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
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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) 23 × 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) x4y²z
(c) x4y3
(d) x4y3z
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) x4y²z
(c) x4y3
(d) x4y3z
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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