Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Ex 3.2

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Ex 3.2

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Ex 3.2

Question 1.
Fill in the blanks.

(i) Unit digit of 124 × 36 × 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) – d
(iii) – b
(iv) – f
(v) – a
(vi) – e

Question 3.
Find the unit digit of expanded form.
(i) 25²³
(ii) 11¹⁰
(iii) 46¹⁵
(iv) 100¹²
(v) 29²¹
(vi) 19¹²
(vii) 24²⁵
(viii) 34¹⁶
Solution:
(i) 25²³
Unit digit of base 25 is 5 and power is 23. Thus the unit digit of 25²³ is 5.

(ii) 11¹⁰
Unit digit of base 11 is 1 and power is 10. Thus the unit digit of 11¹⁰ is 1.

(iii) 46¹⁵
Unit digit of base 46 is 6 and power is 15. Thus the unit digit of 46¹⁵ is 6.

(iv) 100¹²
Unit digit of base 100 is 0 and power is 12. Thus the unit digit of 100¹² is 0.

(v) 29²¹
Unit digit of base 29 is 9 and power is 21 (odd power).
Therefore, unit digit of 29²¹ is 9.

(vi) 19¹²
Unit digit of base 19 is 9 and power is 12 (even power).
Therefore, unit digit of 19¹² is 1.

(vii) 24²⁵
Unit digit of base 24 is 4 and power is 25 (odd power).
Therefore, unit digit of 24²⁵ is 4.

(viii) 34¹⁶
Unit digit of base 34 is 4 and power is 16 (even power).
Therefore, unit digit of 34¹⁶ is 6.

Question 4.
Find the unit digit of the following numeric expressions.
(i) 114²⁰ + 115²¹ + 116²²
(ii) 10000¹⁰⁰⁰⁰ + 11111¹¹¹¹¹
Solution:
(i) 114²⁰ + 115²¹ + 116²²
In 114²⁰ unit digit of base 114 is 4 and power is 20 (even power).
∴ Unit digit of 114²⁰ is 6.
In 115²¹ unit digit of base 115 is 5 and power is 21 (Positive Integer).
∴ Unit digit of 115²¹ is 5.
In 116²² unit digit of base 116 is 6 and power is 22 (Positive Integer).
∴ Unit digit of 116²² is 6.
∴ Unit digit of 114²⁰ + 115²¹ + 116²² can be obtained by adding 6 + 5 + 6 = 17.
Unit digit of 114²⁰ + 115²¹ + 116²² is 7.

(ii) 10000¹⁰⁰⁰⁰ + 11111¹¹¹¹¹
In 10000¹⁰⁰⁰⁰ the unit digit of base 10000 is 0 and power is 10000.
Unit digit of 10000¹⁰⁰⁰⁰ is 0.
In 11111¹¹¹¹¹ the unit digit of base 11111 is 1 and power is 11111.
Unit digit of 11111¹¹¹¹¹ is 1.
Unit digit of 10000¹⁰⁰⁰⁰⁰ + 11111¹¹¹¹¹ 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 × 65)⁰ is
(i) 2
(ii) 5
(iii) 0
(iv) 1
Answer:
(iv) 1

Question 7.
The unit digit of the numeric expression 10⁷¹ + 10⁷² + 10⁷³ is
(i) 0
(ii) 3
(iii) 1
(iv) 2
Answer:
(i) 0