KCET · Maths · Linear Programming
If \( |x-2| \leq 1 \), then
- A \( \mathrm{x} \in[1,3] \)
- B \( \mathrm{x} \in(1,3) \)
- C \( x \in[-1,3) \)
- D \( x \in(-1,3) \)
Answer & Solution
Correct Answer
(A) \( \mathrm{x} \in[1,3] \)
Step-by-step Solution
Detailed explanation
Given that, \(|x-2| \leq 1\)
We know that, \(|x| \leq a \Rightarrow-a \leq x \leq a\)
So, \(-1 \leq x-2 \leq 1\)
\(\Rightarrow 1 \leq x \leq 3\)
Therefore \(x \in[1,3]\)
We know that, \(|x| \leq a \Rightarrow-a \leq x \leq a\)
So, \(-1 \leq x-2 \leq 1\)
\(\Rightarrow 1 \leq x \leq 3\)
Therefore \(x \in[1,3]\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The distance of the point \( (1,2,1) \) from the line \( \frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2} \) isKCET 2019 Easy
- If \(\mathrm{m}\) is the slope of one of the lines represented by \(a x^{2}+2 h x y+b^{2}=0\), then \((h+b m)^{2}\) is equal toKCET 2010 Hard
- If \([x]\) is the greatest integer function not greater than \(x\), then \(\int_0^8[x] d x\) is equal toKCET 2022 Medium
- The differential equation \(y \frac{d y}{d x}+x=\) crepresentsKCET 2008 Medium
- If \( f(x)=8 x^{2}, g(x)=x^{\frac{1}{3}} \) then \( f o g(x) \) isKCET 2017 Hard
- A sphere increases its volume at the rate of \(\pi \mathrm{cc} / \mathrm{s}\). The rate at which its surface area increases when the radius is \(1 \mathrm{~cm}\) isKCET 2011 Medium
More PYQs from KCET
- In zygote intrafallopian tube transfer, the embryo upto __________ stage is transferred into the fallopian tubeKCET 2025 Hard
- The degree of the differential equation \( \left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{2}=\frac{d^{2} y}{d x^{2}} \) isKCET 2017 Easy
- From which of the given plants is the drug whose skeletal structure is given below extracted?
KCET 2018 Easy - The percentage of \(s\)-character in the hybrid orbitals of nitrogen in \(\mathrm{NO}_{2}^{+}, \mathrm{NO}_{3}^{-}\)respectively areKCET 2020 Easy
- Which of the following statements are correct with reference to single slit diffraction pattern?KCET 2021 Easy
- The reagent which can do the conversion \(\mathrm{CH}_{3} \mathrm{COOH} \longrightarrow \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{OH}\) isKCET 2021 Easy