GATE CS 2023 Q10 — General Aptitude

To determine the correct transformations, let us analyze the changes in orientation from figure $\mathbf{P}$ to $\mathbf{Q}$, and then from $\mathbf{Q}$ to $\mathbf{R}$:

1. Step 1: Transformation from $\mathbf{P}$ to $\mathbf{Q}$ (Operation 1)
   • Observe the orientation of the main features in $\mathbf{P}$. The long straight edge of the figure is initially vertical.
   • In figure $\mathbf{Q}$, this long edge has become horizontal, and the protruding elements have rotated to point downwards.
   • This corresponds to a clockwise rotation by $90^{\circ}$ about an axis perpendicular to the plane of the figure.
   • This eliminates options B and D.
2. Step 2: Transformation from $\mathbf{Q}$ to $\mathbf{R}$ (Operation 2)
   • Comparing $\mathbf{Q}$ and $\mathbf{R}$, we see that the left-to-right orientation of the features remains identical.
   • However, the top-to-bottom orientation is inverted (the parts pointing downwards in $\mathbf{Q}$ are pointing upwards in $\mathbf{R}$).
   • An inversion along the vertical axis (top-to-bottom flip) is achieved by a reflection along a horizontal line.
   • A reflection along a vertical line would have flipped the left and right sides, which is not the case here. This eliminates option C.

Thus, the correct sequence of operations is a clockwise rotation by $90^{\circ}$ followed by a reflection along a horizontal line.