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GATE 2026 CS (CS1) – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly 15 credits of core courses and exactly 20 credits of project. In addition, a student has to enroll for a minimum of 10 credits of specialization courses. The maximum credits of elective courses that a student can enroll for is ______

  1. 10
  2. 15
  3. 20
  4. 25

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Correct answer: (D) 25

Explanation

Let the credits enrolled for core courses, project, specialization courses, and elective courses be $C$, $P$, $S$, and $E$, respectively.

From the problem statement:
- $C = 15$ (fixed)
- $P = 20$ (fixed)
- $S \ge 10$
- $E \ge 0$
- Total credits $T = C + P + S + E \le 70$

Substituting $C$ and $P$:
$$15 + 20 + S + E \le 70 \implies 35 + S + E \le 70 \implies S + E \le 35$$

To maximize the elective credits $E$, we must minimize the specialization credits $S$. Since the minimum specialization credits required is $S = 10$:
$$10 + E \le 35 \implies E \le 25$$

Thus, the maximum credits of elective courses is 25. Therefore, option (D) is correct.