Choose the correct answer from the options given below:

Series A Analysis:

Looking for the pattern in the given numbers:

$\frac{2 \times 3 \times 4 \times 5}{10} = \frac{120}{10} = 12$

$\frac{5 \times 6 \times 3 \times 2}{10} = \frac{180}{10} = 18$

Applying the same pattern:

$\frac{5 \times 2 \times 9 \times 2}{10} = \frac{180}{10} = 18$

Missing number: $18$

---

Series B Analysis:

Pattern: $(\text{first} \times \text{second}) + (\text{third} \times \text{fourth}) = \text{result}$

Checking: $(2 \times 5) + (1 \times 3) = 10 + 3 = 13$

Checking: $(5 \times 1) + (4 \times 3) = 5 + 12 = 17$

Applying pattern:

$(5 \times 1) + (4 \times 6) = 5 + 24 = 29$

Missing number: $29$

---

Series C Analysis:

Pattern: $(\text{first} - \text{second}) \times (\text{third} - \text{fourth}) = \text{result}$

Checking: $(15 - 8) \times (10 - 8) = 7 \times 2 = 14$

Checking: $(9 - 5) \times (8 - 6) = 4 \times 2 = 8$

Applying pattern:

$(11 - 8) \times (6 - 4) = 3 \times 2 = 6$

Missing number: $6$

---

Series D Analysis:

Pattern: $(\text{first} \times \text{second}) - (\text{third} \times \text{fourth}) = \text{result}$

Checking: $(7 \times 4) - (5 \times 3) = 28 - 15 = 13$

Checking: $(8 \times 4) - (9 \times 3) = 32 - 27 = 5$

Applying pattern:

$(9 \times 4) - (8 \times 3) = 36 - 24 = 12$

Missing number: $12$

---

Matching the results:

Series A: $18$ → Match with option IV

Series B: $29$ → Match with option III

Series C: $6$ → Match with option I

Series D: $12$ → Match with option II

The correct option is Option 4.