 30 degrees from the vertical (North). At 1:30, it has moved halfway to the 2 o'clock mark (an additional 15 degrees).

Standard position = 30 degrees + 15 degrees = 45 degrees East of North.

Apply the Clock's Rotation:

Since the clock is rotated 45 degrees clockwise, we add this rotation to the standard position.

Total direction = 45 degrees (standard position) + 45 degrees (clock rotation) = 90 degrees from North.

90 degrees from North is East.