Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Functions

NDA 2023 · Mathematics · Functions

Paragraph: Consider the function f(x)=|x-2|+|3-x|+|4-x| , where x ∈...

Paragraph: Consider the function f(x)=∣x−2∣+∣3−x∣+∣4−x∣f(x)=|x-2|+|3-x|+|4-x|, where x∈Rx \in \mathbb{R}
Question: At what value of xx does the function attain minimum value?

Options

  1. A22
  2. B33
  3. C44
  4. D00

Correct answer

B. 33

Step-by-step solution

f(x)=∣x−2∣+∣3−x∣+∣4−x∣f(2)=0+1+2=3f(3)=1+0+1=2f(4)=2+1+0=3f(0)=2+3+4=9∴x=3f(x)=|x-2|+|3-x|+|4-x|f(2)=0+1+2=3f(3)=1+0+1=2f(4)=2+1+0=3f(0)=2+3+4=9\therefore \quad x=3 is correct.
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