Which of the following sets are empty sets ?
(i) {`x:x^(2)=2` and x is a rational number}
(ii) {`x:x` is an integer neither positive nor negative}
(iii) {`x:x` is a boy student in a girls college}
(iv) {`x:xlt5` and also `x gt 5`}
(v) `{x:x` is a real number and `x^(2)lt0}`

Answer

To determine which of the given sets are empty sets, we will analyze each option step by step.

### Step 1: Analyze the first set
**Set (i):** {x : x² = 2 and x is a rational number}

- The equation x² = 2 has solutions x = ±√2.
- √2 is an irrational number.
- Since there are no rational solutions to this equation, the set is empty.

**Conclusion:** This set is an empty set.

### Step 2: Analyze the second set
**Set (ii):** {x : x is an integer neither positive nor negative}

- The only integer that is neither positive nor negative is 0.
- Therefore, this set contains the element 0.

**Conclusion:** This set is not an empty set.

### Step 3: Analyze the third set
**Set (iii):** {x : x is a boy student in a girls college}

- A girls college consists only of girl students.
- Hence, there cannot be any boy students in a girls college.

**Conclusion:** This set is an empty set.

### Step 4: Analyze the fourth set
**Set (iv):** {x : x < 5 and x > 5}

- It is impossible for a number to be both less than 5 and greater than 5 at the same time.
- Therefore, there are no elements that satisfy this condition.

**Conclusion:** This set is an empty set.

### Step 5: Analyze the fifth set
**Set (v):** {x : x is a real number and x² < 0}

- The square of any real number is always non-negative (x² ≥ 0).
- Therefore, there are no real numbers for which x² is less than 0.

**Conclusion:** This set is an empty set.

### Final Conclusion
The empty sets among the options are:
- Set (i)
- Set (iii)
- Set (iv)
- Set (v)

Thus, the empty sets are **1, 3, 4, and 5**.

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