In each of these questions, two equation (I) and (II) are given. You have to solve both the equations and give answer

$\begin{array}{ll}\text{I.}& 2x^2=338\\ \text{II.}& y=\sqrt{169}\end{array}$

The correct answer is If x ≤ y.

To compare the values of $x$ and $y$, let us solve both given equations step-by-step.

Step 1: Solve Equation (I) for $x$

The first equation is given as:

$2x^2=338$

Divide both sides of the equation by 2:

$x^2=\frac{338}{2}$

$x^2=169$

Taking the square root on both sides gives two possible values for $x$ (both positive and negative):

$x=\±\sqrt{169}$

$x=+13\text{ or }x=-13$

Step 2: Solve Equation (II) for $y$

The second equation is given as:

$y=\sqrt{169}$

The principal square root symbol ($\sqrt{}$) denotes only the non-negative real root. Therefore:

$y=13$

Step 3: Compare the values of $x$ and $y$

1. When $x=13$ and $y=13$: here, $x=y$.

2. When $x=-13$ and $y=13$: here, $x<y$.

Combining both cases, we get $x\le y$.