Read the following information carefully to answer the questions that follow.
In a survey of 25 students, it was found that 15 have taken Mathematics. 12 have taken Physics and 11 taken Chemistry, 5 have taken Mathematics and Chemistry, 9 have taken Mathematics and Physics, 4 have taken Physics and Chemistry and 3 have taken all the three subjects.
The number of students who have taken only Physics, is
(a)2
(b)3
(c)5
(d)6

Options

A. 2
B. 3
C. 5
D. 6

Answer

To solve the problem, we will use the information provided to find the number of students who have taken only Physics. We will use a Venn diagram approach to visualize the relationships between the subjects.

### Step-by-Step Solution:

1. **Identify the total number of students and the number of students in each subject:**
- Total students surveyed = 25
- Students taking Mathematics (M) = 15
- Students taking Physics (P) = 12
- Students taking Chemistry (C) = 11

2. **Identify the number of students taking combinations of subjects:**
- Students taking both Mathematics and Chemistry (M ∩ C) = 5
- Students taking both Mathematics and Physics (M ∩ P) = 9
- Students taking both Physics and Chemistry (P ∩ C) = 4
- Students taking all three subjects (M ∩ P ∩ C) = 3

3. **Calculate the number of students taking only two subjects:**
- Students taking only Mathematics and Chemistry (M ∩ C) but not Physics:
\[ (M \cap C) - (M \cap P \cap C) = 5 - 3 = 2 \]
- Students taking only Mathematics and Physics (M ∩ P) but not Chemistry:
\[ (M \cap P) - (M \cap P \cap C) = 9 - 3 = 6 \]
- Students taking only Physics and Chemistry (P ∩ C) but not Mathematics:
\[ (P \cap C) - (M \cap P \cap C) = 4 - 3 = 1 \]

4. **Calculate the total number of students taking Physics:**
- Total students taking Physics = 12
- We have already accounted for:
- Students taking only Physics and Chemistry = 1
- Students taking only Mathematics and Physics = 6
- Students taking all three subjects = 3
- Therefore, the number of students taking only Physics:
\[ \text{Only Physics} = \text{Total Physics} - (\text{Only Physics and Chemistry} + \text{Only Mathematics and Physics} + \text{All three subjects}) \]
\[ = 12 - (1 + 6 + 3) = 12 - 10 = 2 \]

5. **Conclusion:**
- The number of students who have taken only Physics is **2**.

### Final Answer:
The number of students who have taken only Physics is **(a) 2**.