This page covers CTET Paper II Circular Seating Arrangement with complete concept notes, 21 graded practice MCQs, key points and exam-specific tips. Free to study.
In circular seating, positions are relative to each other. There is no first or last position. The key is to fix one person's position first, then arrange others relative to that person
💡Key Rules
1) Always fix one person's position to eliminate rotational possibilities 2) Clockwise and anti-clockwise directions matter 3) 'Opposite' means diametrically across 4) Adjacent means immediate left or right 5) Use process of elimination systematically.
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Formula Block
Memorise — at least one formula appears in every paper
Total circular arrangements of n people = (n-1)! This is because we fix one position to avoid counting rotations as different arrangements. For restrictions like couples sitting together, treat them as single units.
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Exam Patterns
What examiners ask — read before attempting PYQs
→Common question types include
immediate neighbors, opposite positions, counting positions between people, and conditional arrangements. Most questions give 6-8 people with 4-6 conditions
⚡Shortcut Trick 1 - The Fixed Position Method
Always start by placing one person at the 'top' of the circle. This eliminates confusion about rotational arrangements. Mark positions as 1,2,3... clockwise from this fixed person
⚡Shortcut Trick 2 - The Opposite Formula
In a circle of n people, if person A is at position x, then the person opposite to A is at position x + n/2 (if n is even). For odd numbers, no one sits exactly opposite
✏️Worked Example 1
Six friends A,B,C,D,E,F sit around a circular table. B sits two places to the right of A. C sits opposite to A. D sits immediately left of C.
Where does E sit
→Solution Step-by-Step
1
Fix A at position 1 (top)
2
B sits two places right of A, so B at position 3
3
C sits opposite A. In 6-person circle, opposite of position 1 is position 4. So C at position 4
4
D sits immediately left of C. Left of position 4 is position 3. But B is already there. This means left of C is position 5. Wait - let me recalculate. If we number 1,2,3,4,5,6 clockwise, then left of 4 is position 3. Since B occupies 3, there's a contradiction
🔑Let me recheck
immediate left of position 4 is position 5 (going anti-clockwise). So D at position 5.
Step 5: Remaining positions are 2 and 6. E and F occupy these
→Answer
E sits at either position 2 or 6
✏️Worked Example 2
Seven people sit in a circle. P sits third to the right of Q. R sits second to the left of P. How many people sit between Q and R when counted clockwise from Q
→Solution Step-by-Step
1
Fix Q at position 1
2
P sits third to right of Q, so P at position 4
3
R sits second to left of P
→Left of position 4 going anti-clockwise
position 3 is first left, position 2 is second left. So R at position 2
Step 4: Count from Q(position 1) to R(position 2) clockwise: only position 7 comes between them
Answer: 1 person sits between Q and R
⚡Shortcut Trick 3 - The Gap Counting Formula
To count people between positions A and B clockwise: if B > A, count = B - A - 1. If B < A, count = n - A + B - 1 (where n is total people)
→Most Common Trap
Students often confuse 'left' and 'right' directions
💡Remember
in clockwise numbering, right means higher numbers, left means lower numbers. Also, 'second to the right' means there's one person in between, not sitting in the second chair. Many students miss this and count wrong positions.
Test Circular Seating Arrangement under exam conditions
Four friends — Aman, Bhavna, Chirag, and Divya — sit around a circular table. Aman sits immediately to the right of Bhavna. Who sits immediately to the left of Aman?
Practice 2easy
Four colleagues—Vikram, Xena, Yash, and Zara—sit around a circular table for a meeting. Vikram sits opposite Yash. Xena sits immediately to the right of Vikram. Which statement is definitely true?
Practice 3easy
Four friends—Arun, Bhavna, Chitra, and Deepak—sit around a circular table. Arun sits immediately to the right of Bhavna. Chitra sits immediately to the left of Bhavna. Who sits immediately to the right of Deepak?
Practice 4easy
Five people—P, Q, R, S, and T—sit around a circular table facing the center. Q sits second to the left of P. R sits immediately to the right of P. Who sits immediately to the left of Q?
Practice 5easy
Five people—M, N, O, P, and Q—sit around a circular table facing the center. O sits second to the left of M. P sits immediately to the right of M. N and Q are the remaining two. If N sits immediately to the left of M, who sits immediately to the right of O?
Practice 6easy
Four people—Ravi, Sita, Tina, and Uday—sit around a circular table. Ravi does not sit opposite to Sita. Tina sits immediately to the right of Ravi. Which of the following must be true?
Practice 7easy
Five people—P, Q, R, S, and T—sit around a circular table facing the center. Q sits third to the right of P. R sits immediately to the left of P. Who sits immediately to the right of S?
Practice 8easy
Five friends—Aman, Bhavesh, Chirag, Diya, and Esha—sit around a circular table. Aman sits immediately to the left of Bhavesh. Chirag sits second to the right of Aman. Diya sits immediately to the right of Chirag. Where does Esha sit?
Practice 9easy
Six people—A, B, C, D, E, and F—sit around a circular table. A sits third to the right of B. C sits immediately to the left of A. D sits immediately to the right of B. E and F occupy the remaining seats. If we count clockwise from B, who is the second person?
Practice 10easy
Four friends—Arun, Bhavna, Chitra, and Deepak—sit around a circular table. Arun sits immediately to the right of Bhavna. Chitra sits immediately to the left of Bhavna. Where does Deepak sit?
Practice 11easy
Five people—P, Q, R, S, and T—sit around a circular table facing the centre. Q sits third to the right of P. How many people sit between P and Q if we count clockwise from P to Q?
Practice 12easy
Four friends — Aman, Bhavna, Chetan, and Diya — are sitting around a circular table. Aman is sitting immediately to the right of Bhavna. Chetan is sitting immediately to the left of Bhavna. Who is sitting immediately to the right of Diya?
Practice 13easy
Four people—M, N, O, and P—sit around a circular table. M sits immediately to the right of N. O sits immediately to the right of M. P sits in the remaining position. If we go clockwise from N, in what order do we encounter all four people?
Practice 14easy
Four students—Isha, Jaya, Karan, and Lina—sit around a circular table. Isha sits immediately to the left of Jaya. Karan sits immediately to the left of Isha. Lina sits in the remaining position. Which of the following is true?
Practice 15easy
Six colleagues—A, B, C, D, E, and F—sit around a circular conference table. A sits immediately to the right of B. D sits immediately to the right of A. C sits immediately to the right of D. If E and F are the remaining two, and E sits immediately to the right of C, where does F sit?
Practice 16easy
Four friends—Arun, Bhavna, Chitra, and Deepak—sit around a circular table. Arun sits immediately to the right of Bhavna. Chitra sits immediately to the left of Bhavna. Where does Deepak sit?
Practice 17easy
Seven people sit around a circular table. Person X sits third to the right of Person Y. If we count counter-clockwise from Y to X, how many people sit between Y and X?
Practice 18easy
Four friends—Arun, Bhavna, Chitra, and Deepak—sit around a circular table. Bhavna sits immediately to the right of Arun. Chitra sits immediately to the right of Bhavna. Where does Deepak sit?
Practice 19easy
Four students—Raj, Sam, Tina, and Uma—sit around a circular table. Raj is not adjacent to Sam. Tina sits immediately to the right of Raj. Uma sits immediately to the left of Raj. What is the seating order clockwise starting from Raj?
Practice 20easy
Four friends—Arun, Bina, Chetan, and Diya—sit around a circular table. Arun sits immediately to the right of Bina. Chetan sits immediately to the left of Bina. Where does Diya sit?
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