The north pole of a bar magnet is rapidly introduced into a solenoid at one end (say A). Which of the following statements correctly depicts the phenomenon taking place? (a) No induced emf is developed.
(b) The end A of the solenoid behaves like a south pole.
(c) The end A of the solenoid behaves like north pole.
(d) The end A of the solenoid acquires positive potential.

The correct option is;

(b) The end A of the solenoid behaves like a north pole

Explanation:

According to Lenz's law we have that the induced emf direction in the solenoid due to the rapid introduction of the bar magnet will be such that the electric current induced will have a resultant magnet field that will  oppose to the movement of the north pole of the bar magnet that resulted in the magnetic field

Therefore, the opposing magnetic pole to the north pole of a magnet is a north pole and the solenoid end A will act like the north pole.

d.7.5cm is your answer

i think its c if i'm wrong