All 6 Geometry questions the Punjab PSC asked between 2021 and 2025, each with a worked answer and the exam it came from. First 10 free to read.
Free to read, with the worked answer and the exam each one came from. The book prints this topic in the order the Commission favours, so these are the ones to know first.
ABCD is a square, and l and m are straight lines. You are told that each of the vertices (corner points), A, B, C and D, of the square lies on one of the lines, l or m.
Answer each question below, independent of the other questions. That is, in addition to the information given above, if additional information is given in a question, that additional information holds only for that question and not for the other questions in the section
Since AB = AC, the angles opposite them are equal: angle ACB = angle ABC = 60°. The third angle is then 180° − 60° − 60° = 60°, so the triangle is equilateral and all three sides, including AC and BC, are equal. The complement of angle BCA is 90° − 60° = 30°, no side is longer than another, and there is no right angle, so (a), (b) and (c) are false.
Each of the two lines must carry two vertices of the square. So l and m are either two sides, which add no new triangles, or the two diagonals AC and BD. With the diagonals, the lines are perpendicular at the centre O. This makes four right-angled triangles at O (AOB, BOC, COD, DOA). Each diagonal also cuts the square into two right-angled triangles with the right angle at a vertex (ABC, ADC, BAD, BCD). > 4 (right angle at O) + 4 (right angle at a corner) = 8 So the maximum is eight.
Let the coconut tree be h m tall, the pine h − 6, and the gap between them d. Each fallen top makes a right triangle with the stump and the ground. > Coconut: (h − 12)² = 12² + d² > Pine: (h − 14)² = 8² + d² > Subtracting: (h − 12)² − (h − 14)² = 80, so 4h − 52 = 80 and h = 33 The coconut tree is 33 metres tall.
Let the side be s. The shortened sides s − 12, s − 13 and s − 14 form a right triangle. s − 12 is the hypotenuse, the longest side. > (s − 12)² = (s − 13)² + (s − 14)² > s² − 24s + 144 = 2s² − 54s + 365 → s² − 30s + 221 = 0 > (s − 17)(s − 13) = 0 → s = 17 (s = 13 gives a negative side) The sides become 5, 4 and 3, a right triangle.
All four sides are equal. AB = sqrt(4² + 5²) = sqrt(41), and BC, CD and DA are also sqrt(41). So ABCD is at least a rhombus. The diagonals differ: AC = sqrt(9² + 9²) = 9sqrt(2), but BD = sqrt(1² + 1²) = sqrt(2). Adjacent sides are not perpendicular either: slopes 5/4 and 4/5 multiply to 1, not −1. So it is not a square. > sides: AB = BC = CD = DA = sqrt(41) > diagonals: AC = 9sqrt(2), BD = sqrt(2) → unequal
Divide each side of the big triangle into k equal parts and draw lines parallel to the sides: it splits into k² identical small equilateral triangles. So n must be a perfect square. > 256 = 16² 186, 216 and 296 are not perfect squares, so only 256 is possible.
The Commission set 6 Geometry questions across 7 papers between 2021–2025. That is the whole set, not a sample — every one of them is in the book, and the 6 most-asked are on this page free.
Not in this set — each of these 6 was set once in the years covered. Questions elsewhere in the book do repeat, and carry a badge saying how often.
Here. Every question on this page is a solved MCQ: the four options as printed, the correct answer, and a worked explanation in plain English — not just a letter. The rest of the 6 are in the book, in the same form.
Switch to Attempt mode at the top of the questions. You get one question at a time and it is marked the moment you pick an option, with the reason underneath — the same way the exam feels, on your phone.
The questions are on screen rather than in a downloadable file, so they stay current and correct. The printed book has all 6 of these plus the rest of the Reasoning & Aptitude section, and every buyer gets the whole thing online as well.
The exams behind these questions, most first. A paper here is a sitting: a question set in two papers of the same sitting counts once.
| Exam | Year | Questions |
|---|---|---|
| Remote Sensing and Geographic Information System Officer (Group-B) | 2025 | 2 |
| Agriculture Development Officer | 2024 | 1 |
| Scientific Assistant (Cyber Forensics) (Group B) | 2023 | 1 |
| Scientific Officer (Polygraph) (Group B) | 2023 | 1 |
| Scientific Assistant (Polygraph) (Group B) | 2023 | 1 |
| Scientific Officer (Cyber Forensics) (Group B) | 2023 | 1 |
| Junior Engineers (Civil) and 04 Posts of Junior Engi | 2021 | 1 |