⭐ Sabse Important Points · एक नज़र में
- Arithmetic Progression (AP): Difference between consecutive terms is constant; nth term = a + (n-1)d.
- Letter Shift Coding: Each letter is shifted by a fixed number (e.g., +2: A→C, B→D).
- Geometric Progression (GP): Ratio between consecutive terms is constant; nth term = a * r^(n-1).
- Blood Relation Symbols: Use + for male, - for female, = for spouse, vertical line for parent-child, horizontal for siblings.
- Letter Position: A=1, B=2, ..., Z=26; reverse position = 27 - forward position.
- Direction Sense: Net displacement after right-angle turns = sqrt(x^2 + y^2); use signs for east/west and north/south.
Introduction · परिचय
General Mental Ability for BPSC covers reasoning, quantitative aptitude, and data interpretation. It tests logical thinking, numerical ability, and problem-solving speed. Key areas include series, coding-decoding, blood relations, direction sense, syllogism, percentages, averages, ratios, time-work, and speed-distance. This revision note focuses on high-yield concepts with examples and exam tips.
Number and Letter Series
Series questions require identifying the pattern governing a sequence of numbers or letters. Common patterns include arithmetic progression (constant difference), geometric progression (constant ratio), squares/cubes, alternating operations, and combined series. For letter series, convert letters to positions (A=1, B=2, ..., Z=26) and look for shifts.
📐 Formula / Rule Box · सूत्र याद रखो
nth term of AP
a_n = a + (n-1)d
nth term of GP
a_n = a * r^(n-1)
⭐ Key Points · याद रखने वाली बातें
- Arithmetic Progression (AP): Difference between consecutive terms is constant; nth term = a + (n-1)d.
- Geometric Progression (GP): Ratio between consecutive terms is constant; nth term = a * r^(n-1).
- Letter Position: A=1, B=2, ..., Z=26; reverse position = 27 - forward position.
- Alternating Series: Two or more interleaved series; check odd and even positions separately.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Find the next term: 2, 6, 12, 20, 30, ?
✅ Solution: 42
💡 Explanation: Differences: 4, 6, 8, 10 (increase by 2). Next difference = 12, so 30 + 12 = 42. Alternatively, terms are n(n+1): 1*2=2, 2*3=6, 3*4=12, 4*5=20, 5*6=30, 6*7=42.
Coding-Decoding and Blood Relations
Coding-decoding tests pattern recognition in letter/number substitution. Blood relations require drawing a family tree with standard symbols (male: +, female: -, marriage: =, siblings: horizontal line, offspring: vertical line). Direction sense involves tracking net displacement using Pythagoras when turns are at right angles.
- Identify symbols/relations
- Draw family tree or direction diagram
- Apply given conditions
- Determine required relation/displacement
⭐ Key Points · याद रखने वाली बातें
- Letter Shift Coding: Each letter is shifted by a fixed number (e.g., +2: A→C, B→D).
- Blood Relation Symbols: Use + for male, - for female, = for spouse, vertical line for parent-child, horizontal for siblings.
- Direction Sense: Net displacement after right-angle turns = sqrt(x^2 + y^2); use signs for east/west and north/south.
- Substitution Coding: Words replaced by numbers or symbols; decode by matching repeated words.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: If 'P + Q' means P is father of Q, 'P - Q' means P is mother of Q, and 'P * Q' means P is sister of Q, then in 'A + B - C * D', how is A related to D?
✅ Solution: Grandfather
💡 Explanation: A + B: A is father of B. B - C: B is mother of C. C * D: C is sister of D. So B is mother of both C and D. A is father of B, hence A is grandfather of D.
Practice Questions · खुद हल करके देखो
पहले खुद try karo, phir “Answer dekho” dabakar check karo. 👇
Q1Find the missing term: 3, 8, 15, 24, ?, 48
👀 Answer dekho
✅ Answer: 35
💡 Explanation: Differences: 5, 7, 9, 11, 13 (odd numbers increasing by 2). So 24 + 11 = 35, and 35 + 13 = 48.
Q2If in a certain code, 'MOTHER' is written as 'NPUIFS', how is 'FATHER' written?
👀 Answer dekho
✅ Answer: GBUIFS
💡 Explanation: Each letter is shifted +1: M→N, O→P, T→U, H→I, E→F, R→S. Applying to FATHER: F→G, A→B, T→U, H→I, E→F, R→S gives GBUIFS.
Q3A man walks 5 km north, turns right and walks 3 km, then turns right and walks 5 km. How far is he from the starting point?
👀 Answer dekho
✅ Answer: 3 km
💡 Explanation: Net north-south displacement = 5 - 5 = 0; net east-west = 3 km east. Distance = 3 km.
⚠️ Common Mistakes · ये गलतियाँ बिल्कुल मत करना
- Assuming a single pattern in series without checking alternating or combined patterns; always test differences, ratios, and squares/cubes.
- In blood relations, confusing 'maternal' vs 'paternal' or forgetting that 'sister of brother' can be sister; draw the full tree.
- In direction sense, ignoring the final direction or using Pythagoras when turns are not at right angles; verify angles.
- In coding-decoding, applying the shift in the wrong direction (forward vs backward); check with the given example.
⚡ Quick Revision · Exam से पहले 2 मिनट में दोहराओ
- Series Patterns: Check differences, ratios, squares/cubes, and alternating series first.
- Blood Relation Symbols: + male, - female, = spouse, vertical parent-child, horizontal siblings.
- Direction Sense: Use Pythagoras for right-angle turns; track net displacement with signs.
- Coding-Decoding: Identify shift (+/-) or substitution pattern from the example.
- Time Management: Attempt reasoning questions in 1-1.5 minutes; skip lengthy puzzles and return later.