Series and patterns

2011 · Q24

Consider the following figures:

Figure 1:

Figure 2:

What is the missing number?

1. (a)7
2. (b)8
3. (c)9UPSC key
4. (d)10

2013 · Q48

Consider the following matrix:

What is the number at ‘X’ in the above matrix?

1. (a)5
2. (b)8
3. (c)9UPSC key
4. (d)11

2013 · Q50

Examine the following three figures in which the numbers follow a specific pattern:

The missing number (?) in the third figure above is

1. (a)7
2. (b)16UPSC key
3. (c)21
4. (d)28

2014 · Q42

Consider the table given below in which the numbers bear certain relationship among themselves along the rows:

Which one of the following numbers is the missing number indicated above by X?

1. (a)19
2. (b)15UPSC key
3. (c)14
4. (d)8UPSC key

2015 · Q12

Consider the following matrix:

What is the missing number at '?' in the matrix?

1. (a)5UPSC key
2. (b)0
3. (c)7
4. (d)3

2015 · Q13

What is the missing number 'X' of the series 7, X, 21, 31, 43?

1. (a)11
2. (b)12
3. (c)13UPSC key
4. (d)14

2018 · Q3

Consider the following pattern of numbers:

What is the number at? in the above pattern?

1. (a)17UPSC key
2. (b)19
3. (c)21
4. (d)23

2018 · Q59

Consider the sequence given below:

4/12/95, 1/1/96, 29/1/96, 26/2/96, ....

What is the next term of the series?

1. (a)24/3/96
2. (b)25/3/96UPSC key
3. (c)26/3/96
4. (d)27/3/96

2019 · Q48

What is X in the sequence

132, 129, 124, 117, 106, 93, X?

1. (a)74
2. (b)75
3. (c)76UPSC key
4. (d)77

2019 · Q51

What is X in the sequence

4, 196, 16, 144, 36, 100, 64, X?

1. (a)48
2. (b)64UPSC key
3. (c)125
4. (d)256

2019 · Q54

Consider the following sequence that follows some arrangement:

c_accaa_aa_bc_b

The letters that appear in the gaps are

1. (a)abba
2. (b)cbbbUPSC key
3. (c)bbbb
4. (d)cccc

2019 · Q70

In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7?

1. (a)1UPSC key
2. (b)2
3. (c)3
4. (d)None

2020 · Q13

A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?

1. (a)34
2. (b)36
3. (c)38UPSC key
4. (d)40

2020 · Q15

Consider the following arrangement that has some missing letters:

abab_b_bcb_dcdcded_d

The missing letters which complete the arrangement are

1. (a)a, b, c, d
2. (b)a, b, d, e
3. (c)a, c, c, eUPSC key
4. (d)b, c, d, e

2020 · Q34

Consider the following sequence of numbers:

5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6

How many odd numbers are followed by the odd number in the above sequence?

1. (a)5
2. (b)6UPSC key
3. (c)7
4. (d)8

2020 · Q49

What is the missing term @ in the following?

ACPQ: BESU :: MNGI: @

1. (a)NPJL
2. (b)NOJM
3. (c)NPIL
4. (d)NPJMUPSC key

2021 · Q26

Replace the incorrect term by the correct term in the given sequence

3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40

where odd terms and even terms follow the same pattern.

1. (a)0UPSC key
2. (b)1
3. (c)3
4. (d)6

2021 · Q27

Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly.

1. (a)9B
2. (b)3A
3. (c)3BUPSC key
4. (d)3C

2021 · Q28

You are given two identical sequences in two rows:

What is the entry in the place of C for the Sequence-II?

1. (a)2·5
2. (b)5
3. (c)9·375UPSC key
4. (d)32·8125

2021 · Q40

In the English alphabet, the first 4 letters are written in opposite order; and the next 4 letters are written in opposite order and so on; and at the end Y and Z are interchanged. Which will be the fourth letter to the right of the 13ᵗʰ letter?

1. (a)N
2. (b)TUPSC key
3. (c)H
4. (d)I

2021 · Q50

What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822?

1. (a)603
2. (b)605
3. (c)607UPSC key
4. (d)608

2021 · Q65

In the series _b_a_ba_b_abab_aab; fill in the six blanks ( _ ) using one of the following given four choices such that the series follows a specific order.

1. (a)bababa
2. (b)baabba
3. (c)bbaabb
4. (d)abababUPSC key

2022 · Q4

What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?

1. (a)105
2. (b)120
3. (c)150
4. (d)225UPSC key

2022 · Q29

In the series AABABCABCDABCDE..., which letter appears at the 100th place?

1. (a)G
2. (b)H
3. (c)IUPSC key
4. (d)J

2022 · Q75

What is the value of X in the sequence 2, 12, 36, 80, 150, X?

1. (a)248
2. (b)252UPSC key
3. (c)258
4. (d)262

2023 · Q24

If 7 ⊕ 9 ⊕ 10 = 8, 9 ⊕ 11 ⊕ 30 = 5, 11 ⊕ 17 ⊕ 21 = 13, what is the value of 23 ⊕ 4 ⊕ 15?

1. (a)6UPSC key
2. (b)8
3. (c)13
4. (d)15

2023 · Q40

Choose the group which is different from the others:

1. (a)17, 37, 47, 97
2. (b)31, 41, 53, 67
3. (c)71, 73, 79, 83
4. (d)83, 89, 91, 97UPSC key

2023 · Q54

40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?

1. (a)14
2. (b)15UPSC key
3. (c)16
4. (d)17

2023 · Q55

What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ..., A?

1. (a)H
2. (b)IUPSC key
3. (c)J
4. (d)M

2023 · Q75

Consider the sequence

ABC_ _ ABC_ DABBCD_ ABCD

that follows a certain pattern.

Which one of the following completes the sequence?

1. (a)DACB
2. (b)CDAB
3. (c)DCCA
4. (d)DDCAUPSC key

2023 · Q80

The letters of the word “INCOMPREHENSIBILITIES” are arranged alphabetically in reverse order. How many positions of the letter/letters will remain unchanged?

1. (a)None
2. (b)One
3. (c)TwoUPSC key
4. (d)Three

2024 · Q24

Consider the sequence

A _ BCD _ BBCDABC _ DABC _ D

that follows a certain pattern. Which one of the following completes the sequence?

1. (a)B, A, D, C
2. (b)B, A, C, D
3. (c)A, A, C, DUPSC key
4. (d)A, A, D, C

2024 · Q46

What is the sum of the first 28 terms in the following sequence?

1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, ⋯

1. (a)83
2. (b)84UPSC key
3. (c)85
4. (d)86

2024 · Q79

What will come in place of ∗ in the sequence 3, 14, 39, 84, ∗, 258?

1. (a)150
2. (b)155UPSC key
3. (c)160
4. (d)176

2025 · Q8

What comes at X and Y respectively in the following sequence?

January, January, December, October, X, March, October, Y, September

1. (a)July, May
2. (b)July, AprilUPSC key
3. (c)June, May
4. (d)June, April

2025 · Q16

If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?

1. (a)70
2. (b)66
3. (c)65UPSC key
4. (d)64

2025 · Q30

Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence?

1. (a)B, C, B, C, A
2. (b)A, C, B, C, A
3. (c)B, C, B, A, CUPSC key
4. (d)C, B, B, A, C

2025 · Q36

What is X in the sequence 24, X, 12, 18, 36, 90?

1. (a)18
2. (b)12UPSC key
3. (c)9
4. (d)6

2025 · Q60

What is X in the sequence 1, 3, 6, 11, 18, X, 42?

1. (a)26
2. (b)27
3. (c)29UPSC key
4. (d)30

2026 · Q18

A pattern formed by two characters a and b is repeated more than once in the following string:

× b × a × a × × a × a × bab

What is × × in the 7th and 8th positions from the left in the above string?

1. (a)aa
2. (b)ab
3. (c)ba
4. (d)bbUPSC key

2026 · Q57

In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is

1. (a)29
2. (b)37
3. (c)43
4. (d)47UPSC key