The treatment of the bacterial cell with divalent cations leads to

The correct answer is Option (4) → Increased efficiency with which DNA enters the bacterium

DNA is hydrophilic, so it cannot pass through the cell membrane on its own. A bacterium must first be made competent, that is, able to take up DNA.

Option (1) Increase in hydrophilic nature of DNA molecule — Incorrect. The cation treats the bacterial cell, not the DNA. DNA is already hydrophilic, and that is the very reason it cannot cross the membrane.

Option (2) Decreases efficiency with which DNA enters the bacterium — Incorrect. This states the effect backwards. The treatment is done to let more DNA in.

Option (3) Change in permeability of cell wall — Incorrect. The DNA does pass through pores in the cell wall, but the effect the book names is a higher efficiency of DNA entry. A loose phrase about the wall does not state it.

Option (4) Increased efficiency with which DNA enters the bacterium — Correct. Treating the cells with a divalent cation such as calcium makes them competent. After this, recombinant DNA is forced in by a heat shock at 42°C.

NCERT Extract:
Cloning Vectors – “… Recombinant DNA) Since DNA is a hydrophilic molecule, it cannot pass through cell membranes. Why? In order to force bacteria to take up the plasmid, the bacterial cells must first be made ‘competent’ to take up DNA. This is done by treating them with a specific concentration of a divalent cation, such as calcium, which increases the efficiency with which DNA enters the bacterium through pores in its cell wall.”