The explanation for the correct option:

$1.$ Vitamins are the nutrients, which are required in trace amounts for the proper functioning and development of the body.

$2.$Vitamins are of two types, that is, water-soluble and fat-soluble vitamins.

$3.$ The vitamins, which are soluble in water are the water-soluble vitamins.

$4.$ There are 9 water-soluble vitamins, of which 8 comes under the vitamin B complex, and the remaining one is vitamin $C$.

$5.$ Thus, vitamin B is water-soluble, not fat-soluble.

The explanation for the incorrect options:

Option $A:$

$1.$ Vitamin A is a fat-soluble vitamin, which is involved in cellular communication, immune function, growth and development, and female and male reproduction.

$2.$ Fat-soluble vitamins are the vitamins, which are stored in the liver, fatty tissues, and muscles of the body.

Option $C:$

$1.$ Vitamin $D$ is also a fat-soluble vitamin.

$2.$ It assists in monitoring the amount of phosphate and calcium in the body.

$3.$ This vitamin is needed to keep the teeth, bones, and muscles healthy.

Option $D:$

$1.$ Vitamin $E$ is a fat-soluble vitamin, it exhibits many forms, of which alphatocopherol is the only one utilized by the body of humans.

$2.$ It acts as a powerful antioxidant and is required for cellular signaling and immune health in the body.