Comprehension:
The following questions are based on the information given below:
In a school of 4000 students 3000 know English, 2000 know French and 500 know Hindi, 1500 know French and English, 300 know French and Hindi, 200 know English and Hindi and 50 know all the three languages.
How many do not know any of the three languages?

Options

A. A.500
B. B.450
C. C.550
D. D.600

Answer

To solve the problem, we will use the principle of inclusion-exclusion.

### Step-by-Step Solution:

1. **Identify the total number of students and the number of students knowing each language:**
- Total students (U) = 4000
- Students knowing English (E) = 3000
- Students knowing French (F) = 2000
- Students knowing Hindi (H) = 500

2. **Identify the number of students knowing combinations of languages:**
- Students knowing both French and English (F ∩ E) = 1500
- Students knowing both French and Hindi (F ∩ H) = 300
- Students knowing both English and Hindi (E ∩ H) = 200
- Students knowing all three languages (E ∩ F ∩ H) = 50

3. **Apply the principle of inclusion-exclusion to find the total number of students knowing at least one language:**
\[ n(E \cup F \cup H) = n(E) + n(F) + n(H) - n(E \cap F) - n(F \cap H) - n(E \cap H) + n(E \cap F \cap H) \]

Plugging in the values:
\[ n(E \cup F \cup H) = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 \]

4. **Calculate the total:**
\[ n(E \cup F \cup H) = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 \]
\[ = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 \]
\[ = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 \]
\[ = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 = 3550 \]

5. **Find the number of students who do not know any of the three languages:**
\[ \text{Students not knowing any language} = U - n(E \cup F \cup H) \]
\[ = 4000 - 3550 = 450 \]

### Final Answer:
The number of students who do not know any of the three languages is **450**.