If P is a prime number and P divides $$\text{Q}^2$$​, then P will NOT necessarily divide:

Correct option is B

Solution:​
Option A: 3Q ​
Since P divides Q , it must also divide 3Q (as 3Q is a multiple of Q).

P divides 3Q .
Option B: Q + 1 
P divides Q, but there is no guarantee that P divides Q + 1.
Example: Let P = 3, Q = 6.
3 divides $$6^2 = 36$$​, and 3 divides 6 .
But 3 does not divide 6 + 1 = 7 .
P does not necessarily divide Q + 1 
Option C: $$2Q^2$$​​
Since P divides $$Q^2$$​ , it must also divide $$2Q^2$$​(as 2$$Q^2$$​ is a multiple of $$Q^2).$$​
P divides $$2Q^2$$​​
Option D: Q 
We already established that P divides Q.
 P divides Q 
Thus, P does not necessarily divide Q + 1.
Answer (B) Q + 1.