# Reasoning practice questions (Group 4) > This page has practice questions on Reasoning for the Group 4 / VAO (Combined Civil Services Examination-IV) exam, 20 in all: new questions our editors prepared and the founder approved, not previous-year questions. Tap “Answer and explanation” under each question for the correct answer and a short, sourced explanation. For previous-year papers and official answer keys, see tnpsc.gov.in. Last updated: 2026-10-27 · By TNPSC Guide editorial team URL: https://www.tnpscguide.com/exams/group-4/questions/reasoning ### Question 1 A hall has 5 rows, each row has 4 long benches, and each bench seats 3 students. On each of the four benches of the last row 2 students sit, on one bench of the row before it one student sits, and every other bench has 3. How many students are in the hall? - A. 56 - B. 60 - C. 54 - D. 48 Correct answer: C. 54 Seats in all: 3 × 4 × 5 = 60; each bench of the last row has 1 empty seat, 4 in all; one bench of the row before has 2 empty seats; empty seats 4 + 2 = 6; students 60 − 6 = 54. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், p. 110 (PDF p. 114)) ### Question 2 Two shorts A, B and four shirts p, q, r, s are listed systematically as Ap, Aq, Ar, As, Bp, ... Which pair comes 7th? - A. Bq - B. Bs - C. Br - D. Ar Correct answer: C. Br Four with A: Ap, Aq, Ar, As (1-4); then with B: Bp (5), Bq (6), Br (7), Bs (8); so the 7th is Br; there are 8 pairs, none missed and none repeated. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், pp. 110-111 (PDF pp. 114-115)) ### Question 3 Three floors are to be painted red, blue and green, each colour once. If the colour of one floor is fixed, in how many ways can the other two floors be painted? - A. 2 - B. 1 - C. 3 - D. 6 Correct answer: A. 2 With green fixed for one floor, the other two take red-blue or blue-red: 2 ways; fixing each of the three colours in turn gives 3 × 2 = 6 ways in all. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், pp. 111-112 (PDF pp. 115-116)) ### Question 4 Four-digit numbers are written using each of the digits 2, 4, 7, 8 once only. How many of them are greater than 7000? - A. 12 - B. 6 - C. 18 - D. 24 Correct answer: A. 12 Using each of four digits once, 6 numbers begin with each digit; those greater than 7000 begin with 7 or 8: 6 + 6 = 12 (out of 24). Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், p. 112 (PDF p. 116)) ### Question 5 Of the 12 solutions of a 3 × 3 Sudoku, how many have 1 in the top-left cell? - A. 2 - B. 6 - C. 3 - D. 4 Correct answer: D. 4 Two first rows begin with 1, (1, 2, 3) and (1, 3, 2); each has 2 second rows and 1 third row; so 2 × 2 = 4 (a third of 12). Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3.1 சுடோகு), pp. 114-115 (PDF pp. 118-119)) ### Question 6 A list of the numbers written with the digits 1, 2, 3, each once, runs systematically as 123, 132, 213, 231, 312, ... Which number completes the list? - A. 321 - B. 313 - C. 213 - D. 331 Correct answer: A. 321 The list is in increasing order: starting with 1, 123 and 132; with 2, 213 and 231; with 3, 312 and 321; so the missing number is 321. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3 முறையான பட்டியலை முழுமையாக்குதல்), p. 113 (PDF p. 117)) ### Question 7 A list of the pairs that can be made from the four people A, B, C, D runs systematically as AB, AC, AD, BC, BD, ... Which pair completes the list? - A. BA - B. CB - C. CD - D. DA Correct answer: C. CD Each letter is paired only with the letters after it: A with B, C, D; B with C, D; C with D; so the last pair is CD (6 pairs in all). Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3 முறையான பட்டியலை முழுமையாக்குதல்), p. 113 (PDF p. 117)) ### Question 8 Match the following on Sudoku. (a) Row (நிரை) - 1. The numbers 1 to 4 (b) Column (நிரல்) - 2. Vertical cells (c) 3 × 3 Sudoku - 3. The numbers 1 to 3 (d) 4 × 4 Sudoku - 4. Horizontal cells - A. (a) 2, (b) 4, (c) 3, (d) 1 - B. (a) 4, (b) 2, (c) 3, (d) 1 - C. (a) 4, (b) 2, (c) 1, (d) 3 - D. (a) 4, (b) 3, (c) 2, (d) 1 Correct answer: B. (a) 4, (b) 2, (c) 3, (d) 1 Horizontal cells form a row and vertical cells a column; a 3 × 3 Sudoku uses only 1-3 and a 4 × 4 Sudoku only 1-4; so (a) 4, (b) 2, (c) 3, (d) 1. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3.1 சுடோகு), p. 113 (PDF p. 117)) ### Question 9 When two dice are rolled, what is the probability that the number on the first die is greater than the number on the second? - A. 1/2 - B. 7/12 - C. 5/12 - D. 1/6 Correct answer: C. 5/12 Of the 36 ordered pairs, 6 have equal numbers; half of the other 30 have the first number larger: 15 (1 when the first is 2, 2 when it is 3, ..., 5 when it is 6: 1 + 2 + 3 + 4 + 5 = 15); 15/36 = 5/12. Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 8 புள்ளியியலும் நிகழ்தகவும், p. 331 (PDF p. 337)) ### Question 10 What is the shape of a standard die, and which numbers are on its faces? - A. A sphere; the numbers 1 to 6 - B. A cube; the different numbers 1 to 6 - C. A cube; the numbers 0 to 5 - D. A cube; the numbers 1 to 8 Correct answer: B. A cube; the different numbers 1 to 6 A standard die is a cube with the different numbers 1 to 6 on its faces. Source: கணக்கு, ஒன்பதாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard IX, Tamil medium; Samacheer Kalvi) (இயல் 9 நிகழ்தகவு, p. 308 (PDF p. 314)) ### Question 11 On a fair die the opposite faces add up to 7. If the top face shows 3, which number is on the bottom face? - A. 6 - B. 1 - C. 4 - D. 5 Correct answer: C. 4 The top and bottom faces are opposite; 7 − 3 = 4; the opposite pairs are 1-6, 2-5 and 3-4. Source: கணக்கு, ஒன்பதாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard IX, Tamil medium; Samacheer Kalvi) (இயல் 9 நிகழ்தகவு, p. 308 (PDF p. 314)) ### Question 12 In a square, the midpoints of the four sides are joined in order (a rhombus), and the two midlines joining the midpoints of opposite sides are drawn. How many triangles are there in this figure? - A. 8 - B. 12 - C. 16 - D. 4 Correct answer: B. 12 4 triangles at the corners outside the rhombus; the midlines cut the rhombus into 4 small triangles; 4 more triangles each made of two neighbouring small ones; 4 + 4 + 4 = 12 (a systematic list of vertices also gives 12). Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (பயிற்சி 6.1), p. 118 (PDF p. 122)) ### Question 13 The midpoints of the three sides of a triangle are joined by straight lines. How many triangles are there in this figure altogether? - A. 5 - B. 4 - C. 6 - D. 8 Correct answer: A. 5 Joining the midpoints gives 4 small triangles; two or three of them together do not form a triangle; all four together form the big one; 4 + 1 = 5 in all. Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3.3 படத்திற்குள் பல படங்கள்), p. 117 (PDF p. 121)) ### Question 14 A five-pointed star is drawn with five straight lines. How many small triangles are there at its points? - A. 10 - B. 3 - C. 5 - D. 6 Correct answer: C. 5 Each point is a small triangle; with five points there are 5 small triangles (a pentagon is left in the middle). Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம் (6.3.3 படத்திற்குள் பல படங்கள்), p. 117 (PDF p. 121)) ### Question 15 In the textbook's +4 table (e is A, f is B, ..., d is Z), which word is the secret fec? - A. JIG - B. CBZ - C. AZX - D. BAY Correct answer: D. BAY 4 places back: f → B, e → A; from c go b, a, then wrap to the end of the alphabet, z, y, so c → Y; fec is BAY. Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 7 தகவல் செயலாக்கம் (7.7 குறியாக்கவியல்), p. 263 (PDF p. 269)) ### Question 16 What is cryptology? - A. A table that gives numbers to letters - B. The science of communicating in a secure form - C. A method of writing each word backwards - D. A method of writing the alphabet backwards Correct answer: B. The science of communicating in a secure form Cryptology is the science of communicating in a secure form; military, political and private communication all need information security. Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 7 தகவல் செயலாக்கம் (7.7 குறியாக்கவியல்), p. 262 (PDF p. 268)) ### Question 17 Consider the following statements on cryptology. 1. The true message in its usual form is the plain text. 2. Cipher text is usually written in capital letters. 3. Plain text is usually written in capital letters. Which of these are correct? - A. 1 and 2 only - B. 1 only - C. 2 and 3 only - D. 1, 2 and 3 Correct answer: A. 1 and 2 only The message in its usual form is the plain text; cipher text is usually in capitals and plain text in small letters; so 1 and 2 are correct and 3 is wrong. (The textbook's own +4 table in Example 7.8 does the opposite, with the secret letters small and their meanings in capitals; statement 2 gives the usual rule.) Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 7 தகவல் செயலாக்கம் (7.7 குறியாக்கவியல்), p. 262 (PDF p. 268)) ### Question 18 A sequence is defined by a₁ = 2, a₂ = 2 and aₙ = aₙ₋₁ / (aₙ₋₂ + 2) for n ≥ 3. What is its 5th term? - A. 1/8 - B. 1/20 - C. 1/11 - D. 1/16 Correct answer: B. 1/20 a₃ = a₂/(a₁ + 2) = 2/4 = 1/2; a₄ = a₃/(a₂ + 2) = (1/2)/4 = 1/8; a₅ = a₄/(a₃ + 2) = (1/8) ÷ (5/2) = 1/20. Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 55 (PDF p. 61)) ### Question 19 Consider the following statements on sequences. 1. A sequence with a finite number of terms is a finite sequence. 2. A sequence with an infinite number of terms is an infinite sequence. 3. Every function is a sequence. Which of these are correct? - A. 1 only - B. 2 and 3 only - C. 1 and 3 only - D. 1 and 2 only Correct answer: D. 1 and 2 only Finitely many terms make a finite sequence and infinitely many an infinite one; every sequence is a function, but not every function is a sequence; so 1 and 2 are correct and 3 is wrong. Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 53 (PDF p. 59)) ### Question 20 What is the next term of the sequence 1/3, 1/7, 1/11, 1/15, ...? - A. 1/16 - B. 1/60 - C. 5/19 - D. 1/19 Correct answer: D. 1/19 The numerator stays 1; the denominators 3, 7, 11, 15 grow by 4; the next denominator is 15 + 4 = 19, so the next term is 1/19. Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 54 (PDF p. 60)) ## Sources - [Official syllabus page](https://www.tnpsc.gov.in/english/syllabus.html) - [Notifications](https://www.tnpsc.gov.in/English/Notification.aspx)