$\frac{105}{?}=19\times 6+27-{\left(8\right)}^2-\frac{112}{2}$

What value should come in place of (?) in the following questions?

The correct option is 5.

We need to find the value of the unknown quantity, represented by standard variable $x$ or $?$, in the given algebraic expression:

$\frac{105}{x}=19\times 6+27-{\left(8\right)}^2-\frac{112}{2}$

Let's break down the right-hand side of the equation step-by-step using the BODMAS/PEMDAS rule of operations.

Step 1: Simplify powers and divisions on the right side
Evaluate the square term: $8^2=64$
Evaluate the division term: $\frac{112}{2}=56$
Evaluate the multiplication term: $19\times 6=114$

Step 2: Substitute these values back into the right side of the equation

$\frac{105}{x}=114+27-64-56$

Step 3: Perform addition and subtraction from left to right
First, add: $114+27=141$
Then subtract 64: $141-64=77$
Finally, subtract 56: $77-56=21$

So the simplified equation becomes:

$\frac{105}{x}=21$

Step 4: Solve for $x$

$x=\frac{105}{21}$

$x=5$

Thus, the value that should replace the question mark (?) is 5.