Exercise 3.2

Exercise 3.2

1. Fill in the blanks.

(i) Unit digit of 124 × 36 × 980 is 0.

(ii) When the unit digit of the base and its expanded form of that number is 9, then the exponent must be odd power.

2. Match the following:

Answer :

i) 20¹⁰ (c) 0

ii) 121¹¹ (d) 1

iii) 444⁴¹ (b) 4

iv) 25¹⁰⁰ (f) 5

v) 716⁸³ (a) 6

vi) 729⁷²⁵ (e) 9 

3. Find the unit digit of expanded form.

(i) 25²³

Unit digit of base 25 is 5 and power is 23 (Odd number).

Thus, the unit digit of 25²³ is 5.

(ii) 11¹⁰

Unit digit of base 11 is 5 and power is 10 (Even number).

 Thus, the unit digit of 11¹⁰ is 1.

(iii) 46¹⁵

Unit digit of base 46 is 6 and power is 15 (Odd number).

 Thus, the unit digit of 46¹⁵ is 6.

(iv)100¹²

Unit digit of base 100 is 0 and power is 12 (Even number).

Thus, the unit digit of 100¹² is 0.

(v) 29²¹

Unit digit of base 29 is 9 and power is 21 (Odd number).

Thus, the unit digit of 29²¹ is 9.

(vi) 19¹²

Unit digit of base 19 is 9 and power is 12 (Even number).

Thus, the unit digit of 19¹² is 1.

(vii) 24²⁵

Unit digit of base 24 is 4 and power is 25(Odd number).

Thus, the unit digit of 24²⁵ is 4.

(viii) 34¹⁶

Unit digit of base 34 is 4 and power is 16 (Even number).

Thus, the unit digit of 34¹⁶ is 6.

4. Find the unit digit of the following numeric expressions.

(i) 114²⁰ + 115²¹ + 116²²

Unit digit of base 114 is 4 and power is 20 (Even number).

Thus the unit digit of 114²⁰ is 6.

Unit digit of base 115 is 5 and power is 21 (Odd number).

Thus the unit digit of 115²¹ is 5.

Unit digit of base 116 is 6 and power is 22 (Even number).

Thus the unit digit of 116²² is 6.

6 + 5 + 6 = 17

Unit digit of 17 is 7.

So, Unit digit of 114²⁰ + 115²¹ +116²² is 7.

(ii) 10000¹⁰⁰⁰⁰ + 11111¹¹¹¹¹

Unit digit of 10000 is 0 and Power is 10000 (Even number).

So, Unit digit of l0000¹⁰⁰⁰⁰ is 0.

Unit digit of 11111 is 1 and power is 11111 (Odd number). So, Unit digit of 11111¹¹¹¹¹ is 1.

Objective type questions

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

6. The unit digit of (32 × 65)⁰ is

(i) 2

(ii) 5

(iii) 0

(iv) 1

Answer: (iv) 1

7. The unit digit of the numeric expression 10⁷¹ + 10⁷² + 10⁷³ is

(i) 0

(ii) 3

(iii) 1

 (iv) 2

Answer: (i) 0

ANSWERS:

Exercise 3.2

1. (i) 0 (ii) odd

2. Group A Group B

(i) : (c)

(ii) : (d)

(iii) : (b)

(iv) : (f)

(v) : (a)

(vi) : (e)

3. (i) 5 (ii) 1 (iii) 6 (iv) 0   (v) 9 (vi) 1 (vii) 4 (viii) 6

4. (i) 7 (ii) 1

Objective type questions

5. (ii) 5

6. (iv) 1

7. (i) 0