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:

	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

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

SabDekho

The Complete Educational Website

Bihar Board

UP Board

IAS Notes

Jac Board

MP Board

सम्पूर्ण व्याकरण

जीवनी

निबंध

टेन्स

सामान्य ज्ञान

Rajasthan Board

NCERT Solutions in Hindi

NCERT Solutions in English