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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.
Answers:
(i) 0
(ii) Odd
Question 2.
Match the following:
Group A | Group B | ||
(i) | 2010 | (a) | 6 |
(ii) | 12111 | (b) | 4 |
(iii) | 44441 | (c) | 0 |
(iv) | 25100 | (d) | 1 |
(v) | 71683 | (e) | 9 |
(vi) | 729725 | (f) | 5 |
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