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## Class 10 Maths MCQs Chapter 1 Real Numbers

1. The decimal form of \(\frac{129}{2^{2} 5^{7} 7^{5}}\) is

(a) terminating

(b) non-termining

(c) non-terminating non-repeating

(d) none of the above

**Answer**

Answer: c

2. HCF of 8, 9, 25 is

(a) 8

(b) 9

(c) 25

(d) 1

**Answer**

Answer: d

3. Which of the following is not irrational?

(a) (2 – √3)2

(b) (√2 + √3)2

(c) (√2 -√3)(√2 + √3)

(d)\(\frac{2 \sqrt{7}}{7}\)

**Answer**

Answer: c

4. The product of a rational and irrational number is

(a) rational

(b) irrational

(c) both of above

(d) none of above

**Answer**

Answer: b

5. The sum of a rational and irrational number is

(a) rational

(b) irrational

(c) both of above

(d) none of above

**Answer**

Answer: b

6. The product of two different irrational numbers is always

(a) rational

(b) irrational

(c) both of above

(d) none of above

**Answer**

Answer: b

7. The sum of two irrational numbers is always

(a) irrational

(b) rational

(c) rational or irrational

(d) one

## Answer

Answer: a

8. If b = 3, then any integer can be expressed as a =

(a) 3q, 3q+ 1, 3q + 2

(b) 3q

(c) none of the above

(d) 3q+ 1

**Answer**

Answer: a

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

(a) 4

(b) 6

(c) no common factor

(d) only 1

## Answer

Answer: b

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

(a) whole numbers

(b) integers

(c) natural numbers

(d) even numbers

## <strongAnswer

Answer: a

11. Which number is divisible by 11?

(a) 1516

(b) 1452

(c) 1011

(d) 1121

**Answer**

Answer: b

12. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by

(a) x

(b) y

(c) xy

(d) \(\frac{x}{y}\)

**Answer**

Answer: b

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

(a) 17

(b) 11

(c) 34

(d) 45

**Answer/ Explanation**

Answer: a

Explaination:(a); [Hint. Algorithm 398 – 7 – 391; 436 – 11 = 425; 542 – 15 = 527; HCF of 391, 425, 527 = 17]

14. 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

(a) 52

(b) 56

(c) 48

(d) 63

**Answer/ Explanation**

Answer: a

Explaination:(a); [Hint. HCF of 312, 260, 156 = 52]

15. 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 ?

(a) 36 minutes

(b) 18 minutes

(c) 6 minutes

(d) They will not meet

**Answer/ Explanation**

Answer: a

Explaination:(a); [Hint. LCM of 18 and 12 = 36]

16. Express 98 as a product of its primes

(a) 2² × 7

(b) 2² × 7²

(c) 2 × 7²

(d) 2^{3} × 7

**Answer**

Answer: c

17. 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.

(a) 98 kg

(b) 290 kg

(c) 200 kg

(d) 350 kg

**Answer/ Explanation**

Answer: a

Explaination:(a); [Hint. HCF of 490, 588, 882 = 98 kg]

18. For some integer p, every even integer is of the form

(a) 2p + 1

(b) 2p

(c) p + 1

(d) p

**Answer**

Answer: b

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

(a) 2p + 1

(b) 2p

(c) p + 1

(d) p

**Answer**

Answer: a

20. m² – 1 is divisible by 8, if m is

(a) an even integer

(b) an odd integer

(c) a natural number

(d) a whole number

**Answer**

Answer: b

21. If two positive integers A and B can be ex-pressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is

(a) xy²

(b) x^{4}y²z

(c) x^{4}y^{3}

(d) x^{4}y^{3}z

**Answer**

Answer: d

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

(a) always rational

(b) rational or irrational

(c) always irrational

(d) zero

**Answer**

Answer: c

23. If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is

(a) xy²

(b) x^{4}y²z

(c) x^{4}y^{3}

(d) x^{4}y^{3}z

**Answer**

Answer: a

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

(a) 260

(b) 75

(c) 65

(d) 13

**Answer**

Answer: d

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

(a) 5

(b) 60

(c) 20

(d) 100

**Answer**

Answer: b

Explaination:(b); [Hint. LCM of 2, 3, 4, 5 = 60

26. The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is

(a) 840

(b) 2520

(c) 8

(d) 420

**Answer**

Answer: a

27. The decimal expansion of the rational number \(\frac{14587}{250}\) will terminate after:

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Answer**

Answer: c

28. The decimal expansion of the rational number \(\frac{97}{2 \times 5^{4}}\) will terminate after:

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Answer**

Answer: d

29. The product of two consecutive natural numbers is always:

(a) prime number

(b) even number

(c) odd number

(d) even or odd

**Answer**

Answer: b

30. If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 × p, then the value of p is

(a) 5

(b) -5

(c) 4

(d) -4

**Answer/ Explanation**

Answer: b

Explaination:(b); [Hint. HCF of 408 and 1032 is 24, .-. 1032 x 2 + 408 x (-5)]

31. The number in the form of 4p + 3, where p is a whole number, will always be

(a) even

(b) odd

(c) even or odd

(d) multiple of 3

**Answer**

Answer: b

32. When a number is divided by 7, its remainder is always:

(a) greater than 7

(b) at least 7

(c) less than 7

(d) at most 7

**Answer**

Answer: c

33. (6 + 5 √3) – (4 – 3 √3) is

(a) a rational number

(b) an irrational number

(c) a natural number

(d) an integer

**Answer**

Answer: b

34. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is

(a) 24

(b) 16

(c) 8

(d) 48

**Answer**

Answer: a

35. According to the fundamental theorem of arith-metic, if T (a prime number) divides b2, b > 0, then

(a) T divides b

(b) b divides T

(c) T2 divides b2

(d) b2 divides T2

**span style=”color: #ff00ff;”>Answer**

Answer: a

36. The number ‘π’ is

(a) natural number

(b) rational number

(c) irrational number

(d) rational or irrational

**Answer**

Answer: c

37. If LCM (77, 99) = 693, then HCF (77, 99) is

(a) 11

(b) 7

(c) 9

(d) 22

**Answer**

Answer: a

38. Euclid’s division lemma states that for two positive integers a and b, there exist unique integer q and r such that a = bq + r, where r must satisfy

(a) a < r < b

(b) 0 < r ≤ b

(c) 1 < r < b

(d) 0 ≤ r < b

**Answer**

Answer: d

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