Step-by-step Solution:

Let's analyze each statement one by one:
(A) Ogive graph is used to measure the median of the collection of datas.
This statement is true. An `Ogive graph` (cumulative frequency curve) is specifically used to find the median of a dataset. The median corresponds to the point where the cumulative frequency reaches half of the total frequency.
(B) Two events \( A \) and \( B \) are such that \( P(A) = \frac{1}{2} \), \( P(B) = \frac{7}{12} \), and \( P(\text{not } A \text{ and not } B) = \frac{1}{4} \), then \( A \) and \( B \) are independent events.
To check if \( A \) and \( B \) are independent, we need to verify if: \[ P(A \cap B) = P(A) \cdot P(B) \] Given: \[ P(\text{not } A \text{ and not } B) = \frac{1}{4} \] This is equivalent to: \[ P(A^c \cap B^c) = \frac{1}{4} \] Using De Morgan's law: \[ P(A^c \cap B^c) = 1 - P(A \cup B) \] So: \[ 1 - P(A \cup B) = \frac{1}{4} \implies P(A \cup B) = \frac{3}{4} \] Now, using the inclusion-exclusion principle: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substitute the known values: \[ \frac{3}{4} = \frac{1}{2} + \frac{7}{12} - P(A \cap B) \] Solve for \( P(A \cap B) \): \[ P(A \cap B) = \frac{1}{2} + \frac{7}{12} - \frac{3}{4} = \frac{6}{12} + \frac{7}{12} - \frac{9}{12} = \frac{4}{12} = \frac{1}{3} \] Now, check if \( P(A \cap B) = P(A) \cdot P(B) \): \[ P(A) \cdot P(B) = \frac{1}{2} \cdot \frac{7}{12} = \frac{7}{24} \] Since \( \frac{1}{3} \neq \frac{7}{24} \), \( A \) and \( B \) are not independent. Thus, (B) is false.
(C) Relation for mean, mode and median is given by Mode \( = 3 \) Median - 2 Mean. This is a well-known empirical relationship for moderately skewed distributions. It is approximately true for many datasets. Thus, (C) is true.
(D) The number of two-digit even numbers formed from digits 1, 2, 3, 4, 5 is 10.
To form a two-digit even number, the last digit must be even. From the digits 1, 2, 3, 4, 5, the even digits are 2 and 4. For each choice of the last digit:
- If the last digit is 2, the first digit can be 1, 3, 4, or 5 (4 choices).
- If the last digit is 4, the first digit can be 1, 2, 3, or 5 (4 choices).
Total number of two-digit even numbers: \[ 4 + 4 = 8 \] Thus, (D) is false.