Disparate (adjective)

1. Fundamentally distinct or different in kind; not comparable.
2. Comprising inherently unlike elements; incongruous.

Origin:

Late 16th century: from latin disparatus, from dis- (expressing negation) + parare 'prepare, arrange'.

Examples:

1. The two theories are disparate and cannot be reconciled.
2. The disparate elements of the painting created a chaotic and confusing image.
3. The disparate data points made it difficult to draw any meaningful conclusions.
4. The disparate groups of people were brought together by a shared goal.
5. The disparate cultures of the two countries made it challenging for them to find common ground.