We can write 4 x (- 8) as
4 x (- 8) = (- 8) + (- 8) + (- 8) + (- 8)
It can be represented on the number line as under:

We have, 8 x (- 2) = (- 2) + (- 2) + (- 2) + (-2) + (-2) + (-2) + (-2) + (-2)
It can be represented on the number line as under:

We have, 3 x (-7) = (-7) + (-7) + (-7)
It can be represented on the number line as under:

We have,
10 x (-1) = (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1)
It can be represented on the number line as under:
.

(i) 49
(ii) 28

23rd January

(i) 300 m below ground level
(ii) 210 m below ground level

As per the given information, we can draw the given diagram.

Let A be the point above the sea level and B be the point below the sea level.
\(\therefore\) Vertical distance between points A and B = Distance between point A and sea level + Distance between point B and sea level.
= AO + OB = 8848 + 10911 = 19759 m

For two integers, which are greater than -4, but their difference is smaller than -2.
So, first integer = - 3 and second integer = -1
Their difference = - 3 -1 = - 4
Hence, - 4 is smaller than -2.

For two integers which are smaller than -5 but their difference is -5.
So, first integer = -11 and second integer = -6
Their difference = -11 - (-6) = -11 + 6 = - 5

Given, marks for every correct answer = + 3
Marks for every incorrect answer = - 2
(i) Total marks scored by Radhika = 20
Marks scored for correct answer = 12 \(\times\) 3 = 36
\(\therefore\) Marks given for incorrect answers
= Total marks - Marks given for correct answers
= 20 -36= -16
\(\therefore\) Number of incorrect answers
= \(\frac { Total\ Marks\ of\ incorrect\ answers }{ Marks\ of\ every\ incorrect\ answer } \)
= \(\frac { \left( -16 \right) }{ \left( -2 \right) } =\frac { -16 }{ -2 } \)= 8
Hence, Radhika attempted 8 questions incorrectly
(ii) Marks obtained by Mohini = - 5
Marks obtained for 7 correct answers = 7 \(\times\) 3 = 21
\(\therefore\)Marks obtained for incorrect answers
= - 5 - 21 = - 26
\(\therefore\)Number of incorrect answers
= \(\frac { Total~ Marks \ obtained \ for \ incorrect \ answers }{ Marks \ of \ every \ incorrect \ answer } \)
= \(\frac { -26 }{ -2 } \)
= 13

(i) We know that, 3 \(\div\) 1= 3, so 3 \(\div\) (- 1)= - 3
On comparing with a \(\div\) b = - 3, we get a = 3 and b = -1
Hence, the required pair of integers is (3, -1).
(ii) We know that, 12 \(\div\) 4 = 3, so 12 \(\div\)(- 4) = - 3
On comparing with a \(\div\) b = - 3, we get a = 12 and b = -4
Hence, the required pair of integers is (12, - 4).
(iii) We know that, 9 \(\div\) 3 = 3, so 9 \(\div\) (- 3) = - 3
On comparing with a \(\div\) b = - 3, we get a = 9 and b = -3
Hence, the required pair of integers is (9, - 3).
(iv) We know that,12 \(\div\) 4 = 3, so (-12) \(\div\) 4 = -3
On comparing with a \(\div\) b = - 3, we get a = -12 and b=4
Hence, the required pair of integers is (-12, 4).
(v) We know that, 15 \(\div\) 5 = 3, so 15 + (- 5) = -3
On comparing with a \(\div\) b = - 3, we get a = 15 and b = -5
Hence, the required pair of integers is (15, - 5).

Given, total number of questions = 10
Marks for a correct answer = 5
Marks for an incorrect answer = (- 2)
Marks for not attempted the question = 0
(i) Mohan's score = (Correct questions \(\times\) Marks) + (Incorrect questions \(\times\) Marks)
= 4 \(\times\) (5) + 6 \(\times\) (- 2)
= 20 + (-12) = 20 -12 = 8
(ii) Reshmas score = 5 \(\times\) 5 + 5 \(\times\) (- 2)
=25 + (-10) = 15
(iii) Heena's score = 2 \(\times\) 5 + 5 \(\times\) (- 2) + 3 \(\times\) 0
=10 + (-10) + 0 = 0