What will come in the place of the question mark ‘?’ in the following question?

${\left(66\right)}^2-{\left(34\right)}^2+{?}^2={\left(60\right)}^2$

The correct option is 20.

To find the value that comes in place of the question mark ‘?’, we start with the given algebraic equation:

${\left(66\right)}^2-{\left(34\right)}^2+{?}^2={\left(60\right)}^2$

We can use the algebraic identity for the difference of two squares, $a^2-b^2=(a+b)(a-b)$, to simplify the term ${\left(66\right)}^2-{\left(34\right)}^2$:

${\left(66\right)}^2-{\left(34\right)}^2=(66+34)(66-34)$

Calculating the values inside the brackets:

$66+34=100$

$66-34=32$

So,

${\left(66\right)}^2-{\left(34\right)}^2=100\times 32=3200$

Now, calculate the right-hand side of the equation:

${\left(60\right)}^2=3600$

Substitute these values back into the main equation:

$3200+{?}^2=3600$

Subtract 3200 from both sides to solve for ${?}^2$:

${?}^2=3600-3200$

${?}^2=400$

Taking the square root on both sides:

$?=\sqrt{400}=20$

Thus, the value of ‘?’ is 20.