# CAT Practice : Functions

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A perfect combo of combinatorics and Functions.

## Domain and Range

Q.7: How many elements are present in the domain of 9–xCx+1?
1. 5
2. 6
3. 4
4. 7

Choice B. 6

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## Detailed Solution

For nCr to be defined, we should have r greater than or equal to zero and, n greater than or equal to r.

Therefore 9 – x ≥ x + 1 or 4 ≥ x and

also x + 1 > 0 or x > –1

Therefore x takes on the values {–1,0,1,2,3,4}

Therefore domain = {–1,0,1,2,3,4} and range = {10C0,9C1,8C2,7C3,6C4,5C5}

There are 6 elements in the domain.

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Functions.