Real Numbers Class 10 Questions with Solutions | Real Numbers Class 10 Questions

Q 21 :
The last number that is divisible by all the numbers from 1 to 8 (both inclusive) is

840
2520
8
420

1

2

3

4

(1)

Explanation: LCM of 1, 2, 3, 4, 5, 6, 7, 8 = $2^{3} \times 3 \times 5 \times 7$ = 840

Q 22 :
The product of two consecutive natural numbers is always

Prime number
Even number
Odd number
Even or Odd

1

2

3

4

(2)

Q 23 :
If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 x p, then the value of p is

5
– 5
4
– 4

1

2

3

4

(2)

Explanation HCF of 408 and 1032 is 24,

$∴$ 1032 x 2 + 408 x (p) = – 24

408p = 24 – 2064

408p = 0150 2040

$p = \frac{- 2040}{408} = - 5$

Q 24 :
The number in the form of 4p + 3, where p is a whole number, will always be

Even
Odd
Even or Odd
Multiple of 3

1

2

3

4

(2)

Explanation:

$p = 1 p = 2 4 (p) + 3 = 7 4 (p) + 3 = 11$

Q 25 :
If $p^{2} = \frac{32}{50}$ , then p is a/an

Whole number
Integer
Rational Number
Irrational number

1

2

3

4

(3)

We have, $p^{2} = \frac{32}{50} = \frac{16}{25}$

$∴$ $p = \pm \frac{4}{5}$ (Rational Number)

Q 26 :
The LCM of smallest 2-digit number and smallest composite number is

12
4
20
40

1

2

3

4

(3)

Smallest 2 digit number = 10 = 2 x 5

Smallest composite number = $4 = 2^{2}$

$∴$ LCM (10, 4) = $2^{2}$ x 5 = 20

Q 27 :
The ratio of HCF to LCM of the least composite number and the least prime number is:

1 : 2
2 : 1
1 : 1
1 : 3

1

2

3

4

(1)

Least Composite number is = $4 = 2^{2}$

Least Prime number is $2 = 2^{1}$

HCF (4, 2) is $2^{1} = 2$

LCM (4, 2) is $2^{2} = 4$

$∴ \frac{HCF}{LCM} = \frac{2}{4} = \frac{1}{2} i . e ., 1 : 2$

Q 28 :
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two Sections - Section A and Section B of grade X. There are 32 students in Section A and 36 students in Section B.

Q: If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is

2
4
6
8

1

2

3

4

(2)

Explanation: HCF x LCM = 32 x 36

$HCF = \frac{32 \times 36}{LCM} = \frac{1152}{288} = 4$

$∴$ HCF = 4

Topic Question Set

Q 21 :
The last number that is divisible by all the numbers from 1 to 8 (both inclusive) is

Q 22 :
The product of two consecutive natural numbers is always

Q 23 :
If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 x p, then the value of p is

Q 24 :
The number in the form of 4p + 3, where p is a whole number, will always be

Q 25 :
If $p^{2} = \frac{32}{50}$ , then p is a/an

Q 26 :
The LCM of smallest 2-digit number and smallest composite number is

Q 27 :
The ratio of HCF to LCM of the least composite number and the least prime number is:

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Topic Question Set

Q 21 : The last number that is divisible by all the numbers from 1 to 8 (both inclusive) is

Q 22 : The product of two consecutive natural numbers is always

Q 23 : If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 x p, then the value of p is

Q 24 : The number in the form of 4p + 3, where p is a whole number, will always be

Q 25 : If p2 = 3250, then p is a/an

Q 26 : The LCM of smallest 2-digit number and smallest composite number is

Q 27 : The ratio of HCF to LCM of the least composite number and the least prime number is:

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Q 21 :
The last number that is divisible by all the numbers from 1 to 8 (both inclusive) is

Q 22 :
The product of two consecutive natural numbers is always

Q 23 :
If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 x p, then the value of p is

Q 24 :
The number in the form of 4p + 3, where p is a whole number, will always be

Q 25 :
If $p^{2} = \frac{32}{50}$ , then p is a/an

Q 26 :
The LCM of smallest 2-digit number and smallest composite number is

Q 27 :
The ratio of HCF to LCM of the least composite number and the least prime number is: