Karnataka 1st PUC Mathematics Sequence and Series MCQ with Answers

GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION (PRE-UNIVERSITY)
18TH CROSS, MALLESHWARAM, BENGALURU – 560 012
CHAPTERWISE MULTIPLE CHOICE QUESTIONS FOR COMPETATIVE EXAM
SUBJECT: MATHEMATICS – I PUC
NAME OF THE CHAPTER: SEQUENCE AND SERIES

SYNOPSIS
 Sequence: Arrangement of numbers or terms using some rule is called sequence.
 Finite/ Infinite Sequence: If the number of terms in the sequence is finite then it is called
finite sequence. Otherwise sequence is infinite
 Series: If 𝑎1 , 𝑎2 , 𝑎3 , … … . . , 𝑎𝑛 is any sequence then 𝑎1 + 𝑎2 + 𝑎3 + ⋯ … . . +𝑎𝑛 is called series
and it is denoted by ∑𝑛𝑟=1 𝑎𝑟 = ∑𝑎𝑟
 Geometric Progression[G.P] : A sequence is said to be in G.P if ratio of any two
consecutive terms are same. If 𝑎1 , 𝑎2 , 𝑎3 , 𝑎4 , … … … … . . 𝑎𝑛 is in G.P then
𝑎2 𝑎 𝑎
= 𝑎3 = ⋯ . = 𝑎 𝑛 is called common ratio and it is denoted by 𝑟
𝑎1 2 𝑛−1

 The consecutive terms of a G.P is given by 𝑎, 𝑎𝑟, 𝑎𝑟 2 , … … … . , 𝑎𝑟 𝑛−1
 The 𝑛th 𝑜𝑟 last term of G.P is given by 𝑇𝑛 or 𝒍 = 𝒂𝒓𝒏−𝟏
 Sum of 𝑛 terms of G.P: If 𝑎 is the first term and 𝑟 is the common ratio then sum of 𝑛
𝒂(𝒓𝒏 −𝟏) 𝒂(𝟏−𝒓𝒏 )
terms is given by 𝑺𝒏 = , where 𝑟 > 1 and 𝑺𝒏 = , where 𝑟 < 1
𝒓−𝟏 𝟏−𝒓

 If 𝑎 is the first term and 𝑟 is the common ratio then sum of ∞ terms is given by
𝒂
𝑺∞ = , |𝒓| < 𝟏
𝟏−𝒓
 Geometrical Mean (G. M.): G.M. of any n positive numbers a1 , a2 , a3 , … . . an is
(a1 . a2 . a3 … . . an )1/n.

 Product of n GM's inserted between 'a' and 'b' is equal to n th power of the single GM
between 'a' and 'b' i.e. ∏𝑛𝑟=1 𝐺𝑟 = (G)n where G = √𝑎𝑏
 In a G.P. every term (except first) is GM of its two terms which are at equidistant from it.
i.e. Tr = √𝑇𝑟−𝑘 𝑇𝑟+𝑘 k < r
 In a finite G.P. , the number of terms be odd then its middle term is the G.M. of the first
and last term.

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 If a1 , a2 , a3 … . an is a G.P. of non zero, non negative terms, then log a1 , log a2 , … … . log an is an
A.P. and vice-versa.
 If a1 , a2 , a3 ...... and b1 , b2 , b3 ...... are two G.P.'s then a1 b1 , a2 b2 , a3 b3 …. is also in G.P.
 Relation between A.M., & G.M.
A, G are AM and GM respectively between two numbers 'a' and 'b' then
a+b
A= , G = √ab, ⇒ A ≥ G
2
n(n+1)
 Sum of first n natural numbers ⇒ ∑nr=1 r = 2

 Sum of first 𝑛 odd natural numbers ⇒ ∑𝑛𝑟=1 (2𝑟 − 1) = 𝑛2
 Sum of first 𝑛 even natural numbers ⇒ ∑𝑛𝑟=1 2𝑟 = 𝑛(𝑛 + 1)
n(n+1)(2n+1)
 Sum of squares of first n natural numbers ⇒ ∑nr=1 r 2 = 6
n(n+1)2
 Sum of cubes of first n natural numbers ⇒ ∑nr=1 r 3 = [ ]
2
𝑛(𝑛2 +2)
 1 + 3 + 7 + 13 + ⋯ … . +𝑛 terms = 3
𝑛2 (𝑛+1)
 1 + 5 + 12 + 22 + 35 + ⋯ … … + n terms = 2

 If 𝑟 th term of an A.P. 𝑇𝑟 = 𝐴𝑟 3 + 𝐵𝑟 2 + 𝐶𝑟 + 𝐷, then sum of n term of AP is
𝑆𝑛 = ∑𝑛𝑟=1 𝑇𝑟 = 𝐴∑𝑛𝑟=1 𝑟 3 + 𝐵∑𝑛𝑟=1 𝑟 2 + C∑nr=1 r + D∑nr=1 1
 If number of terms in an A.P./G.P. is odd then its mid term is the A.M./G.M. between
the first and last number.
 If the number of terms in an A.P./G.P. is even then A.M./G.M. of its two middle terms is
equal to the A.M./G.M.between the first and last numbers.
1 1 1
 If a, b, c are in A.P. then bc , ac , ab are in A.P.

 If a, b, c are in G.P. then a2 , b2 , c 2 are in G.P.
1 1 1
 If a2 , b2 , c 2 are in A.P. then b+c , c+a , a+b are in A.P.

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Multiple choice questions
1. 𝟕th term of the sequence √𝟐, √𝟏𝟎, 𝟓√𝟐, … …. is (Easy)
1) 125√10 2) 25√2 3) 125 4) 125√2
2. Which term of the G.P., 5, 10, 20, 40, ……. is 5120? (Easy)
1) 9th 2) 10th 3)11th 4) 12th
3. If the first term of a G.P. be 5 and common ratio be -5, then which term is 3125
(Easy)

1) 6th 2) 5th 3) 7th 4) 8th
4. The mth term of an A.P. is n and its nth term is m. Its pth term is (Average)
1) m – n + p 2) m + n – p 3) m + n + p 4) m – n - p
5. If 𝒂, 𝒃, 𝒄 are three consecutive terms of an A.P and 𝒙, 𝒚, 𝒛 are three consecutive terms
of a G.P., then the value of 𝒙𝒃−𝒄 . 𝒚𝒄−𝒂 . 𝒛𝒂−𝒃 is : (KCET 2018) (Average)
1) 0 2) 𝑥𝑦𝑧 3) – 1 4) 1
6. Consider an infinite geometric series with first term 𝒂 and common ratio 𝒓. If the
𝟑
sum is 4 and the second term is 𝟒, then: (KCET 2014) (Difficult)
4 3 1 3 3 1
1) 𝑎 = 7 , 𝑟 = 7 2) 𝑎 = 3, 𝑟 = 4 3) 𝑎 = 2, 𝑟 = 8 4) 𝑎 = 2 , 𝑟 = 2

7. If the 𝟐nd and 𝟓th terms of G.P are 24 and 3 respectively, then the sum of 𝟏st six
terms is: (KCET 2015) (Easy)
189 189 179 2
1) 2) 3) 4) 189
2 5 2

8. If the third term of a G.P. is 4 then the product of its first 5 terms is (Easy)
1) 43 2) 44 3) 45 4) None of these
9. The 𝟐𝟎th term of the series 𝟐 × 𝟒 + 𝟒 × 𝟔 + 𝟔 × 𝟖 + ____ will be (Easy)
1) 1600 2) 1680 3) 420 4) 840
10. If the 𝟏𝟎th term of a geometric progression is 9 and 𝟒th term is 4, then its 𝟕th term
is (Average)
4 9
1) 6 2) 36 3) 9 4) 4
𝟓 𝟓 𝟓 𝟓
11. If the 𝒏th term of geometric progression 𝟓, − 𝟐 , 𝟒 , − 𝟖 , … is 𝟏𝟎𝟐𝟒, then the value of 𝒏

is (Average)
1) 11 2) 10 3) 9 4) 4

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𝒂 𝒂
12. If 𝒂𝟏 , 𝒂𝟐 , 𝒂𝟑 , … … 𝒂𝟏𝟎 is a geometric progression and 𝒂𝟑 = 𝟐𝟓, then 𝒂𝟗 equals
𝟏 𝟓

(KCET 2022) (Easy)
1) 3(52 ) 2) 54 3) 53 4) 2(52 )
𝟏 𝟑
13. The sum of the first five terms of the series 𝟑 + 𝟒 𝟐 + 𝟔 𝟒 + ⋯ … will be (Average)
9 3 7 9
1) 39 16 2) 18 16 3) 39 16 4) 13 16

14. The angles of a triangle are in A. 𝑷 and the greatest angle is double the least angle,
then sine of the third angle is (KCET 2026) (Average)
√3 1 1
1) 2 2) 3) 2 4) 0
√2

15. The sum of the series 𝟑 + 𝟑𝟑 + 𝟑𝟑𝟑 + ⋯ + 𝒏 terms is (Average)
1 1
1) 27 (10𝑛+1 + 9𝑛 − 28) 2)27 (10𝑛+1 − 9𝑛 − 10)
1
3) 27 (10𝑛+1 + 10𝑛 − 9) 4) None of these

16. If in a geometric progression {𝒂𝒏 }, 𝒂𝟏 = 𝟑, 𝒂𝒏 = 𝟗𝟔 and 𝑺𝒏 = 𝟏𝟖𝟗 then the value of 𝒏 is
(Average)
1) 5 2) 8 3) 7 4) 6
17. Three numbers are in G.P. such that their sum is 38 and their product is 1728. The
greatest number among them is (Difficult)
1) 18 2) 16 3) 14 4) None of these
18. If we insert two numbers between √𝟐 and 4 so that the resulting sequence is in G.P,
then the inserted numbers in the order are (KCET 2026) (Easy)
1) 8, √2 2) √2, 8 3) √8, 2 4) 2, √8
19. If three geometric means be inserted between 2 and 32, then the third geometric
mean will be (Easy)
1) 8 2) 4 3) 16 4) 12
20. The two geometric means between the number 1 and 64 are (Easy)
1) 1 and 64 2) 8 and 16 3) 2 and 16 4) 4 and 16
21. If 𝒂, 𝒃, 𝒄 are in G.P., then (Easy)
1) 𝑎2 , 𝑏 2 , 𝑐 2 are in G.P. 2) 𝑎2 (𝑏 + 𝑐), 𝑐 2 (𝑎 + 𝑏), 𝑏 2 (𝑎 + 𝑐) are in G.P.
𝑎 𝑏 𝑐
3) 𝑏+𝑐 , 𝑐+𝑎 , 𝑎+𝑏 are in G.P. 4) None of the above

22. If 𝟒th , 𝟏𝟎th and 𝟏𝟔th terms of a G.P. are 𝒙, 𝒚 and 𝒛 respectively, then
(KCET 2025) (Average)
𝑥+𝑧
1) y = √𝑥𝑧 2) 𝑥 = √𝑦𝑧 3) 𝑦 = 4) 𝑧 = √𝑥𝑦
2

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23. If 𝑺𝒏 stands for sum to 𝒏-terms of a G.P. with ' 𝒂′ as the first term and ' 𝒓 ' as the
common ratio then 𝐒𝐧 : 𝐒𝟐𝐧 is (KCET 2024) (Easy)
1 1
1) 𝑟 𝑛 + 1 2) n 3) 𝐫 n − 1 4) n
r −1 r +1

24. The sum can be found of a infinite G.P. whose common ratio is 𝒓 (Average)
1) For all values of 𝑟 2) For only positive value of 𝑟
3) Only for 0 < 𝑟 < 1 4) Only for −1 < 𝑟 < 1(𝑟 ≠ 0)
25. The sum of infinite terms of a G.P. is 𝒙 and on squaring the each term of it, the
sum will be 𝒚, then the common ratio of this series is (Difficult)
𝑥 2 −𝑦 2 𝑥 2 +𝑦 2 𝑥 2 −𝑦 𝑥 2 +𝑦
1) 𝑥 2 +𝑦 2 2) 𝑥 2 −𝑦 2 3) 𝑥 2 +𝑦 4) 𝑥 2 −𝑦

26. If 𝑺 is the sum to infinity of a G.P., whose first term is 𝒂, then the sum of the first
𝒏 terms is (Average)
𝑎 𝑛 𝑎 𝑛 𝑎 𝑛
1) 𝑆 (1 − 𝑆 ) 2) 𝑆 [1 − (1 − 𝑆 ) ] 3) 𝑎 [1 − (1 − 𝑆 ) ] 4) None of these

27. If three numbers be in G.P., then their logarithms will be in (Easy)
1) A.P. 2) G.P. 3) H.P. 4) None of these
28. If 𝑨𝟏 , 𝑨𝟐 are the two A.M.'s between two numbers 𝒂 and 𝒃 and 𝑮𝟏 , 𝑮𝟐 be two G.M.'s
𝑨 +𝑨
between same two numbers, then 𝑮𝟏 ⋅𝑮 𝟐 = (Average)
𝟏 𝟐

𝑎+𝑏 𝑎+𝑏 2𝑎𝑏 𝑎𝑏
1) 𝑎𝑏 2) 2𝑎𝑏 3) 𝑎+𝑏 4) 𝑎+𝑏

29. If the A.M. is twice the G.M. of the numbers 𝒂 and 𝒃, then 𝒂: 𝒃 will be (Average)
2−√3 √3+2 √3−2 2+√3
1) 2+√3 2) 3) 4) 2−√3
√3−2 √3+2

30. The sum to 𝒏 terms of the series 𝟐 + 𝟒𝟐 + 𝟔𝟐 + ____ is 𝟐
(Average)
𝑛(𝑛+1)(2𝑛+1) 𝑛(𝑛+1)(2𝑛+1) 𝑛(𝑛+1)(2𝑛+1) 2𝑛(𝑛+1)(2𝑛+1)
1) 2) 3) 4)
3 9 6 3
𝟏 𝟏 𝟏 𝟏
31. 𝟏.𝟐 + 𝟐.𝟑 + 𝟑.𝟒 + ⋯ … . . + ⋯ … . 𝒏.(𝒏+𝟏) equals (Average)
1 2𝑛 𝑛 2
1) 𝑛(𝑛+1) 2) 𝑛+1 3) 𝑛+1 4) 𝑛(𝑛+1)

32. The sum of the series 𝟏𝟐 . 𝟐 + 𝟐𝟐 . 𝟑 + 𝟑𝟐 . 𝟒 + ____ to 𝒏 terms is (Average)
𝑛3 (𝑛+1)3 (2𝑛+1) 𝑛(𝑛+1)(3𝑛2 +7𝑛+2)
1) 2)
24 12
𝑛(𝑛+1) 𝑛(𝑛+1)
3) [𝑛(𝑛 + 1) + (2𝑛 + 1)] 4) [6𝑛(𝑛 + 1) + 2(2𝑛 + 1)]
6 12

33. If the 𝟒th , 𝟕th and 𝟏𝟎th terms of a G.P. be 𝒂, 𝒃, 𝒄 respectively, then the relation
between 𝒂, 𝒃, 𝒄 is (Average)
𝑎+𝑐
1) 𝑏 = 2) 𝑎2 = 𝑏𝑐 3) 𝑏 2 = 𝑎𝑐 4) 𝑐 2 = 𝑎𝑏
2

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34. The number which should be added to the numbers 2, 14, 62 so that the resulting
numbers may be in G.P., is (Easy)
1) 1 2) 2 3) 3 4) 4
35. The terms of a G.P. are positive. If each term is equal to the sum of two terms that
follow it, then the common ratio is (Average)
√5−1 1−√5
1) 2) 3) 1 4) 2√5
2 2

36. If the ratio of the sum of first three terms and the sum of first six terms of a G.P.
be 𝟏𝟐𝟓: 𝟏𝟓𝟐, then the common ratio 𝒓 is (Average)
3 5 2 3
1) 5 2) 3 3) 3 4) 2

37. If 𝒏 geometric means between 𝒂 and 𝒃 be 𝑮𝟏 , 𝑮𝟐 , … . . 𝑮𝒏 and a geometric mean be 𝑮,
then the true relation is (Average)
1) 𝐺1 ⋅ 𝐺2 … … . . 𝐺𝑛 = 𝐺 2) 𝐺1 ⋅ 𝐺2 … … … 𝐺𝑛 = 𝐺 1/𝑛
3) 𝐺1 ⋅ 𝐺2 … … . . 𝐺𝑛 = 𝐺 𝑛 4) 𝐺1 ⋅ 𝐺2 … … … 𝐺𝑛 = 𝐺 2/𝑛
38. If the 𝒑th , 𝒒th and 𝒓th term of a G.P. are 𝒂, 𝒃, 𝒄 respectively, then 𝒂𝒒−𝒓 . 𝒃𝒓−𝒑 . 𝒄𝒑−𝒒 is
equal to (Average)
1) 0 2) 1 3) 𝑎𝑏𝑐 4) 𝑝𝑞𝑟
𝟏 𝟏𝟔
39. If the 𝟓th term of a G.P. is 𝟑 and 𝟗th term is 𝟐𝟒𝟑, then the 𝟒th term will be (Average)
3 1 1 2
1) 2) 3) 4)
4 2 3 5
𝒄 𝒑 𝒃 𝒓 𝒂 𝒒
40. If 𝒂, 𝒃, 𝒄 are 𝒑th , 𝒒th and 𝒓th terms of a G.P., then (𝒃) (𝒂) ( 𝒄 ) is equal to (Average)

1) 1 2) 𝑎𝑃 𝑏 𝑞 𝑐 𝑟 3) 𝑎𝑞 𝑏 𝑟 𝑐 𝑝 4) 𝑎𝑟 𝑏 𝑝 𝑐 𝑞
41. If 𝐥𝐨𝐠 𝒙 𝒂, 𝒂𝒙/𝟐 and 𝐥𝐨𝐠 𝒃 𝒙 are in G.P., then 𝒙 = (Average)
1) −log(log 𝑏 𝑎) 2) −log 𝑎 (log 𝑎 𝑏)
3) log 𝑎 (log 𝑒 𝑎) − log 𝑎 (log 𝑒 𝑏) 4) log 𝑎 (log 𝑒 𝑏) − log 𝑎 (log 𝑒 𝑎)

42. The 𝟔th term of a G.P. is 32 and its 𝟖th term is 128, then the common ratio of the
G.P. is (Easy)
1) – 1 2) 2 3) 4 4) -4
43. The third term of a G. P. is 9. The product of its first five terms is :
(KCET 2019) (Easy)
1) 310 2) 35 3) 312 4) 39
44. If the sum of an infinite G.P. be 9 and the sum of first two terms be 5 , then the
common ratio is (Average)
1) 1/3 2) 3/2 3) 3/4 4) 2/3

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45. If the sum of three terms of G.P. is 19 and product is 216, then the common ratio
of the series is (Average)
3 3
1) − 2) 2 3) 4) 3
2 2

46. The sum of the series 𝟔 + 𝟔𝟔 + 𝟔𝟔𝟔 + ____ upto 𝒏 terms is (Easy)
1) (10𝑛−1 − 9𝑛 + 10)/81 2) 2(10𝑛+1 − 9𝑛 − 10)/27
3) 2(10𝑛 − 9𝑛 − 10)/27 4) None of these

47. If the sum of 𝒏 terms of a G.P. is 255 and 𝒏th terms is 128 and common ratio is 2,
then first term will be (Average)
1) 1 2) 3 3) 7 4) None of these
48. If 𝟏 + 𝒂 + 𝒂𝟐 + 𝒂𝟑 + ⋯ … . . +𝒂𝒙 = (𝟏 + 𝒂)(𝟏 + 𝒂𝟐 )(𝟏 + 𝒂𝟒 ) then 𝒙 is equal to (Average)
1) 3 2) 5 3) 7 4) None of these
49. The sum of a G.P. with common ratio 3 is 364, and last term is 243, then the
number of terms is (Average)
1) 6 2) 5 3) 4 4) 10
𝒂𝒏+𝟏 +𝒃𝒏+𝟏
50. If the geometric mean between 𝒂 and 𝒃 is , then the value of 𝒏 is (Average)
𝒂𝒏 +𝒃𝒏

1) 1 2) −1/2 3) 1/2 4) 2
51. The G.M. of the numbers 𝟑, 𝟑𝟐 , 𝟑𝟑 , … . , 𝟑𝒏 is (Average)
2 𝑛+1 𝑛 𝑛−1
1) 3𝑛 2) 3 2 3) 32 4) 3 2
𝟏
52. The product of three geometric means between 4 and 𝟒 will be (Easy)

1) 4 2) 2 3) -1 4) 1
53. The sum of 3 numbers in geometric progression is 38 and their product is 1728.
The middle number is (Easy)
1) 12 2) 8 3) 18 4) 6
54. If the product of three consecutive terms of G.P. is 216 and the sum of product of
pairwise is 156, then the numbers will be (Easy)
1) 1, 3, 9 2) 2, 6, 18 3) 3, 9, 27 4) 2, 4, 8
55. The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be
(Easy)
1) 6 2) 3 3) 4 4) 1
56. If 𝒚 = 𝒙 − 𝒙𝟐 + 𝒙𝟑 − 𝒙𝟒 + ____ ∞, then value of 𝒙 will be (Average)
1 𝑦 1 𝑦
1) 𝑦 + 𝑦 2) 1+𝑦 3) 𝑦 − 𝑦 4) 1−𝑦

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57. Consider an infinite G.P. with first term a and common ratio 𝒓, its sum is 4 and the
second term is 𝟑/𝟒, then (Average)
7 3 3 1 3 1
1) 𝑎 = , 𝑟 = 2) 𝑎 = , 𝑟 = 3) 𝑎 = 2, 𝑟 = 4) 𝑎 = 3, 𝑟 =
4 7 2 2 8 4

58. If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3 , then its
first term and common ratio are (Average)
1) 3/2, ½ 2) 1, ½ 3) 3/2, 2 4) None of these
59. If the arithmetic and geometric means of 𝒂 and 𝒃 be 𝑨 and 𝑮 respectively, then the
value of 𝑨 − 𝑮 will be (Average)
2
𝑎−𝑏 𝑎+𝑏 √𝑎−√𝑏 2𝑎𝑏
1) 2) 3) [ ] 4) 𝑎+𝑏
𝑎 2 √2

60. If the arithmetic mean of two numbers be 𝑨 and geometric mean be 𝑮, then the
numbers will be (Easy)
1) 𝐴 ± (𝐴2 − 𝐺 2 ) 2) √𝐴 ± √𝐴2 − 𝐺 2
𝐴±√(𝐴+𝐺)(𝐴−𝐺)
3) 𝐴 ± √(𝐴 + 𝐺)(𝐴 − 𝐺) 4) 2

61. The geometric mean of two numbers is 6 and their arithmetic mean is 6.5 . The
numbers are (Easy)
1) (3,12) 2) (4,9) 3) (2,18) 4) (7,6)
62. If the product of three terms of G.P. is 512. If 8 added to first and 6 added to
second term, so that number may be in A.P., then the numbers are (Average)
1) 2, 4, 8 2) 3, 6, 12 3) 4, 8, 16 4) None of these
63. If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the
quadratic equation is (KCET 2024) (Easy)
1) 𝑥 2 − 10𝑥 − 16 = 0 2) 𝑥 2 + 10𝑥 + 16 = 0
3) 𝑥 2 + 10𝑥 − 16 = 0 4) 𝑥 2 − 10𝑥 + 16 = 0
𝟏 𝟏 𝟏
64. The sum of (𝒏 + 𝟏) terms of 𝟏 + 𝟏+𝟐 + 𝟏+𝟐+𝟑 + ⋯ … is (Average)
𝑛 2𝑛 2 2(𝑛+1)
1) 𝑛+1 2) 𝑛+1 3) 𝑛(𝑛+1) 4) 𝑛+2
𝟑 𝟓 𝟏
65. 𝒏th term of the series 𝟏 + 𝟕 + 𝟕𝟐 + 𝟕𝟐 + ⋯ …. is (KCET 2023) (Average)
2𝑛−1 2𝑛+1 2𝑛−1 2𝑛+1
1) 2) 7𝑛+1 3) 7𝑛−1 4)
7𝑛 7𝑛

2026-27 MATHEMATICS CET MATERIAL Page 8 of 9

SEQUENCE AND SERIES
1 2 3 4 5 6 7 8 9 10
4 3 2 2 4 2 4 3 2 1
11 12 13 14 15 16 17 18 19 20
1 2 1 1 2 4 1 4 3 2
21 22 23 24 25 26 27 28 29 30
1 1 4 4 3 2 1 1 4 4
31 32 33 34 35 36 37 38 39 40
3 2 3 2 1 1 3 1 2 1
41 42 43 44 45 46 47 48 49 50
1 2 1 2 3 2 1 3 1 2
51 52 53 54 55 56 57 58 59 60
2 4 1 2 3 4 4 1 3 3
61 62 63 64 65
2 3 4 4 3

2026-27 MATHEMATICS CET MATERIAL Page 9 of 9