September 21, 2021 # Class 10 Maths Chapter 1 Real Numbers extras

Class 10 Maths Chapter 1 Real Numbers : – Here are some extra questions for class 10 maths chapter-1 in the form of mcqs (Multiple Choice Questions). According to the new cbse guidelines, there will be a plenty of questions of Multiple choice questions in board exams. Here are some extra questions with solution in quiz form, pdf form and word form. You can download class 10 maths chapter 1 real numbers extra questions pdf with solutions. Easy downloadable, user friendly.

## Important Questions with solutions

Real Numbers – Quiz -1 (1 Mark Questions) MCQs

1. (1) Sum of a Rational and an Irrational number is
1. (a) Rational
1. (b) Irrational
1. (c) Both (a) and (b)
1. (d) None of these

Solution – (b) Irrational Number Sum of A rational number and an Irrational number is Irrational Number. For Example 2(rational number) + √2(Irrational number) = Irrational Number

1. (2) A lemma is an axiom used for proving
1. (a) Other statement
1. (b) No statement
1. (d) None of these

Solution – (a) Other statement A Lemma is an axiom used for proving Other statement.

1. (3) The smallest Composite Number is:
1. (a) 5
1. (b) 3
1. (c) 2
1. (d) 4

Solution – (d) 4 A number which is divisible by a number other than self and 1, is called Composite number.

1. (4) 2.353535…   is:                         (CBSE Board Exam Question 2020(Basic))
1. (a) A terminating decimal number
• (b) A rational number
• (c) An irrational number
• (d) An integer

Solution – (b) A rational number A non-termination recurring decimal number is a rational number.

1. (5) 2.101100110001…. is:
1. (a) A terminating decimal number
2. (b) A rational number
3. (c) An irrational number
4. (d) None of these

Solution – (c) An Irrational number A non-terminating non recurring number is an Irrational number.

Class 10 Maths Chapter 1 Real numbers Quiz – 2

Class 10 Maths Chapter 1 Real number Quiz – 3

1. (6) Which of the following is the decimal expansion of an Irrational number :
1. (a) 4.573
2. (b) 0.12121212….
3. (c) 501.020020002…..
4. (d) 6.09

Solution – (c) 501.020020002………. A non-terminating non recurring number is an Irrational number.

1. (7) The decimal form of 5/8 is:
1. (a) Terminating decimal number
2. (b) Non – Terminating Non recurring decimal number
3. (c) Non – Terminating recurring decimal number
4. (d) None of these

Solution – (a) Terminating decimal number 5/8 = 0.625 ( Terminating decimal number )

1. (8) √3 and π are :
• (a) Rational Numbers
• (b) Irrational Numbers
• (c) Integers
• (d) None of these

Solution – (b) Irrational number √3 and π = Non terminating non recurring decimal number So it is an irrational number.

1. (9) If HCF of two numbers is 1, the two numbers are called relatively   _____ or _____
• (a) Prime, Co-prime
• (b) Composite, prime
• (c) Both (a) and (b)
• (d) None of these

Solution – (c) Prime and Co-prime HCF = 1 Composite and Prime HCF = 1

1. (10) 5^½ (½ is the power of 5) is a:
• (a) Rational Numbers
• (b) Irrational Numbers
• (c) Integers
• (d) None of these

Solution – (a) Irrational number 5^½ is an Irrational number

CBSE new guidelines for Class 10 and Class 12 session 2021-22

11. 120 can be expressed as a product of its prime factors as-

• (a) 5 x 8 x 3
• (b)15 x 2³
• (c) 10 x 2² x 3
• (d)5 x 2³ x 3 (CBSE Board Exam 2020 Basic Question)
• Solution – (d) 120 = 5 x 2³ x 3
• 12.   Which of the following is not irrational?
• (a) (4-√5)/5
• (b) (√4 – √5)5
• (c) (√4 – √5) (√4+√5)
• (d) None of these
• Solution – (c) (√4 – √5) (√4+√5)
• =      4² – 5²
•   =   16 – 25  =  – 9 (Rational Number)

13. The product of two different irrational numbers is always –

• (a) An Irrational number
• (b) A rational number
• (c) Both of  above
• (d) None of  above
• Solution – (c) Both of These
• Sometimes can be a rational number and sometimes can be an irrational number.

14. If  b = 2, then any integer can be expressed as a =

•  (a) 2q, 2q+1
•     (b) 2q
•     (c) 2q, 2q+1,2q+2
•     (d) 1

Answer – (a)  a = bq+r    where b = 2

So   r = 0, 1

a = 2q + 0, a = 2q + 1

a = 2q, 2q + 1

15. The product of three consecutive positive integers is divisible by

(a)    8

(b)    5

(c)    6

(d)    No common factor

Answer – (c) We can understand by an example

Let these consecutive numbers are 1,2,3

Product of these numbers = 6

6 is divisible by 6.

16. For some integer p, every odd integer is of the form-

(a)  2p+1

(b)  2p

(c)  p+1

(d)  p

Answer – (a) a = bq +r ,  To find odd or even we always divisor as 2, so b = 2

r = 0,1   So     a = 2q + 0 (even) and a = 2q +1 (odd)

17.   For positive integers a and 3, there exist unique integers q and r such that a=3q+r, where r must satisfy:

•  (a) 0 ≤ r <3
•  (b) 0 < r <3
•   (c) 0 < r ≤3
•   (d) 1 < r < 3
•  Answer – (a) by Euclid’s Division Lemma

18.   The ratio between the LCM and HCF of 5,15,20 is:

(a) 9: 1

(b)  4: 3

(c)  11: 1

(d)  12:1

Answer – (d)  LCM of 5,15,20 = 60

HCF of 5,15,20 = 5

Ratio = 60 : 5

12 : 1

19. If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A and B is –

(a) 2

(b)1

(c) 3

(d) 4

Answer – (b) let n = 1 then A = 15, B = 8, HCF of A and B = 1

20. 125^⅓ (⅓ is the power of 125) is a:

(a)  Rational Number

(b)  Irrational Number

(c)  Integer

(d)   None of these

Answer – (a) 125^⅓ = 5 (Rational Number)

21.  LCM of 2² x 5²x 7x 13² and 2 x 5³ x 7² x 13³ is :

• (a) 2 x 5² x 7² x13²
• (b) 2x 5³ x 7
• (c) 2 x 5³ x 7 x 13³
• (d) 1
• (c) 2² x 5³ x 7x 13² and 2 x 5³ x 7² x 13³
•  LCM =   2 x 5³ x 7 x 13³  (Maximum powers of both the number)
•  22.  HCF of a x b²and a³ x b
1. (a) ax b
2. (b) a³ x b
3. (c) a³ x b
4. (d) a³ x b²

Answer – (d) a x b² and a³ x b⁵     HCF =   a³ x b² (Lowest power in both the numbers)

23. Which of the numbers have HCF = 1 ?

1. (a) 923 and 27
2. (b) 27 and 9
3. (c) 11 and 121
4. (d) 171 and 19

Answer – (a) HCF of 23 and 27 = 1 because

23 = 23 x 1

27 = 3 x 3 x 3 x 1 Both has the number 1 in common so HCF = 1

24. If x² = 5, then x is

1. (a) Rational number
2. (b) Irrational number
3. (c) Integer
4. (d) None of these
6. (b) x² = 5
1. x = √5 ( under root 2)  (which is an irrational number)

25. Express 7/64 as decimal expansion

• (a) 0.1414…
• (b) 0.10937….
• (c) 0.1234….
• (d) None of these
• Answer – (b) decimal expansion of 7/64 = 0.10937…..

26. Give the LCM of a³b and ab²

1. (a) a³b²
2. (b) ab²
3. (c) a³b
4. (d) ab

(b) a³b and ab²

LCM = ab² (Highest power of a and b)

1. 27. HCF of 8, 9 and 25 –
1. (a) 8
2. (b) 10
3. (c) 1
4. (d) None of these
5. Answer – (c) 8 = 2 x 2 x 2 x 1
1. 9 = 3 x 3 x 1
2. 25 = 5 x 5 x 1
3. HCF = 1 (Common of all these)

28. Examine – (3 + √2 )²

1. (a) Rational number
2. (b) Irrational number
3. (c) Integer
4. (d) None of these
6. (b) Irrational number
7. (3 + √2 )²
8. = 9 + 6 √2  + 2
9. = 11 + 6 √2

29. Prime factorisation of 156:

1. (a) 2² x 3
2. (b) 2 x 3 x13
3. (c) 2² x 3³ x 13²
4. (d) 2² x 3 x 13
5. Answer – (d) 156 = 2² x 3 x13

30. HCF of (19,171) = 19 find LCM

1. (a) 19
2. (b) 119
3. (c) 342
4. (d) 171
6. HCF x LCM = a x b
7. 19 x LCM = 19 x 171
8. LCM = (19 x 171)/ 19
9. = 171

31.   3 x 2 x1 + 3 is a –

1. (a) Prime number
2. (b) Co – prime
3. (c) Composite number
4. (d) None of these
5. Answer – (c) Composite number
1. = 3 x 2 x1 + 3
2. = 3(2 + 1)
3. = 3 x 3  (multiplication of prime numbers is always a composite number)

32.    Which number will not have end with digit 0.

1. (a) (10)ⁿ
2. (b) (220)ⁿ
3. (c) 6ⁿ
4. (d) None of these
6. = (2 x 3)ⁿ
7. = 6 does not have 5 in its any factor. For the number ending with 0 should have 5 in their factors.

33.     A person has 180 blue pens and 150 red pens. He wants to pick them into packets containing equal number of pens of the same colour. What is the maximum numbers of pens that each packet can hold?

1. (a) 10
2. (b) 20
3. (c) 30
4. (d) 40
6. Finding HCF for 180 and 150
7. 180 = 2 x 2 x 3 x 3 x 5
8. 150 = 2 x 3 x 5 x 5
9. HCF = 2 x 3 x 5 = 30

34.   Three balls toll at intervals of 12 minutes, 15 minutes and 18 minutes respectively. If they start tolling together, after what time will they next toll together?

1. (a) 12
2. (b) 90
3. (c) 180
4. (d) 1
5. Answer – (c) Finding LCM for 12,15,18
6. 12 = 2 x 2 x 3
7. 15 = 3 x 5
8. 18 = 2 x 3 x 3
9. LCM = 2 x 2 x 3 x 3 x 5 = 180

35. The largest number which divides 650 and 1170.

1. (a) 13
2. (b) 130
3. (c) 260
4. (d) None of these
5. Answer – (b) Finding HCF
6. 650 = 2 x 5 x 5 x 13
7. 1170 = 2 x 3 x 3 x 5 x13
8. HCF = 2 x 5 x 13 = 130

36.     Which of the following is terminating decimal expansion-

1. (a) 29/243
2. (b) 77/210
3. (c) 17/8
4. (d) 6/15
1. =   17/2³
6. When denominator is having the powers of 5 and 2 then the number will be terminating decimal expansion.

37.   In a terminating decimal expansion how many number will be after decimal in – 35/50

1. (a) 1
2. (b) 2
3. (c) 3
4. (d) 4
1. = 35/(2 x 5²) Maximum power of 2 or 5 is 2. So decimal expansion will also be after 2 digits.

38. Terminating decimal expansion of 15/1600

1. (a) 0.9375
2. (b) 0.15
3. (c) 0.009375
4. (d) 0.00015.
6. = 15/(2⁶ x 5²)             (1600 = 2⁶ x 5²)
7. = (15 x 5⁴)/(2⁶ x 5² x 5⁴)    (multiplying by 5⁴ in both numerator and denominator)
8. =  9375/(10)⁶
9. =   0.009375

39. Which is not terminating decimal expansion –

1. (a) 29/243
2. (b) 17/8
3. (c) 15/100
4. (d) 39/64
6.        = 29/7³       (Denominator does not have 2 or 5 or both so it will be non-terminating decimal number)

40. Which is a rational number?

(a) 2.300300030000…. (b) √3 2/3

(c) 2/3 (d) None of these

Answer – (c) 2/3 is the rational number.

A number is in the form of p/q is a rational number. 