37 - 0
For subtraction 37 - 0 = 37
Verification First integer (x) = 37          [given]
Second integer (y) = 0                 [given]
For closure property x - y = 37 - 0 = 37 (integer) i.e. subtraction is closed.

Preceding integers = -10, -9, -8
Succeeding integers = -6, -5, -4

Given, a = 75 and b = 84
\(\therefore\) LHS = a - (-b) = 75 - (-84) = 75 + 84 =159
and RHS = a + b = 75 + 84 = 159
Hence, LHS = RHS

We have, 7, - 5, 4, 0 and - 4
Since every positive integer is greater than 0 and every negative integer is less than O. So, rearrange the given numbers in ascending order i.e. -5, - 4, 0, 4, 7.
In order to represent the given integers on the number line, we draw a line and mark a point on it almost in the middle (say0) of the line.
Now, starting from 0 and count 4 units on the right of the middle point, we get 4 and further count 3 units from 4 to the right, we obtain 7.
Again, starting from 0 and count 4 units to the left of it, we obtain - 4 and further count 1 unit from its left, we get -5.

(-21) - (30) = (-21) + (-30) = -51     [\(\because\) (- )(-) = (+), higher integer sign is (-)]

The appropriate numbers at each dot from left to right are respectively
- 15, - 13, - 11, - 7, - 5, - 3, - 1, 1,5,7,9, 11 and 13.

Since, in the product there are 5 integers of minus sign (i.e., an odd number of integers).
∴ The sign of the product is negative.
Thus, (-1) x (-1) x (-1) x (-1) x (-1) = -1

(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.

Given, Jack's score ofIst round = 25
Score of IInd round = - 5
Score of IIIrd round = - 10
Score of IVth round = 15
and score of Vth round = 10
Now, total score = Sum of score of all rounds
= 25 + (- 5) + (-10) + 15 + 10 = 25 - 5 -10 + 15 + 10
= (25 + 15 + 10) + (- 5 -10)
=(40+10)+(-15) =50-15=35
Hence, the total score of Jack was 35.

Number line with all numbers is shown below:

From the above number line, the temperature of the indicated places are as follow:

For a pair of integers whose product is -12 and there lies seven integers between them.
First integer = - 2 and second integer = 6
Their product = - 2 \(\times\) 6 = -12
Total number of integers lying between -2 to 6 = 7    [excluding the given integers].

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