CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

CAT Questions | Algebra | Functions - Domain and Range

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–xCx+1?

  1. 5
  2. 6
  3. 4
  4. 7

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: A perfect combo of combinatorics and Functions.

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.

The question is "How many elements are present in the domain of 9–xCx+1? "

Hence the answer is "6"

Choice B is the correct answer.


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