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( 1, 3), ( 0, 4), (– 1, 5), (– 2, 6)

(i) (-16, +4) because (- 16) ÷ 4 = -4 

(ii) (20, -5) because 20 ÷ (-5) = – 4

(iii) (—8, 2) because (-8) ÷ 2 =- 4 

(iv) (24, -6) because 24 ÷ (-6) = – 4 

(v) (-36, 9) because (-36) ÷ 9 = – 4 

(OR)

– 140, – 130, – 120, – 110, – 101 (there can be many answers).

i) – 5, – 10 

Integers between – 5, – 10 are – 6, – 7, – 8, – 9 

smallest Integer – 9 

biggest integer = – 6 

ii) 3, – 2 

Integers between 3 and – 2 are – 1,0, 1, 2 

smallest integer = – 1 

biggest integer= 2

 iii) – 8, 5 

Integers between – 8 and 5 are 4, 3, 2, 1, 0, – 1, – 2, – 3, – 4, – 5, – 6, – 7 

smallest integer = – 7 

biggest integer = 4

(a) 0 and -7

-6, -5, -4, -3, -2, -1

(b) -4 and 4

-3, -2, -1, 0, 1, 2, 3

(c) -8 and -15

-14, -13, -12, -11, -10, -9

(d) -30 and -23 .

-29, -28, -27, -26, -25, -24

(– 23) + 47 is same as 47 + (– 23).

True

(– 5) × (33) = 5 × ( – 33)

True

Total marks scored = 20
Number of correct answer = 12
Marks of for correct answer = 12 × 3 = 36
Also
Marks for incorrect answer = (-2) × Number of incorrect answer
Marks for not attempt answer = 0 × Number of not attempt = 0
Now,
Total marks = marks for correct answer + marks for incorrect answer + marks for not attempt
20 = 36 + (-2) × No of incorrect answers + 0
20 – 36 = (-2) × No of incorrect answers
-16 = (-2) × No of incorrect answer
\(\frac{-16}{-2}\) = No of incorrect answers
8 = No of incorrect answers
So, Radhika attempted 8 questions incorrectly

Correct option is  C) – 3

Correct option is  D) – 2

Correct option is A (-3)

-6 (- 3) 

= -6 + 3 

= -3

Correct option is  A) – 3

-6 -(3) = -6 + 3 = -3

Correct option is  B) 24

Correct option is  D) – 30

B) 10, C) – 10

{12 – \(\overline{14-8}\) + 7} – 15 (Vinculum)

= {12 – 6 + 7} – 15

= {12 + 7 – 6} – 15 (Curly bracket) 

= {19 – 6} – 15 = 13 – 15 (Subtraction) 

= – 2

D) cannot determine

any number divided by zero is always underfined.

∴ 11/0 is not defined.

so, can not be determine.

Correct option is  B) – 1

(1 x -1) x (1 x -1) x .... x (1 x -1) (11times)

= -1 x -1 x -1 x ......... x -1 (11 times) 

= (-1)¹¹

^{= -1}

Correct option is  A) – 48

-8 + 16 - 24 + 32 - 64  

= 48 - 96 

= -48 

Correct option is (A) -48

48 - 96 = -48
 

8 × 3 –\(\overline{13-7}\) (Vinculum)

= 8 × 3 – 6 (Multiplication) 

= 24 – 6 (Subtraction) 

= 18

False.

Example:

Consider 3 different integers 5, 10 and -15.

Sum of 3 integers = 5 + 10 + (-15)

= 5 + 10 – 15

= 15 – 15

= 0

Therefore, the sum of three different integers can be zero.

On the number line, 10 is to the right of zero.

Positive integers are always coming right to the 0, so positive integers always greater than 0.

On the number line, –15 is to the left of zero.

Negative integers are always comes left to the 0, so negative integers always less than 0.

On the number line, 10 is to the right of zero. 

The additive inverse of 14 is -14.

-14

Additive inverse of an integer is obtained by changing the sign of the integer.

∴ Additive inverse of 14 is -14.

The additive inverse of 0 is 0.

1

Additive inverse of an integer is obtained by changing the sign of the integer.

∴ Additive inverse of -1 is 1.

The smallest integer is 0.

False

6 and –6 are at the same distance from 0 on the number line. 

True

True

The integer 6 is 6 units to the right of 0 and the integer -6 is 6 units to the left of 0.

Thus, 6 and -6 are at the same distance from 0 on the number line.

The difference between an integer and its additive inverse is always even.

True

True.

Example:

Consider an integer 5.

Its additive invers is -5

Difference between an integer and its additive inverse = 5 – (-5)

= 5 + 5

= 10

(B) is always positive 

[(–32) ÷ 8 ] ÷ 2 = –32 ÷ [ 8 ÷ 2]

False

True

(-8) × (-10) = 8 × 10 = 80

and  80 ÷ (-8) = -80/8 = -10

True

Let any integer be a.

Its additive inverse is -a.

a + (-a) = a – a = 0

Integers are closed under division.

False

If a, b, c are integers and b ≠ 0 then, a × ( b – c) = a × b – a × c

False

False

When we multiply two integers then their product may or may not be greater than both the integers.

True

Since, product of odd number of negative integers is always a negative integer.

False

As integers are not closed under division.

True. 

5 ÷ 0 is not defined.

So, the division of integers by zero is not defined.

4 × (- 5) = (- 5) × 4 

– (4 × 5) = -(5 × 4) 

– 20 = – 20 

So, for any two integers a and b, 

a × b = b × a.

Correct option is  A) N

Multiplication is not commutative for integers.

False

No, integers are not associative under subtraction. 

(a – b) – c ≠ a – (b – c) 

(6 – 4) – 5 ≠ 6 – (4 – 5) 

2 – 5 ≠ 6-( – 1) 

– 3 ≠ 6 + 1 

– 3 ≠ + 7

False.

5 – 3 ≠ 3 – 5 

2 ≠ – 2, i.e., a – b ≠ b – a. 

Integers are not commutative under subtraction.