RD Sharma solution class 7 chapter 1 Integers objective type questions

objective type questions

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Question 1:

Mark the correct alternatives in each of the following:

(−1) × (−1) × (−1) × (−1) × ... 500 times =

(a) −1                                  (b) 1                                  (c) 500                                  (d) −500                                                     

Answer 1:

The number of integers in the given product is even.

∴ (−1) × (−1) × (−1) × (−1) × ... 500 times

= 1 × 1 × 1 × 1 × ... 500 times

= 1

Hence, the correct answer is option (b).

Question 2:

Mark the correct alternatives in each of the following:

(−1) + (−1) + (−1) + (−1) + ... 500 times =

(a) 500                                  (b) 1                                  (c) −1                                 (d) −500

Answer 2:

(−1) + (−1) + (−1) + (−1) + ... 500 times

= −(1 + 1 + 1 + 1 + ... 500 times)

= −500

Hence, the correct answer is option (d).

Question 3:

Mark the correct alternatives in each of the following:

The additive inverse of −7 is

(a) −7                                  (b) $-\frac{1}{7}$                                  (c) 7                                 (d) $\frac{1}{7}$

Answer 3:

We know that, for every integer a, there exists integer −a such that

a + (−a) = 0 = −a + a

Here, −a is the additive inverse of a and a is the additive inverse of −a.

Now, 7 + (−7) = 0 = −7 + 7

∴ 7 is the additive inverse of −7.

Hence, the correct answer is option (c). 

Question 4:

Mark the correct alternatives in each of the following:

The modulus of an integer x is 9, then

(a) x = 9 only                                  (b) x = −9 only                                  (c) x = ± 9                                  (d) None of these

Answer 4:

The modulus (or absolute value) of an integer is its numerical value regardless of its sign. The absolute value of an integer is always non-negative.

It is given that,

Modulus of x = | x | = 9

Now, | −9 | = 9 and | 9 | = 9

∴ x = −9 or x = 9

⇒ x = ± 9

Hence, the correct answer is option (c).

Question 5:

Mark the correct alternatives in each of the following:

By how much does 5 exceed −4?

(a) 1                                  (b) −1                                  (c) 9                                  (d) −9

Answer 5:

Difference between 5 and −4 = 5 − (−4) = 5 + 4 = 9

Thus, 5 exceed −4 by 9.

Hence, the correct answer is option (c).

Question 6:

Mark the correct alternatives in each of the following:

By how much less than −3 is −7?

(a) 4                                  (b) −4                                  (c) 10                                  (d) −10

Answer 6:

Difference between −3 and −7 = (−3) − (−7) = −3 + 7 = 4

Thus, −7 is less than −3 by 4.

Hence, the correct answer is option (a).

Question 7:

Mark the correct alternatives in each of the following:

The sum of two integers is 24. If one of them is −19, then the other is

(a) 43                                  (b) −43                                  (c) 5                                (d) −5

Answer 7:

Sum of two integers = 24

One of the integers = −19

∴ Other integer = Sum of two integers − One of the integers

                         = 24 − (−19)

                         = 24 + 19

                         = 43

Hence, the correct answer is option (a).

Question 8:

Mark the correct alternatives in each of the following:

What must be subtracted from −6 to obtain −14?

(a) 8                                  (b) 20                                  (c) −20                                 (d) −8

Answer 8:

Let x be subtracted from −6 to obtain −14.

∴  −6 − x = −14

Putting x = 8, we get

LHS = −6 − 8 = −6 + (−8) = −14 = RHS

Thus, 8 must be subtracted from −6 to obtain −14.

Hence, the correct answer is option (a).

Question 9:

Mark the correct alternatives in each of the following:

What should be divided by 6 to get −18?

(a) −3                                  (b) 3                                  (c) −108                                  (d) 108

Answer 9:

Let x be divided by 6 to get −18.

$$\begin{gathered} \therefore x÷6=-18 \\ \Rightarrow \frac{x}{6}=-18 \end{gathered}$$

Putting x = −108, we get

LHS = $\frac{-108}{6}=-\frac{\left|-108\right|}{6}=-\frac{108}{6}=-18$ = RHS

Thus, −108 should be divided by 6 to get −18.

Hence, the correct answer is (c).

Question 10:

Mark the correct alternatives in each of the following:

Which of the following is correct?

(a) −12 > −9                                  (b) −12 < −9                                  (c) (−12) + 9 > 0                               (d) (−12) × 9 > 0

Answer 10:

We know that if a and b are two negative integers, then the integer with greater absolute value is less than the integer with smaller absolute value.

Absolute value of −12 = | −12 | = 12

Absolute value of −9 = | −9 | = 9

∴ −12 < −9

Also,

(−12) + 9 = −3 < 0

and  (−12) × 9 = −(12 × 9) = −108 < 0

Hence, the correct answer is option (b).

Question 11:

Mark the correct alternative in each of the following:

The sum of two integers is −8. If one of the integers is 12, then the other is

(a) 20                                   (b) 4                                   (c) −4                                   (d) −20                                  

Answer 11:

Sum of two integers = −8

One of the integers = 12

∴ Other integer = Sum of two integers − One of the integers

                          = −8 − 12

                          = −8 + (−12)

                          = −20

Hence, the correct answer is option (d).

Question 12:

Mark the correct alternative in each of the following:

On subtracting −14 from −18, we get

(a) 4                                   (b) −4                                   (c) −32                                   (d) −32                                 

Answer 12:

−14 subtracted from −18

= −18 − (−14)

= −18 + 14

= −4

Hence, the correct answer is option (b).

Question 13:

Mark the correct alternative in each of the following:

(−35) × 2 + (−35) × 8 =

(a) −350                                   (b) −70                                   (c) −280                                    (d) 350                                 

Answer 13:

(−35) × 2 + (−35) × 8

= (−35) × (2 + 8)                              [a × b + a × c = a × (b + c)]

= (−35) × 10

= −350

Hence, the correct answer is option (a).

Question 14:

Mark the correct alternative in each of the following:

If x ÷ 29 = 0, then x =

(a) 29                                   (b) −29                                   (c) 0                                  (d) None of these                                 

Answer 14:

We know that if a is a non-zero integer, then 0 ÷ a = 0.

∴ x ÷ 29 = 0

⇒ x = 0

Hence, the correct answer is option (c).

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Question 15:

Mark the correct alternative in each of the following:

If x = (−10) + (−10) + ... 15 times and y = (−2) × (−2) × (−2) × (−2) × (−2), then x − y =   
 
(a) 118                                   (b) −118                                   (c) −182                                  (d) 182                                 

Answer 15:

x = (−10) + (−10) + ... 15 times

   = − (10 + 10 + ... 15 times)

   = −150

y = (−2) × (−2) × (−2) × (−2) × (−2)

   = −(2 × 2 × 2 × 2 × 2)                 (When the number of negative integers in a product is odd, the product is negative)

   = −32

∴ x − y = −150 − (−32) = −150 + 32 = −118

Hence, the correct answer is option (b).

Question 16:

Mark the correct alternative in each of the following:

If a = (−1) × (−1) × (−1) × ... 100 times and b = (−1) × (−1) × (−1) × ... 95 times, then a + b = 

(a) −1                                   (b) −2                                   (c) 0                                   (d) 1                                 

Answer 16:

a = (−1) × (−1) × (−1) × ... 100 times

Here, the number of integers in the product is even.

∴ a = (−1) × (−1) × (−1) × ... 100 times

      = 1 × 1 × 1 × ... 100 times

      = 1

b = (−1) × (−1) × (−1) × ... 95 times

Here, the number of integers in the product is odd.

∴ b = (−1) × (−1) × (−1) × ... 95 times

      = −(1 × 1 × 1 × ... 95 times)

      = −1

So,

a + b = 1 + (−1) = 0

Hence, the correct answer is option (c).

Question 17:

Mark the correct alternative in each of the following:

|| 3 − 12| − 4| =

(a) −5                                   (b) 5                                   (c) 7                                   (d) −7                                 

Answer 17:

|| 3 − 12| − 4|

= || 3 + (−12)| − 4|

= || −9| − 4|

= |9 − 4|                 (Absolute value of an integer is its numerical value regardless of its sign)

= |5|

= 5

Hence, the correct answer is option (b).

Question 18:

Mark the correct alternative in each of the following:

If the difference of an integer a and (−9) is 5, then a =

(a) 4                                   (b) 5                                  (c) −4                                   (d) −9                                 

Answer 18:

a − (−9) = 5            (Given)

⇒ a + 9 = 5  

Putting a = −4, we get

LHS = −4 + 9 = 5 = RHS

∴ a = −4

Hence, the correct answer is option (c).

Question 19:

Mark the correct alternative in each of the following:

The sum of two integers is 10. If one of them is negative, then the other has to be

(a) negative                                                                    (b) positive                                  

(c) may be positive or negative                                     (d) None of these                                 

Answer 19:

It is given that the sum of two integers is 10, which is a positive integer.

But, we know that the sum of two negative integers is always a negative integer.

So, if the sum of two integers is positive and one of them is negative, then the other has to be positive.

For example,

−2 + 12 = 10

−5 + 15 = 10

Thus, the other integer has to be positive.

Hence, the correct answer is option (b).

Question 20:

Mark the correct alternative in each of the following:
 

If x = (−1) × (−1) × (−1) × (−1) × ... 25 times, y = (−3) × (−3) × (−3), then xy

(a) −27                                   (b) 27                                   (c) 26                                  (d) −26                                 

Answer 20:

x = (−1) × (−1) × (−1) × (−1) × ... 25 times

The number of integers in the given product is odd.

∴ x = (−1) × (−1) × (−1) × (−1) × ... 25 times

      = −(1 × 1 × 1 × ... 25 times)

      = −1

y = (−3) × (−3) × (−3)

The number of integers in the given product is odd.

∴ y = (−3) × (−3) × (−3)

      = −(3 × 3 × 3)

      = −27

So,

xy = (−1) × (−27) = 27               (Product of two negative integers is always positive)

Hence, the correct answer is option (b).