Verified Solution • 2025–26 Session moderate

QJEEM20Ma37a0: JEE Main 2020 Mathematics - Class 12 JEEM20Ma37a0 Solution: If a + x = b + y = c + z + 1, where a, b, c, x, y, z are…

If a + x = b + y = c + z + 1, where a, b, c, x, y, z
are non-zero distinct real numbers, then
|xa+yx+ayb+yy+bzc+yz+c| is equal to :

Multiple Choice Options

  • A y(b – a)
  • B y(a – b)
  • C y(a – c)
  • D 0

Step-by-Step Verified Solution

|xa+yx+ayb+yy+bzc+yz+c|

C3 → C3 – C1

= |xa+yayb+ybzc+yc|

C2 → C2 – C3

= |xyayybzyc|

R3 → R3 – R1, R2 → R2 – R1

= |xyay−x0b−az−x0c−a|

= (–y)[(y – x) (c – a) – (b – a) (z – x)]

Given, a + x = b + y = c + z + 1

= (–y)[(a – b) (c – a) + (a – b) (a – c – 1)]

= (–y)[(a – b) (c – a) + (a – b) (a – c) + b – a)

= –y(b – a) = y(a – b)

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