GATE CS 2026 Set 1 Q.8: Data Interpretation and Graphs

For positive real numbers $S$ and $K$ , the function $H_K(S)$ is defined as:
$H_K(S) = \max(S - K, 0)$ . The $\max$ function is defined as:

\max(a, b) = \begin{cases} a, & \text{when } a > b \\ b, & \text{when } a \le b \end{cases}

The graph below shows the plot of a function $N(S)$ versus $S$ .

$N(S)$ can be expressed as _____.

$H_{10}(S) - H_{20}(S)$

$H_{10}(S) - 2H_{20}(S)$

$-H_{10}(S) + H_{20}(S)$

$H_{15}(S) - H_{20}(S)$

Official answer and solution

Solution

Evaluate each piecewise-linear combination of ramp functions $H_K(S) = \max(S - K, 0)$ over the intervals $[0, 10]$ , $[10, 20]$ , and $[20, 30]$ .

From the plot, $N(S)$ is defined piecewise by:

N(S) = \begin{cases} 0, & 0 \le S \le 10 \\ S - 10, & 10 < S \le 20 \\ 10, & S > 20 \end{cases}

Testing $H_{10}(S) - H_{20}(S) = \max(S - 10, 0) - \max(S - 20, 0)$ :

Thus $N(S) = H_{10}(S) - H_{20}(S)$ .

Final answer

Option (A)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 8 of 65
Section: General Aptitude

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