Details given in the question can be described in the figure shown below:

From above figure, it is clear that,
Minimum length of the rope required to draw the water during the rainy season = Distance between pulley and wall of well + Height of well + Distance between water level during the rainy season and ground level
= (0.8 + 1.2 + 15) m = 17 m

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

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

Let the number of steps moved down to be represented by negative integers and number of steps moved up to be represented by positive integers. Given that, the total number of steps to be moved down to reach water level= 9
(i) Number of steps moved down in one jump = - 3
and number of steps moved up in one jump = 2

From the above figure, monkey will reach the water level in 11 jumps.
Alternate Method:
The monkey is sitting on the topmost step i.e. the first step. While going down, the monkey jumps 3 steps down and then jumps back 2 steps up. To reach the water level, he has to jump as follows:
-3 + 2 -3 + 2 -3 + 2 -3 + 2 -3 + 2 -3 = -8
Hence, he takes 11 jumps to reach the water level.
ii) In one jump number of steps moved up = 4
In one jump, number of steps moved down = - 2

Distance covered in single jump = 4 - 2 =2
Now, total number of steps for top = 9
From the above figure, he will reach back the top step in 5 jumps.
Alternate Method
Afterdrinkingwaters,he has to jump as followsto go back:
4 -2 + 4 - 2 + 4 = 8
Hence, he takes 5 jumps to reach back the top
(iii) (a) We have,
-3 + 2 -3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 -3 = -8
(b) 4 - 2 + 4 - 2 + 4 = 8
According to the question, the sum 8 in part (b) represents going up 8 steps.

(a) Since, she deposits Rs 2000 per month
∴ Amount deposit by her in six months
= Rs 2000 \(\times\) (6)
= Rs 12,000
She withdraw Rs 1600 and Rs 5000 in need.
So, withdrawal = - (1600 + 5000)
So, present position of account
= 12000- (1600 + 5000)
= 12000- 6600
= 5400
So, she has balance Rs 5400 in her account.
(b) Multiplication and subtraction of integers.
(c) If you save the money you can use it in need.

Distance towards East denoted (+ve) sign and Distance towards West denoted (-ve) sign.
Since first Ridhaan goes toward East 25 km
So distance covered by him = + 25 km
Again, he goes towards West.
So, distance covered by him on same road
= -35 km.
So,position of Ridhaan from A= + 25 - 35
= -10 km.
(b) Value: Addition of Integers.
(c) Value: A rolling stone can gather no moss.

(a) Score of Mohan= 6 \(\times\) (5) + 4 \(\times\) (- 2)
= 30 + (-8)
=30 - 8 = 22
(b) Rekha's score = 5 \(\times\) (5) + 3 \(\times\) (-2) + 2 \(\times\) 0
= 25 + (-6) + 0
= 25 - 6 = 19
(c) Mayank's score = 5 \(\times\) (5) + 5 \(\times\) (- 2)
= 25 + (-10) = 25 -10 = 15
(d) Jeet's score = 3 \(\times\) (5) + 5 \(\times\) (- 2)
= 15 + (-10) = 15-10 = 5

On Tuesday: -8°C; on Wednesday: -5^oC

(i) 9 km above sea level
(ii) A deposit of Rs.10,000
(iii) 100⁰C below the freezing point
(iv) 5 kg increase in weight
(v) A loss of Rs.25,000

Marks given for 1 correct answer = 5
∴ Marks given for 16 correct answers
= 16 x 5 = 80
Since, Rahul's score = 40
∴ Marks given for incorrect answer
= 40 - 80 = (-40)
Marks for 1 incorrect answer = - 2
∴ Number of incorrect answers
= (-40) + (-2) = 20

Marks for one correct answer = + 5
Marks for one incorrect answer = - 2
Marks given for 4 correct answers = 5 \(\times\) 4 = 20
Score of Jay = - 12
Marks received by him for incorrect answer
= -12-20 = -32
Marks given for one incorrect answer = - 2
∴ Number of incorrect answers = (- 32)  ÷ (- 2)
= (32) ÷ 2 = 16
Hence, total answers, Jay attempted which were incorrect is 16 answers.

We have
\(222-\begin{bmatrix} {1\over3}\{42+(56-\overline{8+9}) \}+108 \end{bmatrix}\)
\(=222-\begin{bmatrix} {1\over3}\{42+(56-17\}+108 \end{bmatrix}\)    [Removing vinculum]
\(=222-\begin{bmatrix} {1\over3}\{42+39 \}+108 \end{bmatrix}\)        [Removing parentheses]
\(=222-\begin{bmatrix} {81\over 3}+108 \end{bmatrix}\)               [Removing braces]
= 222 - [27 + 108]
= 333 -135 = 87

We have
48 - [18- {16- (5 - \(\overline { 4-1 } \) )}]
= 48 - [18- {16- (5 - 3)}]   [Removing vinculum]
= 48 - [18- {16- 2}]         [Removing parentheses]
= 48- [18-14]                 [Removing braces]
= 48-4
=44.

Wehave,
27-[5 + {28-(29-7)}] = 27-[5 + {28-22}]
[Removing the innermost brackets]
= 27- [5 + 6]
[Removing Brackets]
= 27 -11 = 16

399- (- 1) + (- 20) \(\times\) (- 20)- 800
= 399 + 1 + 400 - 800
= 400 + 400 - 800
= 800 - 800 = 0