JEE Main 2020 — Functions Question with Solution
From: JEE Main 2020 (Online) 9th January Evening Slot
Question
Let a – 2b + c = 1.
If f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|, then:
If f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|, then:
Choose an option
Show full solutionCorrect option: A
Correct answer
Aƒ(50) = 1
Step-by-step explanation
R1 R1 + R3 – 2R2
f(x) = \left| {\matrix{ {a + c - 2b} & 0 & 0 \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|
= (a + c – 2b) ((x + 3)2 – (x + 2)(x + 4))
= x2 + 6x + 9 – x2 – 6x – 8 = 1
f(x) = 1
f(50) = 1
f(x) = \left| {\matrix{ {a + c - 2b} & 0 & 0 \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|
= (a + c – 2b) ((x + 3)2 – (x + 2)(x + 4))
= x2 + 6x + 9 – x2 – 6x – 8 = 1
f(x) = 1
f(50) = 1
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2020, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.