QJEEM20Macf52: JEE Main 2020 Mathematics - Class 11 JEEM20Macf52 Solution: Let a – 2b + c = 1. If f ( x ) =

Question

Verified Solution • 2025–26 Session moderate

Let a – 2b + c = 1.

If

f (x) = | \begin{matrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix} |

, then:

Accepted Answer

R₁

\to

R₁ + R₃ – 2R₂

f(x) =

| \begin{matrix} a + c - 2 b & 0 & 0 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix} |

= (a + c – 2b) ((x + 3)² – (x + 2)(x + 4))

= x² + 6x + 9 – x² – 6x – 8 = 1

∴

f(x) = 1

\Rightarrow

f(50) = 1

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