Correct statement about but-1,3-diene
A. Conjugated double bonds are present
B. Reacts with HBr
C. Forms polymer
D. All of these

Hint: But-1,3-diene has two pi-bonds. It can be regarded as the combination of two vinyl groups. Polybutadiene rubber is a polymer made by the polymerization of this compound.

Complete Step by Step Solution:
Hydrocarbons having two double bonds are called dienes.
Dienes are classified into three types depending on the location of double bonds.
1. Isolated dienes
2. Cumulated dienes
C. Conjugated dienes
But-1,3-diene is a conjugated diene. A single bond intervenes in two double bonds i.e., double bonds and single bonds are alternately arranged.
Its structure is as follows:

Image: 1,3-butadiene
So, A is correct.
The addition of HBr to 1,3-butadiene gives a mixture of 1,2 and 1,4 addition products.

Image: Addition of HBr to 1,3-butadiene
The mechanism is as follows:

Image: Mechanism of addition of HBr to 1,3-butadiene.
So, B is correct.
Polybutadiene rubber is a polymer created by the polymerization of this compound.
It is a synthetic rubber.
It is a polymer created from the polymerization of the monomer 1,3-butadiene.
The reaction happens as follows:

Image: Polymerization of 1,3-butadiene
So, C is correct.
As A, B and C are correct. So, D is correct.
So, option D is correct.

Note: The transformation of butadiene to synthetic rubbers is polymerization. It is a process by which small molecules or monomers are attached to give rise to large molecules called polymers leading to the formation of polybutadiene, which is very soft rubber.