Read the statements carefully and write 'T' for true and 'F' for false.
(a) Two parallelograms on the same base and between the same parallel lines are of unequal areas.
(b) The ratio of area of rectangle and a triangle having the same base and between the same parallel is 2 : 1
(c ) The area of a parallelogram is the product of its base and the corresponding altitude.

Options

A. `{:(""(a),(b),(c)),(F,T,F):}`
B. `{:(""(a),(b),(c)),(T,T,T):}`
C. `{:(""(a),(b),(c)),(T,F,T):}`
D. `{:(""(a),(b),(c)),(F,T,T):}`

Explanation

To solve the question, we will evaluate each statement one by one and determine whether it is true (T) or false (F).

### Step-by-step Solution:

1. **Statement (a)**: "Two parallelograms on the same base and between the same parallel lines are of unequal areas."
- **Analysis**: If two parallelograms share the same base and are between the same parallel lines, they must have the same height. The area of a parallelogram is calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]
Since both parallelograms have the same base and height, their areas will be equal.
- **Conclusion**: This statement is **False (F)**.

2. **Statement (b)**: "The ratio of area of rectangle and a triangle having the same base and between the same parallel lines is 2:1."
- **Analysis**: The area of a rectangle is given by:
\[ \text{Area}_{\text{rectangle}} = \text{Base} \times \text{Height} \]
The area of a triangle with the same base and height is:
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Therefore, the ratio of the area of the rectangle to the area of the triangle is:
\[ \text{Ratio} = \frac{\text{Area}_{\text{rectangle}}}{\text{Area}_{\text{triangle}}} = \frac{\text{Base} \times \text{Height}}{\frac{1}{2} \times \text{Base} \times \text{Height}} = 2:1 \]
- **Conclusion**: This statement is **True (T)**.

3. **Statement (c)**: "The area of a parallelogram is the product of its base and the corresponding altitude."
- **Analysis**: The area of a parallelogram is indeed calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]
where the height is the perpendicular distance from the base to the opposite side (altitude).
- **Conclusion**: This statement is **True (T)**.

### Final Answers:
- (a) F
- (b) T
- (c) T