The question is about Domain and Range. A question which combines combinatorics with functions. We need to find out the range and domain of the given function which is defined as combination of two variables. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 6: How many elements are present in the domain of ^{9–x}C_{x+1}?

- 5
- 6
- 4
- 7

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For ^{n}C_{r} 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 = {^{10}C_{0},^{9}C_{1},^{8}C_{2},^{7}C_{3},^{6}C_{4},^{5}C_{5}}

There are 6 elements in the domain.

The question is **"How many elements are present in the domain of ^{9–x}C_{x+1}? "**

Choice B is the correct answer.

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