Answer: Option A. ->
:

Each part: 1.5 Marks
(i) Multiplication of even no. of negative integers gives a positive integer whereas multiple of odd no. of negative integers gives a negative integer.
(a) We have multiplication of three negative integers. So, the product will be negative integers. 
$(-2)\times (-3)\times (-4)=6\times (-4)=(-24)$
(b) We have multiplication of two negative integers and one positive integer. So, the product will be positive integers. 
$2\times (-3)\times (-4)=12\times 2=24$
(c) $\frac{2}{6}\times (-3)\times \frac{4}{10}$
 $=\frac{1}{3}\times -3\times \frac{2}{5}$
$=\frac{-2}{5}$
(ii)  (a) $-12<-4$
(b) $-15<-2$
(c) $-7>-29$     

Answer: Option A. ->
:

Each option:1.5 Marks
As per the question
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
(i) Marks scored by Radhika = 20
Marks obtained for 12 correct answers = 12 $\times$ 3 = 36
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= 20 − 36 = −16
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers
= (−16) $÷$ (−2) = 8
Therefore, she had answered 8 questions incorrectly.
(ii) Marks scored by Mohini = −5
Marks obtained for 7 correct answers
 = 7 $\times$ 3 = 21
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= − 5 − 21 = −26
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers
= (−26) $÷$ (−2) = 13
Therefore, she had answered 13 questions incorrectly.

Answer: Option A. ->
:
Each option: 1 Mark
(a) a = 12, b = −4, c = 2
a $÷$ (b $+$ c) = 12 $÷$ (− 4 $+$ 2) = 12 $÷$ (−2)
 = −6
(a $÷$ b) $+$ (a $÷$ c) = [12 $÷$ (−4)] $+$ [12 $÷$ 2] = −3 $+$ 6 = 3
Hence, a $÷$ (b $+$ c) ≠ (a $÷$ b) $+$ (a $÷$ c)
(b) a = −10, b = 1, c = 1
a $÷$ (b $+$ c) = (−10) $÷$ (1 $+$ 1) = (−10) $÷$ 2
= −5
(a $÷$ b) $+$ (a $÷$ c) = [(−10) $÷$ 1] $+$ [(−10) $÷$ 1]
= − 10 − 10 = −20
Hence, a $÷$ (b $+$ c) ≠ (a $÷$ b) $+$ (a $÷$ c)

Answer: Option A. ->
:

Steps: 2 Marks
Result: 1 Mark
(i) Profit earned by selling one pen = Re 1
Profit earned by selling 45 pens = Rs 45, which we denote by + Rs 45
Total loss = Rs 5, which we denote by (– Rs 5)
Profit earned + Loss incurred = Total loss
Therefore, Loss incurred = Total Loss – Profit earned
= Rs (– 5 – 45) = Rs (–50) = (– 5000 paise)
Loss incurred by selling one pencil = 40paise
which we write as (– 40paise)
So, number of pencils sold
$=(–5000)÷(–40)=125pencils$.
(ii) In the next month, there is neither profit nor loss.
So, Profit earned + Loss incurred = 0
i.e., Profit earned = – Loss incurred.
Now, profit earned by selling 70 pens = Rs 70
Hence, the loss incurred by selling pencils = Rs 70 which we indicate by (– Rs 70) or (– 7,000 paise).
Total number of pencils sold
$=(–7000)÷(–40)=175pencils$.

Answer: Option A. ->
:

Calculations: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Given that
An elevator descends into a mine shaft at the rate of 6 m/min.
The descent starts from 10m above the ground level.
Now, the distance descended is denoted by a negative integer.
Initial height = +10 m
Final depth = −350 m
Total distance to be descended by the elevator = (−350) − (+10) = −360 m
Time taken by the elevator to descend −6 m = 1 min
Thus, time taken by the elevator to descend −360 m = (−360) $÷$ (−6)
= 60 minutes = 1 hour
Hence it will take 1 hour to reach -350m.

Answer: Option A. ->
:

Steps: 2 Marks
Result: 2 Marks
Upward movement is taken as positive while downward movement is taken as negative. Hence, from the question we can conclude that helicopter is moving downward. So, the distance of helipad from the helicopter will be negative integers.
$=-1500m+600m$
$=-900m$. 
Given that the speed of the helicopter is 50 meters per second.
Total distance to be covered = 900 m
Time taken by the helicopter to reach the helipad = 900 $÷$ 50 =18 seconds
Hence, the helicopter will reach the helipad in 18 seconds.

Answer: Option A. ->
:
Steps: 1 Mark
Temperature on Tuesday: 1 Mark
Temperature on Wednesday: 1 Mark
Temperature on Saturday: 1 Mark
Temperature on Monday =$-5^{\circ }C$
Temperature on Tuesday = Temperature on Monday $-2^{\circ }C$
$=-5^{\circ }C-2^{\circ }C=-7^{\circ }C$
Temperature on Wednesday = Temperature on Tuesday $+4^{\circ }C$
$=-7^{\circ }C+4^{\circ }C=-3^{\circ }C$
Therefore, the temperature on Tuesday and Wednesday was $-7^{\circ }C$ and $-3^{\circ }C$ respectively.
Given that
The temperature drops by $2^{\circ }$ each day after Wednesday
The temperature on Wednesday = $-3^{\circ }C$
The temperature on Saturday
$=-3-(2\times 3)=-3-6=-9^{\circ }C$
The temperature on Saturday is $-9^{\circ }C$
 

Answer: Option A. ->
:
Steps: 2 Marks
Answer: 2 Marks
It is given that
Tesla makes a profit of Rs 100 on each car it sells
While it makes a loss of Rs 150 each time they send a rocket into space.
Tesla wants to make a profit of Rs 3000.
Total number of rockets sent to space this year = 10
Total Loss due to the rockets = 10 $\times$ 1500 = Rs 1500
Let $x$ number of cars be sold, so as to make a profit of Rs 3000.
Net Profit = Profit from selling cars - loss due to sending of rockets
So on substituting the values, we get:
3000 = 100 $\times$ $x$ - 1500
$x$ = (3000 + 1500) $÷$ (100)
$x$ = 4500 $÷$ 100
$x$ = 45
So, the total number of cars that need to be sold to make a profit of Rs 3000 are 45.
It is given that, 10 cars have already been sold.
Number of cars that need to be sold to meet the target = 45 - 10 = 35
So, 35 more cars need to be sold to meet the target.

Answer: Option A. ->
:
Each option: 2 Marks
(a) 26 $\times$ (−48) + (−48) $\times$ (−36)
= (−48) $\times$ 26 + (−48) $\times$ (−36) 
($\because$ (b $\times$ a = a $\times$ b))
= (−48) [26 − 36] (a $\times$ b + a $\times$ c) = a (b + c)
= (−48) $\times$ (−10) = 480
(b) 15 $\times$ (−25) $\times$ (−4) $\times$ (−10)
= 15 $\times$ [(−25) $\times$ (−4)] $\times$ (−10)
= 15 $\times$ [100] $\times$ (−10)
= 15 $\times$ (−1000) = −15000
 

Answer: Option A. ->
:
Steps: 2 Marks
Result: 2 Marks
As per the question
Loss incurred while selling 1 bag of grey cement = -Rs 5
Loss incurred while selling 6400 bags of grey cement = (- 5) $\times$ 6400 = - 32000
Let the number of bags of white cement to be sold be x.
Profit earned while selling 1 bag of white cement=Rs 8
Profit earned while selling x bags of white cement
= x $\times$ 8
=8x
In condition of no profit no loss,
Profit earned + Loss incurred = 0
 8x + (-32000) = 0
8x = 32000
x = 4000
Therefore, 4000 bags of white cement must be sold.