Tamil Nadu Board 10th Standard Maths - Chapter 2 Excercise 2.10: Book Back Answers and Solutions
This post covers the book back answers and solutions for Chapter 2 Excercise 2.10 – Maths from the Tamil Nadu State Board 10th Standard Maths textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.
We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.
By going through this material, you’ll gain a strong understanding of Chapter 2 Excercise 2.10 along with the corresponding book back questions and answers (PDF format).
Question Types Covered:
- 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following
- 2 Mark Questions: Answer briefly
- 3, 4, and 5 Mark Questions: Answer in detail
All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.
All the best, Class 10 students! Prepare well and aim for top scores. Thank you!
Chapter 2 Numbers and Sequences Ex 2.10
(1) 1 < r < b
(2) 0 < r < b
(3) 0 < r < 6
(4) 0 < r < b
Answer Key:
(3) 0 < r < b
(1) 0, 1, 8
(2) 1, 4, 8
(3) 0, 1, 3
(4) 1, 3, 5
Answer Key:
(1) 0, 1, 8
Hint: Let the +ve integer be 1, 2, 3, 4 …………
13 = 1 when it is divided by 9 the remainder is 1.
23 = 8 when it is divided by 9 the remainder is 8.
33 = 27 when it is divided by 9 the remainder is 0.
43 = 64 when it is divided by 9 the remainder is 1.
53 = 125 when it is divided by 9 the remainder is 8.
The remainder 0, 1, 8 is repeated.
(1) 4
(2) 2
(3) 1
(4) 3
Answer Key:
(2) 2
Hint:
H.C.F. of 65 and 117
117 = 65 × 1 + 52
65 = 52 × 1 + 13
52 = 13 × 4 + 0
∴ 13 is the H.C.F. of 65 and 117.
65m – 117 = 65 × 2 – 117
130 – 117 = 13
∴ m = 2
(1) 1
(2) 2
(3) 3
(4) 4
Answer Key:
(3) 3
Hint: 1729 = 7 × 13 × 19
Sum of the exponents = 1 + 1 + 1
= 3
(1) 2025
(2) 5220
(3) 5025
(4) 2520
Answer Key:
(4) 2520
Hint:

= 8 × 9 × 5 × 7
= 2520
(1) 1
(2) 2
(3) 3
(4) 4
Answer Key:
(1) 1
Hint:
74k ≡______ (mod 100)
y4k ≡ y4 × 1 = 1 (mod 100)
(1) 3
(2) 5
(3) 8
(4) 11
Answer Key:
(4) 11
Hint:
Fn = Fn-1 + Fn-2
F3 = F2 + F1 = 3 + 1 = 4
F4 = F3 + F2 = 4 + 3 = 7
F5 = F4 + F3 = 7 + 4 = 11
(1) 4551
(2) 10091
(3) 7881
(4) 13531
Answer Key:
(3) 7881
Hint:
t1 = 1
d = 4
tn = a + (n – 1)d
= 1 + 4n – 4
4n – 3 = 4551
4n = 4554
n = will be a fraction
It is not possible.
4n – 3 = 10091
4n = 10091 + 3 = 10094
n = a fraction
4n – 3 = 7881
4n = 7881 + 3 = 7884
n =, n is a whole number.
4n – 3 = 13531
4n = 13531 – 3 = 13534
n is a fraction.
∴ 7881 will be 1971st term of A.P.
(1) 0
(2) 6
(3) 7
(4) 13
Answer Key:
(1) 0
Hint:
6 t6 = 7 t7
6(a + 5d) = 7 (a + 6d) ⇒ 6a + 30d = 7a + 42d
30 d – 42 d = 7a – 6a ⇒ -12d = a
t13 = a + 12d (12d = -a)
= a – a = 0
(1) 16 m
(2) 62 m
(3) 31 m
(4) m
Answer Key:
(3) 31 m
Hint:
t16 = m
S31 = (2a + 30d)
= (2(a + 15d))
(∵ t16 = a + 15d)
= 31(t16) = 31m
(1) 6
(2) 7
(3) 8
(4) 9
Answer Key:
(3) 8
Here a = 1, d = 4, Sn = 120
Sn = [2a + (n – 1)d]
120 = [2 + (n – 1)4] = [2 + 4n – 4)]
= [4n – 2)] = × 2 (2n – 1)
120 = 2n2 – n
∴ 2n2 – n – 120 = 0 ⇒ 2n2 – 16n + 15n – 120 = 0
2n(n – 8) + 15 (n – 8) = 0 ⇒ (n – 8) (2n + 15) = 0
n = 8 or n = (omitted)
∴ n = 8
(1) B is 264 more than A
(2) A and B are equal
(3) B is larger than A by 1
(4) A is larger than B by 1
Answer Key:
(4) A is larger than B by
A = 265
B = 264+63 + 262 + …….. + 20
= 2
= 1 + 22 + 22 + ……. + 264
a = 1, r = 2, n = 65 it is in G.P.
S65 = 1 (265 – 1) = 265 – 1
A = 265 is larger than B
(1)
(2)
(3)
(4)
Answer Key:
(2)
Hint:
The next term is =
(1) a Geometric Progression
(2) an Arithmetic Progression
(3) neither an Arithmetic Progression nor a Geometric Progression
(4) a constant sequence
Answer Key:
(2) an Arithmetic Progression
Hint:
If t1, t2, t3, … is 1, 2, 3, …
If t6 = 6, t12 = 12, t18 = 18 then 6, 12, 18 … is an arithmetic progression
(1) 14400
(2) 14200
(3) 14280
(4) 14520
Answer Key:
(3) 14280
Hint:

120 × 119 = 14280
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