CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

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–xC_x+1?

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

Video Explanation

Explanatory Answer

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

For ⁿC_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 = {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–xC_x+1? "

Hence the answer is "6"

Choice B is the correct answer.