For you liquid = old, outdated tech and solid = deadly missile
But the truth is far from it. Read something about liquid propelled missiles and why rockets are liquid propelled and only cheap rockets are solid propelled.
Not true.
Liquid propelled missiles have much greater control. Its thrust can vary with time and can be increased or decreased or even be stopped in case the mission needs to be aborted.
True.
A solid booster once lit can not stop or change its course.
A booster rocket's, or booster stage's, job is to simply motivate the vehicle. It does not mean steerage mechanisms cannot be installed. It simply mean there is no need to steer the vehicle -- at this time.
Solid fuel can be throttled, not as responsive as liquid fuel, but its output can be modified once its
BURN properties are known, as shown below...
Launch of the Titan 3C Solid-Fuel Rocket
This mixture is in the long cylindical casings, strapped each side of the other three stages of the rocket. As it burns from the bottom up, the propellant is packed in different shapes. It gives a high thrust for the first 50 seconds after ignition and then, to reduce structural stress, burns more slowly after lift-off, giving about one-third of the original thrust for the rest of its total of about 2 minute duty.
A solid fuel rocket may be a stage of a larger vehicle, which can be composed of several rockets, or stages. A solid fuel rocket can contain several stages of its own composed of several shapes. Each shape is carefully studied as to its thrust output, from rise to fall. The sequencing of these shapes are important if the flight path itself contains phases. Each stage, or shape, will be ignited by the flame from the previous shape. Inter-stage, or inter-shape, points are where shut-off mechanisms can be installed, but like steerage mechanisms, shut-off devices can be unneeded. So why install them when weight is a penalty?
That is why the first stage of Prithvi is solid and the final stage is liquid propelled.
Your missiles are solid propelled because creating solid propelled missiles is easier and cheaper. Liquid propelled missiles are very complex to build and very expensive too.
At this point of the totality of the flight, to simply motivate the vehicle, a solid fuel first or boost stage is good enough. Once the vehicle is at a certain desired phase, that first or boost stage is nothing but useless weight so it is better to discard it. This begs the question of why would anyone want to use a liquid fuel stage after this...
Liquid-propellant rocket - Wikipedia, the free encyclopedia
The advantages and disadvantages of liquid fuel are clearly outlined. For the Prithvi, after boost stage discard, the vehicle would be clearly lightened so the superior throttling, or thrust varying capability, of this fuel would make a reasonable argument as to why it is used. But liquid fuel's maintenance requirements begs the question as to why would anyone want to burden field troops with increased technical tasks?