Match the entries of Column I and Column II.
COLUMN - I
(A) For a particle moving in a circle
(B) For a particle moving in a straight line
(C) For a particle undergoing projectile motion with the angle of projection `alpha:0 lt alpha lt pi/2`
(D) For a particle moving in space
COLUMN - II
(P) The acceleration may be perpendicular to its velocity.
(Q) The acceleration may be in the direction of velocity
(R) The acceleration may be at some angle `theta(0 lt theta lt pi/2)` with the velocity.
(S) The acceleration may be opposite to its velocity.

Explanation

To match the entries of Column I with Column II, we need to analyze each case in Column I and determine which statements from Column II are applicable.

### Step-by-step Solution:

**Step 1: Analyze Column I Entry (A) - For a particle moving in a circle**
- In uniform circular motion, the acceleration (centripetal acceleration) is directed towards the center of the circle, which is perpendicular to the velocity.
- Therefore, the matching entry is **(P)**: The acceleration may be perpendicular to its velocity.
- In non-uniform circular motion, there can be tangential acceleration as well, which can create an angle with the velocity. Thus, the matching entry is also **(R)**: The acceleration may be at some angle \( \theta \) (where \( 0 < \theta < \pi/2 \)) with the velocity.
- The acceleration cannot be in the direction of the velocity or opposite to it in uniform circular motion. Thus, entries **(Q)** and **(S)** are not applicable.

**Conclusion for (A)**: Matches with **(P) and (R)**.

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**Step 2: Analyze Column I Entry (B) - For a particle moving in a straight line**
- If a particle is moving in a straight line, the acceleration can be in the same direction as the velocity, which corresponds to **(Q)**: The acceleration may be in the direction of velocity.
- The acceleration cannot be perpendicular to the velocity, as this would cause the particle to move in a circular path. Therefore, **(P)** is not applicable.
- The acceleration can also be opposite to the velocity, which corresponds to **(S)**: The acceleration may be opposite to its velocity (this is known as retardation).
- The acceleration cannot be at some angle with the velocity since the motion is constrained to a straight line. Thus, **(R)** is not applicable.

**Conclusion for (B)**: Matches with **(Q) and (S)**.

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**Step 3: Analyze Column I Entry (C) - For a particle undergoing projectile motion with angle of projection \( \alpha: 0 < \alpha < \pi/2 \)**
- At the highest point of projectile motion, the velocity is horizontal, and the acceleration due to gravity is vertical, making them perpendicular. Thus, it matches with **(P)**: The acceleration may be perpendicular to its velocity.
- At any other point in the trajectory, the velocity and acceleration are not in the same direction, but they can form an angle \( \theta \) (where \( 0 < \theta < \pi/2 \)). Thus, it matches with **(R)**: The acceleration may be at some angle \( \theta \) with the velocity.
- The acceleration is never in the direction of the velocity or opposite to it during projectile motion. Thus, **(Q)** and **(S)** are not applicable.

**Conclusion for (C)**: Matches with **(P) and (R)**.

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**Step 4: Analyze Column I Entry (D) - For a particle moving in space**
- In space, a particle can have acceleration in the direction of its velocity, matching with **(Q)**: The acceleration may be in the direction of velocity.
- The acceleration can also be opposite to the velocity, matching with **(S)**: The acceleration may be opposite to its velocity.
- The acceleration can be perpendicular to the velocity if the particle is given a sideways force, matching with **(P)**: The acceleration may be perpendicular to its velocity.
- Additionally, the acceleration can be at some angle with the velocity, matching with **(R)**: The acceleration may be at some angle \( \theta \) with the velocity.

**Conclusion for (D)**: Matches with **(P), (Q), (R), and (S)**.

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### Final Matching:
- **(A)** → **(P) and (R)**
- **(B)** → **(Q) and (S)**
- **(C)** → **(P) and (R)**
- **(D)** → **(P), (Q), (R), and (S)**