Exercise 3.2 - Chapter 3 Algebra Term 2 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $3.2$
Question 1 .
Fill in the blanks.
(i) Unit digit of $124 \times 36 \times 980$ is
(ii) When the unit digit of the base and its expanded form of that number is 9 , then the exponent must be power.
Answers:
(i) 0
(ii) Odd

Question $2 .$
Match the following:

Answer:
(i) - c
(ii) - $\mathrm{d}$
(iii) $-b$
(iv) $-f$
(v) $-\mathrm{a}$
(vi) - e

Question $3 .$
Find the unit digit of expanded form.
(i) $25^{23}$
(ii) $11^{10}$
(iii) $46^{15}$
(iv) $100^{12}$
(v) $29^{21}$
(vi) $19^{12}$
(vii) $24^{25}$
(viii) $34^{16}$
Solution:
(i) $25^{23}$
Unit digit of base 25 is 5 and power is 23 . Thus the unit digit of $25^{23}$ is 5 .
(ii) $11^{10}$
Unit digit of base 11 is 1 and power is 10 . Thus the unit digit of $11^{10}$ is 1 .
(iii) $46^{15}$
Unit digit of base 46 is 6 and power is 15 . Thus the unit digit of $46^{15}$ is 6 .
(iv) $100^{12}$
Unit digit of base 100 is 0 and power is 12 . Thus the unit digit of $100^{12}$ is 0 .
(v) $29^{21}$
Unit digit of base 29 is 9 and power is 21 (odd power).
Therefore, unit digit of $29^{21}$ is 9 .
(vi) $19^{12}$
Unit digit of base 19 is 9 and power is 12 (even power).
Therefore, unit digit of $19^{12}$ is 1 .

(vii) $24^{25}$
Unit digit of base 24 is 4 and power is 25 (odd power).
Therefore, unit digit of $24^{25}$ is $4 .$
(viii) $34^{16}$
Unit digit of base 34 is 4 and power is 16 (even power).
Therefore, unit digit of $34^{16}$ is 6 .

Question $4 .$
Find the unit digit of the following numeric expressions.
(i) $114^{20}+115^{21}+116^{22}$
(ii) $10000^{10000}+11111^{11111}$
Solution:
(i) $114^{20}+115^{21}+116^{22}$
In $114^{20}$ unit digit of base 114 is 4 and power is 20 (even power).
$\therefore$ Unit digit of $114^{20}$ is 6 .
In $115^{21}$ unit digit of base 115 is 5 and power is 21 (Positive Integer).
$\therefore$ Unit digit of $115^{21}$ is 5 .
In $116^{22}$ unit digit of base 116 is 6 and power is 22 (Positive Integer).
$\therefore$ Unit digit of $116^{22}$ is 6 .
$\therefore$ Unit digit of $114^{20}+115^{21}+116^{22}$ can be obtained by adding $6+5+6=17$.
Unit digit of $114^{20}+115^{21}+116^{22}$ is 7 .

(ii) $10000^{10000}+11111^{11111}$
In $10000^{10000}$ the unit digit of base 10000 is 0 and power is 10000 . Unit digit of $10000^{10000}$ is 0 .
In $11111^{11111}$ the unit digit of base 11111 is 1 and power is 11111 .
Unit digit of $11111^{11111}$ is 1 .
Unit digit of $10000^{100000}+11111^{11111}$ is $0+1=1$

Objective Type Question
Question $5 .$
Observe the equation $(10+y)^{4}=50625$ and find the value of $y$.
(i) 1
(ii) 5
(iii) 4
(iv) 0
Answer:
(ii) 5

Question $6 .$
The unit digit of $(32 \times 65)^{0}$ is
(i) 2
(ii) 5
(iii) 0
(iv) 1

Answer:
(iv) 1

Question $7 .$
The unit digit of the numeric expression $10^{71}+10^{72}+10^{73}$ is
(i) 0
(ii) 3
(iii) 1
(iv) 2
Answer:
(i) 0