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

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## 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.
(i) 0
(ii) Odd

Question 2.
Match the following:

 Group A Exponential form Group B Unit digit of the number (i) 2010 (a) 6 (ii) 12111 (b) 4 (iii) 44441 (c) 0 (iv) 25100 (d) 1 (v) 71683 (e) 9 (vi) 729725 (f) 5

(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
(ii) 5

Question 6.
The unit digit of (32 × 65)0 is
(i) 2
(ii) 5
(iii) 0
(iv) 1 