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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) | 20^{10} |
(a) | 6 |

(ii) | 121^{11} |
(b) | 4 |

(iii) | 444^{41} |
(c) | 0 |

(iv) | 25^{100} |
(d) | 1 |

(v) | 716^{83} |
(e) | 9 |

(vi) | 729^{725} |
(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) 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).

∴ Unit digit of 114^{20} is 6.

In 115^{21} unit digit of base 115 is 5 and power is 21 (Positive Integer).

∴ Unit digit of 115^{21} is 5.

In 116^{22} unit digit of base 116 is 6 and power is 22 (Positive Integer).

∴ Unit digit of 116^{22} is 6.

∴ 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 × 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