The correct answer is (a) keep both l and d constant.

Explanation:
When a strong current is passed through a solenoid, there are two main factors that determine the behavior of the solenoid: the magnetic field produced by the current and the mechanical forces acting on the solenoid.

1. Magnetic Field:
When a current flows through a wire, it creates a magnetic field around the wire. In a solenoid, the wire is wound in the form of a tightly packed coil, resulting in a strong and uniform magnetic field along the axis of the solenoid. This magnetic field is essential for various applications of solenoids, such as electromagnets and inductors.

2. Mechanical Forces:
When a current is passed through a solenoid, mechanical forces are generated due to the interaction between the magnetic field and the current-carrying wire. These forces tend to compress or expand the solenoid along its length and diameter.

Based on these factors, let's analyze the options given:

a. Keep both l and d constant:
When a strong current is passed through the solenoid, the magnetic field is generated, but there are no external forces acting on the solenoid to change its length or diameter. Therefore, both l (length) and d (diameter) remain constant.

b. Decrease both l and d:
This option is incorrect because there are no external forces acting on the solenoid to decrease its length or diameter.

c. Increase both l and d:
This option is incorrect because there are no external forces acting on the solenoid to increase its length or diameter.

d. Decrease l but increase d:
This option is also incorrect because there are no external forces acting on the solenoid to change its length or diameter.

In conclusion, when a strong current is passed through a solenoid, it tends to keep both the length (l) and diameter (d) of the solenoid constant. The magnetic field produced by the current is the main factor influencing the behavior of the solenoid, while there are no external forces that act to change its dimensions.