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

Q 1 :

real numbers class 10 questions with solutions |

201
202
203
204

1

2

3

4

real numbers class 10 questions with solutions |

Q 2 :

HCF Choice 8, 9 25 is

8
9
25
1

1

2

3

4

(4)

Q 3 :

Which of the following is not irrational?

${(2 - \sqrt{3})}^{2}$
${(\sqrt{2} + \sqrt{3})}^{2}$
$(\sqrt{2} - \sqrt{3}) (\sqrt{2} + \sqrt{3})$
None of these

1

2

3

4

(3)

Q 4 :

The Product of a rational and irrational number is

Rational
Irrational
(a) or (b)
None of these

1

2

3

4

(3)

Explanation: Rational No. x Irrational No.

Case I: $\frac{1}{2} \times \sqrt{3} = \frac{\sqrt{3}}{2}$ = Irrational no.

Case II: $\frac{0}{1} \times \sqrt{3} = 0$ = Irrational no.

$∴$ Product of rational no. and irrational no. may be rational no an irrational number

Q 5 :

The sum of a rational and irrational number is

Rational
Irrational
Both of above
None of these

1

2

3

4

(2)

Q 6 :

The product of two different irrational numbers is always

Rational
Irrational
Rational or Irrational
None of these

1

2

3

4

(3)

Q 7 :

The sum of two irrational numbers is

Irrational
Rational
Rational or Irrational
One

1

2

3

4

(3)

Explanation: Irrational no. + Irrational no.

Case I: $\sqrt{2} + \sqrt{2} = 2 \sqrt{2}$

Case II: $2 + \sqrt{3}$ and $2 - \sqrt{3}$

= $2 + \sqrt{3} + 2 - \sqrt{3}$

= 4 = rational no.

$∴$ Sum of two irrational numbers is rational or irrational

Q 8 :

The product of three consecutive positive integers is divisible by

4
6
No common factor
Only 1

1

2

3

4

(2)

Q 9 :

The set A = {0, 1, 2, 3, 4, ...} represents the set of

Whole numbers
Integers
Natural numbers
Even numbers

1

2

3

4

(1)

Q 10 :

Which number is divisible by 11?

1516
1452
1011
1121

1

2

3

4

(2)

Q 11 :

LCM of the given number 'x' and 'y' where y is a multiple of 'x' is given by

x
y
xy
$\frac{x}{y}$

1

2

3

4

(2)

Q 12 :

The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is

17
11
34
45

1

2

3

4

(1)

Explanation: Algorithm 398 - 7 = 391; 436 - 11 = 425; 542 - 15 = 527

$∴$ HCF of 391, 425, 527 = 17

Q 13 :

There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

52
56
48
63

1

2

3

4

(1)

Explanation: HCF of 312, 260, 156 = 52

Q 14 :

There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?

36 minutes
18 minutes
6 minutes
They will not meet

1

2

3

4

(1)

Explanation: LCM of 18 and 12 = 36

Q 15 :

Express 98 as a product of its primes

$2^{2} \times 7$
$2^{2} \times 7^{2}$
$2 \times 7^{2}$
$2^{3} \times 7$

1

2

3

4

(3)

Q 16 :

Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

98 kg
290 kg
200 kg
350 kg

1

2

3

4

98 kg

Explanation: HCF of 490, 588, 882 = 98 kg

Q 17 :

$m^{2} - 1$ is divisible by 8, if m is

An even integer
An odd integer
A natural number
A whole number

1

2

3

4

(2)

Q 18 :

The product of a non-zero rational and an irrational number is

Always rational
Rational or Irrational
Alaways irrational
Zero

1

2

3

4

(3)

Q 19 :

The largest number that which divides 60 and 75, leaving remainders 8 and 10 respectively, is

260
75
65
13

1

2

3

4

(4)

Explanation: Subtract the remainder 8 and 10 from 60 and 75.

Q 20 :

The last number that is divisible by all the numbers from 1 to 5 (both inclusive) is

5
60
20
100

1

2

3

4

(2)

Explanation: LCM of 1, 2, 3, 4, 5 = 60

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 1 :

real numbers class 10 questions with solutions |

Q 2 :

HCF Choice 8, 9 25 is

Q 3 :

Which of the following is not irrational?

Q 4 :

The Product of a rational and irrational number is

Q 5 :

The sum of a rational and irrational number is

Q 6 :

The product of two different irrational numbers is always

Q 7 :

The sum of two irrational numbers is

Q 8 :

The product of three consecutive positive integers is divisible by

Q 9 :

The set A = {0, 1, 2, 3, 4, ...} represents the set of

Q 10 :

Which number is divisible by 11?

Q 11 :

LCM of the given number 'x' and 'y' where y is a multiple of 'x' is given by

Q 12 :

The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is

Q 13 :

There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

Q 14 :

There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?

Q 15 :

Express 98 as a product of its primes

Q 16 :

Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

Q 17 :

$m^{2} - 1$ is divisible by 8, if m is

Q 18 :

The product of a non-zero rational and an irrational number is

Q 19 :

The largest number that which divides 60 and 75, leaving remainders 8 and 10 respectively, is

Q 20 :

The last number that is divisible by all the numbers from 1 to 5 (both inclusive) is

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 1 : real numbers class 10 questions with solutions |

Q 2 : HCF Choice 8, 9 25 is

Q 3 : Which of the following is not irrational?

Q 4 : The Product of a rational and irrational number is

Q 5 : The sum of a rational and irrational number is

Q 6 : The product of two different irrational numbers is always

Q 7 : The sum of two irrational numbers is

Q 8 : The product of three consecutive positive integers is divisible by

Q 9 : The set A = {0, 1, 2, 3, 4, ...} represents the set of

Q 10 : Which number is divisible by 11?

Q 11 : LCM of the given number 'x' and 'y' where y is a multiple of 'x' is given by

Q 12 : The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is

Q 13 : There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

Q 14 : There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?

Q 15 : Express 98 as a product of its primes

Q 16 : Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

Q 17 : m2 - 1 is divisible by 8, if m is

Q 18 : The product of a non-zero rational and an irrational number is

Q 19 : The largest number that which divides 60 and 75, leaving remainders 8 and 10 respectively, is

Q 20 : The last number that is divisible by all the numbers from 1 to 5 (both inclusive) is

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:

Want Us to Email you About Special Offers & Updates?

Q 1 :

real numbers class 10 questions with solutions |

Q 2 :

HCF Choice 8, 9 25 is

Q 3 :

Which of the following is not irrational?

Q 4 :

The Product of a rational and irrational number is

Q 5 :

The sum of a rational and irrational number is

Q 6 :

The product of two different irrational numbers is always

Q 7 :

The sum of two irrational numbers is

Q 8 :

The product of three consecutive positive integers is divisible by

Q 9 :

The set A = {0, 1, 2, 3, 4, ...} represents the set of

Q 10 :

Which number is divisible by 11?

Q 11 :

LCM of the given number 'x' and 'y' where y is a multiple of 'x' is given by

Q 12 :

The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is

Q 13 :

There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

Q 14 :

There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?

Q 15 :

Express 98 as a product of its primes

Q 16 :

Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

Q 17 :

$m^{2} - 1$ is divisible by 8, if m is

Q 18 :

The product of a non-zero rational and an irrational number is

Q 19 :

The largest number that which divides 60 and 75, leaving remainders 8 and 10 respectively, is

Q 20 :

The last number that is divisible by all the numbers from 1 to 5 (both inclusive) is

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: