Cubic parabola is the type of transition curve that is mostly used in Indian Railways.

Explanation:
A transition curve is a curve that is introduced between a straight and a circular curve in railway tracks. It helps in the smooth transition from a straight track to a curved track, reducing the abrupt change in direction and providing a more comfortable ride for passengers.

Types of Transition Curves:
There are various types of transition curves used in railway engineering, such as:

1. Spinal Curve: This type of curve is rarely used in practice and is not commonly found in Indian Railways. It is a mathematical curve that is difficult to lay out and does not provide a smooth transition.

2. Parabolic Curve: This curve is defined by a parabolic equation and is commonly used in many countries. However, in Indian Railways, it is not widely used due to its limitations in terms of flexibility and ease of laying out.

3. Cubic Parabola: This is the most commonly used type of transition curve in Indian Railways. It is defined by a cubic equation and provides a smooth and easy transition from a straight track to a curved track. It has the advantage of being flexible and easy to lay out, making it suitable for the diverse terrains and varying radius of curves in the Indian railway network.

4. Lemniscate Curve: This curve is rarely used in practice and is not commonly found in Indian Railways. It is a closed loop curve with a shape resembling the numeral "8". It is difficult to lay out and does not provide a smooth transition.

Conclusion:
In conclusion, the type of transition curve that is mostly used in Indian Railways is the cubic parabola. It provides a smooth and easy transition from a straight track to a curved track, making it suitable for the diverse terrains and varying radius of curves in the Indian railway network.