In the earlier exercises, students understood the problems based on Integers. Here, they will learn step-by-step tricks followed to answer the objective-type questions, which are important for the exam. RD Sharma Solutions for Class 6, prepared by the faculty at BYJU’S, consist of answers based on the latest CBSE guidelines. To learn more about the methods of solving problems, students can refer to RD Sharma Solutions for Class 6 Maths Chapter 5 Negative Numbers and Integers Objective Type Questions PDF present here.
RD Sharma Solutions for Class 6 Maths Chapter 5: Negative Numbers and Integers Objective Type Questions
Access Answers to Maths RD Sharma Solutions for Class 6 Chapter 5: Negative Numbers and Integers Objective Type Questions
Mark the correct alternative in each of the following:
1. Which of the following statement is true?
(a) − 7 > − 5 (b) − 7 < − 5 (c) (− 7) + (− 5) > 0 (d) (− 7) − (− 5) > 0
Solution:
Option (b) is the correct answer.
In option (a)
We know that − 7 is to the left of – 5
Hence, − 7 < − 5.
In option (c)
We know that (− 7) + (− 5) = − (7 + 5) = − 12.
So − 12 is to the left of 0
Hence (− 7) + (− 5) < 0.
In option (d)
(− 7) − (− 5) = (− 7) + (additive inverse of − 5) = (− 7) + (5) = − (7 − 5) = − 2
We know that − 2 is to the left of 0, so (− 7) − (− 5) < 0.
2. 5 less than − 2 is
(a) 3 (b) − 3 (c) − 7 (d) 7
Solution:
Option (c) is the correct answer.
We know that, 5 less than − 2 = (− 2) − (5) = − 2 − 5 = − 7
3. 6 more than − 7 is
(a) 1 (b) − 1 (c) 13 (d) – 13
Solution:
Option (b) is the correct answer.
We know that, 6 more than − 7 = (− 7) + 6 = − (7 − 6) = − 1
4. If x is a positive integer, then
(a) x + |x| = 0 (b) x − |x| = 0 (c) x + |x| = −2x (d) x = − |x|
Solution:
Option (b) is the correct answer.
We know that if x is a positive integer, then |x| = x
Hence, x + |x| = x + x = 2x and x − |x| = x − x = 0
5. If x is a negative integer, then
(a) x + |x| = 0 (b) x − |x| = 0 (c) x + |x| = 2x (d) x − |x| = − 2x
Solution:
Option (a) is the correct answer.
We know that x is a negative integer, then |x| = −x
It can be written as
x + |x| = x − x = 0 and x − |x| = x − (− x) = x + x = 2x
6. If x is greater than 2, then |2 − x| =
(a) 2 − x (b) x − 2 (c) 2 + x (d) − x – 2
Solution:
Option (b) is the correct answer.
We know that if a is a negative integer, then |a| = − a
It is given that x is greater than 2 where 2 − x is negative
Hence, |2 − x| = − (2 − x) = − 2 + x = x − 2.
7. 9 + |− 4| is equal to
(a) 5 (b) − 5 (c) 13 (d) −13
Solution:
Option (c) is the correct answer.
We know that, |− 4| = 4
Hence 9 + |− 4| = 9 + 4 = 13
8. (− 35) + (− 32) is equal to
(a) 67 (b) − 67 (c) − 3 (d) 3
Solution:
Option (b) is the correct answer.
It can be written as (− 35) + (− 32) = − (35 + 32) = − 67
9. (− 29) + 5 is equal to
(a) 24 (b) 34 (c) − 34 (d) – 24
Solution:
Option (d) is the correct answer.
It can be written as (− 29) + 5 = − (29 − 5) = − 24
10. |− |− 7| − 3| is equal to
(a) − 7 (b) 7 (c) 10 (d) – 10
Solution:
Option (c) is the correct answer.
It can be written as |− |− 7| − 3| = |− 7 − 3| = |− 10| = 10
11. The successor of − 22 is
(a) − 23 (b) − 21 (c) 23 (d) 21
Solution:
Option (b) is the correct answer.
We know that if ‘a’ is an integer a + 1 is its successor.
So the successor of − 22 = − 22 + 1 = − (22 − 1) = − 21
12. The predecessor of – 14 is
(a) – 15 (b) 15 (c) 13 (d) – 13
Solution:
Option (a) is the correct answer.
The predecessor of – 14 is – 15.
13. If the sum of two integers is − 26 and one of them is 14, then the other integer is
(a) − 12 (b) 12 (c) − 40 (d) 40
Solution:
Option (c) is the correct answer.
It is given that the sum of two integers = − 26
One of them = 14
So the other integer = − 26 − 14 = − (26 + 14) = − 40
14. Which of the following pairs of integers have 5 as a difference?
(a) 10, 5 (b) − 10, − 5 (c) 15, − 20 (d) both (a) and (b)
Solution:
Option (d) is the correct answer.
Consider option (a) 10 − 5 = 5
Consider option (b) (− 5) − (− 10) = − 5 + 10 = 5
Consider option (c) 15 − (− 20) = 15 + 20 = 35
15. If the product of two integers is 72 and one of them is − 9, then the other integers is
(a) − 8 (b) 8 (c) 81 (d) 63
Solution:
Option (a) is the correct answer.
It is given that the product of two integers = 72
One of them = − 9
Hence, the other integers = 72 ÷ (− 9) = − 8
16. On subtracting − 7 from − 14, we get
(a) − 12 (b) − 7 (c) −14 (d) 21
Solution:
Option (b) is the correct answer.
It can be written as
Required number = − 14 − (− 7) = − 14 + 7 = − (14 − 7) = − 7
17. The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is
(a) 17 (b) 13 (c) 14 (d) 18
Solution:
Option (b) is the correct answer.
By subtracting 12 and 7 from 64 and 72
We get
64 − 12 = 52 and 72 − 7 = 65
So the required number is the HCF of 52 and 65.
It can be written as
52 = 4 × 13 and 65 = 5 × 13
HCF of 52 and 65 = 13
Hence, the largest number that divides 64 and 72 and leaves the remainder of 12 and 7, respectively, is 13.
18. The sum of two integers is − 23. If one of them is 18, then the other is
(a) −14 (b) 14 (c) 41 (d) −41
Solution:
Option (d) is the correct answer.
It is given as the sum of two integers = − 23
One of them = 18
So the other number = (− 23) − (18) = − 23 − 18 = − (23 + 18) = − 41
Hence, the other number is − 41.
19. The sum of two integers is − 35. If one of them is 40, then the other is
(a) 5 (b) − 75 (c) 75 (d) – 5
Solution:
Option (b) is the correct answer.
It is given that the sum of two integers = − 35
One of them = 40
So the other number = (− 35) − (40) = − 35 − 40 = − (35 + 40) = − 75
Hence, the other number is − 75.
20. On subtracting − 5 from 0, we get
(a) − 5 (b) 5 (c) 50 (d) 0
Solution:
Option (b) is the correct answer.
We know that, 0 − (− 5) = 0 + 5 = 5
Hence by subtracting − 5 from 0, we obtain 5.
21. (− 16) + 14 − (− 13) is equal to
(a) − 11 (b) 12 (c) 11 (d) – 15
Solution:
Option (c) is the correct answer.
It can be written as (− 16) + 14 − (− 13) = (− 16) + 14 + 13 = (− 16) + 27 = 27 − 16 = 11
22. (− 2) × (− 3) × 6 × (− 1) is equal to
(a) 36 (b) − 36 (c) 6 (d) – 6
Solution:
Option (b) is the correct answer.
It can be written as (− 2) × (− 3) × 6 × (− 1) = (2 × 3) × 6 × (− 1) = 6 × 6 × (− 1) = 36 × (− 1)
So we get (− 2) × (− 3) × 6 × (− 1) = − (36 × 1) = − 36
23. 86 + (- 28) + 12 + (- 34) is equal to
(a) 36 (b) − 36 (c) 6 (d) – 6
Solution:
Option (a) is the correct answer.
It can be written as 86 + (−28) + 12 + (−34) = 86 + (−28) − (34 − 12) = 86 + (−28) − 22
On further calculation
86 + (−28) + 12 + (−34) = (86 − 28) − (34 − 12) = (86 − 28) − 22 = 58 − 22 = 36
24. (−12) × (−9) − 6 × (−8) is equal to
(a) 156 (b) 60 (c) −156 (d) – 60
Solution:
Option (a) is the correct answer.
It can be written as (−12) × (−9) − 6 × (−8) = (12 × 9) − 6 × (−8) = 108 − 6 × (−8)
On further calculation
(−12) × (−9) − 6 × (−8) = 108 + 6 × 8 = 108 + 48 = 156
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