Theory:

Nucleus:
The dense, spherical body found at the centre of the cytoplasm is known as the nucleus. It is an important component of the living cell. The nucleus can be seen with the help of a microscope after staining it.
The nucleus is separated from the cell's cytoplasm by a double-layered membrane known as the nuclear membrane. The nuclear membrane contains pores known as the nuclear pores and allows the movement of substances between the cytoplasm and the inside of the nucleus. The inside of the nucleus is jelly-like and is known as the nucleoplasm.
 
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Nucleus
 
When the nucleus is observed with a high magnification microscope, a small spherical structure known as the nucleolus is found. It is a structure that is involved in the synthesis of proteins and contains certain thread-like structures known as the chromosomes, including the deoxyribonucleic acid (DNA) in them. This DNA contains genes which help in inheritance or transfer of characters from the parents to the offspring. The chromosomes can be observed only when the cell divides.
The nucleus is known as the brain of the cell as it acts as the control centre of the cell's activities.
All the contents of the cell are together known as the protoplasm that includes the cytoplasm and the nucleus. Protoplasm is called the living substance of the cell.
Gene: 
The inheritance unit of all living organisms is the gene. It is the structure that controls the transfer of characteristics that are hereditary from the parents to offspring.
Example:
If your father has brown colour eyes, you may also have them, and if your mother has straight hair, you might even have straight hair. This is due to the combinations of the parents genes.
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DNA and gene