ISRO CS 2025 Q.52: solution and answer

ISRO 2025 · CSQ.52 · 1 mark · MCQ

The given Boolean expression is: X'Y'Z' + X'YZ'. Which of the following represents the Karnaugh map for the above expression?

ISRO CS 2025 question 52: Each option is a Karnaugh map drawn as a table. — Figure from the ISRO CS 2025 paper. It is part of the question.

(A)
Figure — map with columns Z', Z and rows X'Y', X'Y, XY, XY'; 1s at (X'Y', Z') and (X'Y, Z'), all other cells 0
(B)
Figure — map with columns Z, Z' and rows X'Y', X'Y, XY, XY'; 1s at (X'Y', Z) and (X'Y, Z), all other cells 0
(C)
Figure — map with columns Y'Z', Y'Z, YZ, YZ' and rows X', X; 1s at (X', YZ) and (X, Y'Z'), all other cells 0
(D)
Figure — map with columns Y'Z', Y'Z, YZ, YZ' and rows X', X; 1s at (X', Y'Z) and (X', YZ), all other cells 0

Answer and solution

ANSWER

The correct map is option (A): 1s in the $Z^{'}$ column of rows $X^{'} Y^{'}$ and $X^{'} Y$ .

Official answer: ASource: ISRO's final answer key of 15 May 2026

Write the expression as minterms with variable order $X Y Z$ : $X^{'} Y^{'} Z^{'} = 000$ (minterm 0) and $X^{'} Y Z^{'} = 010$ (minterm 2).
So the map must have exactly two 1s, in the cells $X = 0, Y = 0, Z = 0$ and $X = 0, Y = 1, Z = 0$ , and 0 in every other cell.
Check by simplifying: $X^{'} Y^{'} Z^{'} + X^{'} Y Z^{'} = X^{'} Z^{'} (Y^{'} + Y) = X^{'} Z^{'}$ . This is a pair of adjacent cells, both with $X = 0$ and $Z = 0$ .
Option (a): the columns are $Z^{'}, Z$ and the 1s are in the $Z^{'}$ column of rows $X^{'} Y^{'}$ and $X^{'} Y$ . These are cells $000$ and $010$ , with every other cell 0. This matches.
Option (b): the columns are ordered $Z, Z^{'}$ , so the 1s are under $Z$ . They represent $X^{'} Y^{'} Z + X^{'} Y Z = X^{'} Z$ , which is a different function.
Option (c): the 1s are at $X^{'} Y Z$ ( $011$ ) and $X Y^{'} Z^{'}$ ( $100$ ). Neither is a term of the expression, so this is wrong.
Option (d): the 1s are at $X^{'} Y^{'} Z$ ( $001$ ) and $X^{'} Y Z$ ( $011$ ). This represents $X^{'} Z$ , which is wrong.

KEY IDEA

Convert each product term to its binary cell (complemented variable = 0), then read the map labels carefully, including the order of the column headings, to find the map with 1s only in those cells.

WATCH OUT FOR

Not noticing that option (b) lists its columns as $Z, Z^{'}$ instead of $Z^{'}, Z$ . Its 1s then sit under $Z$ and show $X^{'} Z$ , not $X^{'} Z^{'}$ . Skimming the grid of 1s and 0s without reading the headings picks the wrong map.

From the ISRO CS 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 6 ISRO Boolean logic questions, with notes

ISRO CS 2025 Q.52: solution and answer

Answer and solution

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