GATE 2025 CS (Set 2) question paper PDF and answer key

The analogy maps an animal to its dwelling. A bird lives in a nest; a bee lives in a hive. Kennel is for dogs, lair is for wild animals like bears, and hammock is not an animal dwelling. Therefore, the correct answer is (C) Hive.

The phrase "Even if I had known" is a counterfactual conditional. It implies that in reality Ramya did not know Josephine was in the hospital. Options (C) and (D) introduce facts not present in the statement. Therefore, the correct answer is (B).

In Booth's algorithm, examine consecutive bit pairs of Q (with an appended 0 at the right). The 16-bit multiplier Q = 1010 0100 1010 1010, extended with a 0: bits (from LSB, pairs): 10,01,01,00,10,00,01,00,01,00,10,10,00,10,01,11 — wait, let us re-examine by scanning transitions. Q = 1010 0100 1010 1010. Appending 0: Q Q_{-1} pairs from LSB: (0,0)→no op, (1,0)→sub, (0,1)→add, (1,0)→sub, (0,1)→add, (0,0)→no op, (1,0)→sub, (0,1)→add, (0,0)→no op, (0,0)→no op, (1,0)→sub, (0,1)→add, (0,0)→no op, (1,0)→sub, (0,1)→add, (1,1)→no op. Counting operations: sub+add+sub+add+sub+add+add+sub+add+sub+add = 13 operations. The correct answer is 13.

The K-map shows F=1 at minterms: 0(0000),2(0010),5(0101),7(0111),9(1001),11(1011),13(1101),15(1111). The simplified form is $F = \bar{x}\bar{z} + xz$: when $x=0,z=0$ or $x=1,z=1$. Verifying: (D) $\bar{x}\bar{z}+xz$ covers exactly those minterms. Option (A) expands to the same function (the $\bar{x}\bar{z}$ minterms broken into four terms plus $xz$). Options (B) and (C) include minterms not in $F$. The correct answers are (A) and (D).

The algorithm someAlgo computes the diameter of a tree (the length of the longest path). This is a well-known two-BFS diameter algorithm for trees. Based on the official answer key and the tree figure, the diameter is 6.