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Important Questions
CBSE CLASS X
Mathematics (Real Numbers)
1. Which of the following numbers has terminating decimal expansion?
A. 37 / 45
B. 21 / 2356
C. 17 / 49
D. 89 / 2232
2. The [HCF x LCM] for the numbers 50 and 20 is
A. 10
B. 100
C. 1000
D. 50
3. Which of the following number has terminating decimal expansion?
A. 37/45
B. 21/ 235 6
C. 17/49
D. 89/2232
4. Euclid’s division lemma states that for two positive integers a asbd b. there exist unique
integers q and r such that a = bq+r, where r must satisfy?
A. 1 < r < b
B. 0 < r <=b
C. 0 <=r < b
D. 0 < r < b
5. The decimal expansion of the number 31/ 22.5 will terminate after
A. One Decimal Place
B. Two Decimal Place
C. Three Decimal Place
D. More than 3 Decimal Place
6. that HCF (2520, 6600) =40, LCM (2520, 6600) =252 x k, then the value of k is:
A. 1650
B. 1600
C. 165
D. 1625
7. If p, q are two co – prime numbers.HCM (p, q) is:
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A.
B.
C.
D.
p
q
pq
1
8. The decimal expansion of the rational number 23/22.5 will terminate after
A. One Decimal Place
B. Two Decimal Place
C. Three Decimal Place
D. More than 3 Decimal Place
9. n 2 - 1 is divisible by 8, if n is
A. 1
B. p
C. q
D. pq
10. If p, q are two prime number, then LCM (p, q) is:
A. 1
B. p
C. q
D. pq
11. If d= HCF (48, 72) the value of d is:
A. 24
B. 48
C. 12
D. 72
12. The decimal expansion of the rational number 11/2^3 5^2 will terminate after:
A. One Decimal Place
B. Two Decimal Place
C. Three Decimal Place
D. More than 3 Decimal Place
13. If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the values of m is:
A. 4
B. 2
C. 3
D. 1
14. If d= LCM (36, 198), then the value of s is:
A. 396
B. 198
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C. 36
D. 1
15. In the adjoining factor tree, find the number m, n:
A. 35/14
B. 14/35
C. 1/7
D. 7/8
16. If x- 23 x 3 x 52, y- 2 2 x 33 then IICF (x, y) is:
A. 12
B. 108
C. 6
D. 36
17. Given that HCF (253, 440) = 11 and LCM (253, 440) = 253 x R. The value of R is:
A. 400
B. 40
C. 440
D. 253
18. The rational number of decimal (0.6) ¯ is:
A. 33/50
B. 2/3
C. 111/167
D. 1/3
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19. If two positive integer a and b are written as a = x2 y2and b = xy2; x,y are prime number
then HCF (a, b) is:
A. xy
B. xy2
C. x2 y3
D. x2 y2
20. Given that HCF (26, 91) = 13, then LCM (26, 91) is:
A. 2344
B. 182
C. 91
D. 364
21. (2 + v5) (2 + v5 )expression is:
A. A rational number
B. A Whole number
C. An irrational number
D. A natural number
22. If the HCF of 85 and 153 is expressible in the form 85n – 153, then value of n is:
A. 3
B. 3
C. 4
D. 1
23. (v2 - v3) (v3 - v2) is
A. A rational number
B. A Whole number
C. An irrational number
D. A natural number
24. A rational number can be expressed as a terminating decimal if the denominator has factors
A. 2, 3 or 5
B. 2 or 3
C. 3 or 5
D. 2 or 5
25. The decimal expansion of 33 / 22x 5 will terminate after:
A. One Decimal Place
B. Two Decimal Place
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C. Three Decimal Place
D. More than 3 Decimal Place
26. Which is not an irrational number?
A. 5 - v3
B. v2 + v5
C. 4 + v2
D. 6 + v9
27. Which is not irrational number?
A. v5 - v3
B. 6 + v9
C. v3 – 1
D. 2v3 – 3
28. How many prime factors are there in prime factorization of 5005.
A. 2
B. 4
C. 6
D. 7
29. 119 2 - 111 2 is:
A. Prime Number
B. Composite number>
C. An odd prime number
D. An odd composite number
30. If least prime factor of a is 3 and least prime factor of b is 7, the least prime factor of (a+ b)
is:
A. 2
B. 3
C. 5
D. 11
31. If product of the HCF and LM of the smallest prime number and the smallest composite
number is:
A. 2
B. 4
C. 6
D. 8
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32. If n is any natural number, then which of the following expression ends with 0:
A. (3 x 2)n
B. (4 x 3)n
C. (2 x 5)n
D. (6 x 2)n
33. If a, b are co prime, then a2 , b2 are:
A. Coprime
B. Not Coprime
C. Odd numbers
D. Even numbers
34. The decimal expansion of the rational number 43 / 24 x 53 will terminate after:
A. a = bq + r, 0 < r < b
B. a = bq + r, 0<= r <=b
C. a = bq + r, 0<= r < b
D. a = bq + r, 0 < b < r
35. Which of the following is not an irrational number?
A. 5 - v3
B. v5 + v3
C. 4 + v2
D. 5 + v9
36. Which of the following is rational?
A. v6 + v9
B. v2 + v4
C. v4 + v9
D. v3 + v5
37. Euclid’s division lemma states that if a and b two positive integer, then there exist unique
integer q and r such that:
A. a = bq + r, 0 < r < b
B. a = bq + r, 0 <= r <=b
C. a – bq + r, 0 <= r < b
D. a – bq + r, 0 <=b < r
38. Which is the following rational number have a terminating decimal expansion?
A. 125/ 441
B. 77 / 210
C. 15 / 1600
D. 129 / 22 x 52 x 72
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39. The value of x in the factor tree is:
A.
B.
C.
D.
30
150
100
50
40. Which of the following rational number have non terminating and repeating decimal
expansion?
A. 15 / 1600
B. 17 / 6
C. 23 / 8
D. 35 / 50
41. According to Euclid’s division algorithms HCF of any two positive integers a and b with a
> b is obtained by applying Euclid’s division lemma to a and b to find q and r such that a =
bq + r where r must satisfy.
A. 1 < r < b
B. 0 < r < b
C. 0 < = r < b
D. 0 < r <=b
42. The decimal expansion of 141 / 120 will terminate after how many places of decimals?
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A.
B.
C.
D.
1
2
3
Will not terminate
43. The decimal expansion of 131 / 120 will terminate after how many places od decimal?
A. 1
B. 2
C. 3
D. Will not terminate
44. According to Euclid’s division algorithm using Euclid’s division lemma for two positive
integer a and b with a > b enables us to find:
A. HCF
B. LCM
C. Decimal expansion
D. Probability
45. The decimal expansion of 6 / 1250 will terminate after how many places of decimal?
A. 1
B. 2
C. 3
D. 4
46. For some integer m, every even integer is of form
A. m
B. m + 1
C. 2m
D. 2m + 1
47. For some integer q, every odd integer is of the form
A. q
B. q + 1
C. 2q
D. 2q + 1
49. If two positive integer a and b are written as
a = x3 y2 and b = xy3 , x, y are prime numbers, then HCF (a, b) is
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A.
B.
C.
D.
xy
xy2
x3 y3
x2 y2
50. If two positive integer p and q can be expresses as
P = ab2 and q = a3b, a, b being prime numbers, then LCM (p, q) is:
A.
B.
C.
D.
ab
a2 b2
a3 b2
a3 b3
51. The product of a non- zero rational and an irrational number is:
A. Always irrational
B. Always rational
C. Always or irrational
D. One
52. The decimal expansion of the rational number 14587 / 1250 will terminate after:
A. One decimal
B. Two decimal
C. Three decimal
D. Four decimal
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