Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Functions

NDA 2024 · Mathematics · Functions

Let z=[y] and y=[x]-x , where [.] is the greatest integer function....

Let z=[y]z=[y] and y=[x]−xy=[x]-x, where [.] is the greatest integer function. If xx is not an integer but positive, then what is the value of zz ?

Options

  1. A−1-1
  2. B00
  3. C11
  4. D22

Correct answer

A. −1-1

Step-by-step solution

We know, {x}+[x]=x⇒x−[x]={x}\{x\}+[x]=x \Rightarrow x-[x]=\{x\} (where {x}\{x\} is fractional port of x.) 0≤x−[x]<1(∵0≤{x}<L)0 \leq x-[x] < 1 \quad(\because 0 \leq\{x\} < L)−1<[x]−x≤0−1<y<0∴[y]=−1\begin{aligned} & -1 < [x]-x \leq 0 \\ & -1 < y < 0 \\ & \therefore \quad[y]=-1\end{aligned}$$
Practice Functions on Quantrex Academy →

More from Functions

Consider the following statements in respect of the function f(x)=x in the interval… NDA 2026Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of… NDA 2026If 2f(x)+f(1-x)=x , then what is f(x) equal to ? NDA 2026For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| .… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs