Statement-1 : The plane 5x + 2z - 8 = 0 contains the line 2x - y + z - 3= 0 and 3x + y + z = 5, and is perpendicular to 2x - y - 5z - 3 = 0.

Statement-2 : The plane 3x + y + z = 5 meets the line x-1 = y + 1 = z - 1 at the point (1, 1, 1).

Statement 1 is True, Statement 2 is False.

The equation of the family of planes containing the line 2x - y + z - 3 = 0, 3x + y + z = 5 is

$2x - y + z - 3 + λ (3x + y + z - 5 ) = 0 $

For $ λ = 1,$ this reduces to 5x + 2z - 8 = 0

So, the plane 5x + 2z - 8 = 0 contains the given line.

Also, $ 2 × 5 - 1 × 0 - 5 ×2 = 0 $

So, the plane 5x + 2z - 8 = 0 is perpendicular to 

2x - y - 5z  - 3 = 0.

Hence, statement-1 is true.

The coordinates of any point on line $\frac{x-1}{1}=\frac{y+1}{1}=\frac{z-1}{1}$ are (r + 1 , r-1, r+1).

If this point lies on the plane 3x + y + z = 5. Then,

$3r + 3 + r - 1 + r + 1 = 5 ⇒ r = \frac{2}{5}$

Thus, the line meets the plane at $\left(\frac{7}{5}, -\frac{3}{5}, \frac{7}{5}\right)$.

So, statement-2 is not true.