CS and IT GATE 2025 SET-2 Questions with Answer

The most appropriate option is:
c) resolve
So the complete sentence is: "Despite his initial hesitation, Rehman's resolve to contribute to the success of the project never wavered."
Explanation:
Resolve means determination or firmness of purpose, which fits the context of unwavering intent despite hesitation.
Ambivalence means having mixed feelings, which does not fit with "never wavered."
Satisfaction is about contentment, not determination.
Revolve is a verb and does not make sense in this context.

A bird lives in a nest. This relationship is between an animal and its home. To solve the analogy, we need to find the place where a bee lives. A kennel is the home of a dog, so it is not correct. A hammock is used by humans for resting, so it is also incorrect. A lair is the home of a wild animal like a lion or tiger, which is not a bee’s home. The correct answer is hive, because bees live in hives, just like birds live in nests.

✅ Final Answer: Hive

Birds live in nests, and bees live in hives. This shows a similar relationship between a creature and its home.

We are given the equation P·e^x = Q·e^-x for all real x.

Multiplying both sides by e^x gives P·e^2x = Q.

Since this must hold true for all real values of x, and e^2x changes with x, the only way the left-hand side remains a constant equal to Q is if P = 0. Substituting P = 0 into the equation gives Q = 0.

✅ Final Answer: Option (a) — P = Q = 0.

Reason: The equation can only hold for all x if both P and Q are zero, since e^2x is not constant.

Let p₁ and p₂ be two arbitrary prime numbers.

Option (a) states that p₁ + p₂ is not a prime number — this is false because, for example, 2 + 5 = 7, which is prime.

Option (b) states that p₁ × p₂ is not a prime number — this is always true, because the product of two primes is always composite (it has factors other than 1 and itself).

Option (c) states that p₁ + p₂ + 1 is a prime number — this is not always true as there is no guarantee.

Option (d) states that p₁ × p₂ + 1 is a prime number — also not always true.

✅ Final Answer: Option (b) — p₁ × p₂ is not a prime number.

Reason: The product of two prime numbers is always composite, because it has at least the two prime factors p₁ and p₂.

Ramya said to Josephine: "Even if I had known that you were in the hospital, I would not have gone there to see you."

The phrase "Even if I had known..." is a past unreal conditional, which means that in reality she did not know about it. The rest of the sentence simply states that even with the knowledge, she still would not have gone.

Therefore, the only logically correct inference is that Ramya did not know that Josephine was in the hospital.

✅ Final Answer: Option (b) — Ramya did not know that Josephine was in the hospital.

Reason: The statement structure implies the condition was not true in reality, so the knowledge about Josephine’s hospitalization was absent.

In the given code examples (IMAGE → FHBNJ and FIELD → EMFJG), the letter shifts vary in each position, with a mix of positive and negative changes rather than a single fixed shift. This means that each position in the word may have its own coding rule.

To find the code for BEACH, we test each option letter by letter to see which matches the shifting style of the examples.

Testing option (d) IBCEC:
B(2) → I(9) = +7 shift
E(5) → B(2) = -3 shift
A(1) → C(3) = +2 shift
C(3) → E(5) = +2 shift
H(8) → C(3) = -5 shift

This pattern of mixed positive and negative shifts (+7, -3, +2, +2, -5) is consistent with the variations seen in the given coded words, especially the ending shift of -5 which appears in the examples.

✅ Final Answer: Option (d) — IBCEC.

Reason: Among all choices, IBCEC matches the irregular positional shift pattern style used in the provided code examples.

Average Turnaround Time: 19 milliseconds

Using Shortest Remaining Time First (SRTF) scheduling for processes P1, P2, P3, and P4 with arrival times 0, 1, 2, and 8 ms and burst times 10, 13, 6, and 9 ms respectively.

Gantt Chart: