SSC Real Numbers Exercise – 1.2 of 10th class

 

SSC Real Numbers Exercise – 1.2 of 10th class

SSC Real Numbers :

  • Positive or negative, Large or small, whole numbers or decimal numbers are all Real Numbers. 

They are called “Real Numbers” because they are not Imaginary Numbers.

EXERCISE – 1.2

1Q.  Express each of the following number as a product of its prime factors.

i)      140         ii) 156              iii) 3825                     iv) 5005                   v) 7429

Sol 140

Real Numbers

        140 = 2 X 2 X 5 X 7 = 22 X 5 X 7

 

Sol ii) 156

 

Real Numbers

156 = 2 X 2 X 3 X 13 = 22 X 3 X 13

Sol :      iii)   3825

 

 

3825 = 3 X 3 X 5 X 5 X 17

= 32 X 52 X 17

Sol :      iv)   5005

 

5005 = 5 X 7 X 11 X 13

Sol :         v)   7429

Real Numbers

7429 = 17 X 19 X 23

 

for Exercise 1.1

SSC Real Numbers

2Q. Find the L.C.M and H.C.F of the following integers by the prime factorization method.

Sol. i) 12, 15 and 21                ii) 17, 23 and 29

iii) 8, 9 and 25                            iv) 72 and 108

 

Sol :      i) 12, 15 and 21

            12 = 2 X 2 X 3 = 22 X 3

            15 = 3 X 5

             21 = 3 X 7

   L.C.M = 22 X 3 X 5 X 7 = 420

   H.C.F = 3

 

 

Sol : ii) 17, 23 and 29

The given numbers 17, 23 and 29 are all primes.

L.C.M = their product

= 17 X 23 X 29 = 11339

H.C.F = 1

 

iii) 8, 9 and 25

            8 = 2 X 2 X 2 = 23

            9 = 3 X 3 = 32

             25 = 5 X 5 = 52

     L.C.M = 23 X 32 X 52 = 1800

 

                 ( OR )

 

8, 9 and 25 are relatively prime, there fore L.C.M is equal to their product. (i.e.) L.C.M = 8 X 9 X 25 = 1800

H.C.F = 1

iv) 72 and 108

Real Numbers

Real Numbers

72 = 23 X 32

108 = 22 X 33

L.C.M = 23 X 33 = 8 X 27 = 216

H.C.F = 22 X 32 = 4 X 9 = 316

 

v)   306 and 657

Real Numbers

 

306 = 2 X 32 X 17

657 = 32 X 73

L.C.M = 2 X 32 X 17 X 73 = 22338

H.C.F = 32 = 9.

SSC Real Numbers

3Q. Check whether 6n can end with the digit ‘0’ for any natural number n.

Sol : Given number = 6n = ( 2 X 3 )n

The prime factors here are 2 and 3 only.

To be end with 0; 6n should have a prime factor 5 and also 2. So,

6n can’t end with zero.

 

SSC Real Numbers

4Q. Explain why 7 X 11 X 13 + 13 and 7 X 6 X 5 X 4 X 3 X 2 X 1 + 5 are composite numbers.

Sol : Given numbers are

7 X 11 X 13 + 13 and

7 X 6 X 5 X 4 X 3 X 2 X 1 + 5

13 ( 7 X 11 + 1 ) and 5 ( 7 X 6 X 4 X 3 X 2 X 1 + 1 )

13 K and 5 L, where K = 78 and

L = 7 X 6 X 4 X 3 X 2 X 1 + 1 = 1009

As the given numbers can be written as product of two numbers, they are composite.

SSC Real Numbers

5Q. How will you show that ( 17 X 11 X 2 ) + ( 17 X 11 X 5 ) is a composite number? Explain.

Sol : ( 17 X 11 X 2 ) + ( 17 X 11 X 5 )

= ( 17 X 11 ) ( 2 + 5 )

= ( 17 X 11 ) ( 7 ) = 187 X 7

 

Now the given expression is written as a product of two integers and hence it is a composite number.

SSC Real Numbers

For Real Number chapter of SSC Examination

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