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Q1. For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, 0 ≤ r < b. If b = 4 then which is not the value of r?
1
2
3
4
Q2. (18 x 25 x 25 + 25) gives a ___ number.
Prime
Composite
Prime and composite
Neither Prime nor composite
Q3. The length, breadth and height of a room is 6m 80 cm, 5m 10 cm and 3 m 40 cm, respectively. Find the longest tape which can measure the dimensions of the room exactly. 
2m 70 cm
2m 40 cm
1m 60 cm
1m 70 cm
Q4. A series of well-defined steps which give a procedure for solving a type of problem is called
Algorithm
Lemma
Procedure
Walkthrough
Q5. What is the HCF of 1076 and 584?
16
12
24
4
Q6. Which of the following rational numbers has a denominator that can be expressed as a product of powers of 2 and 5?
0.14546575
0.141414...
0.23452345...
1.34573457...
Q7. Find the HCF of 1000 and 1125.
100
125
150
75
Q8. Complete the statement :  Any positive odd integer is of the form 6q + 1, or 6q + 3, or ___________, where q is some integer.
6q
6q + 2
6q + 4
6q + 5
Q9. From among a minimum of how many integers can you say that one is divisible by 3?
 3
 1
 4
 5
Q10. How many prime factors are there in prime factorization of 5005?
2
4
6
7
Q11. The HCF of 236 and 137 is
No H.C.F
1
2
3
Q12. HCF of 96 and 404 is
16
4
4696
96
Q13. There are 135 participants in English and 165 in Mathematics in a seminar. What is the minimum number of rooms required to seat them if each room must have the same number of participants from each of the two subjects?
20
15
25
9
Q14. The HCF of 105 and 273 is … 
3
21
7
15
Q15. The product of a non-zero rational and an irrational number is
always irrational
always rational
rational or irrational
1
Q16. A rational number can be expressed as a terminating decimal if its denominator has factors
2, 3 and 5
2 and 3
3 and 5
2 and 5
Q17. Identify the Theorem: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Fundamental Theorem of Arithmetic
Euclid’s Theorem
Composite Theorem
Theorem of factorization
Q18. Euclid’s division lemma can be used to find
LCM of numbers
HCF of numbers
Prime factors of numbers
Product of numbers
Q19. Find HCF of 592 and 252 by using Euclid’s Division Algorithm.
4
6
12
76
Q20. If x and y are odd positive integers then x2 + y2 is _____
even
odd
odd or even
multiple of 2 and  4
Q21. The prime factorization of 210 is
15 x 14
2 x 15 x 7
2 x 5 x 21
2 x 3 x 5 x 7
Q22. 6n is divisible by
2
3
2 and 3 both
5
Q23. Which of the following numbers is irrational?
2.454545…
0.11111….
0.101100101010…….
0.23232323
Q24. Find the HCF of 876 and 255 by Euclid’s division lemma.
37
3
111
5
Q25. Which of  the following is the expression of 4025 as a product of prime factors?
5 x 5 x 16
5 x 805
5 x 5 x 161
5 x 17 x 5
Q26. Find the HCF of 135 and 225 by Euclid’s division lemma.
45
30
90
10
Q27. Given that the H.C.F. of 35 and 49 is 7, what is their LCM?
225
265
245
195
Q28. Which one of the following is true about the prime factors of the denominator of the decimal expansion, 1256.1782?
 It is a product of powers of 2 and 5.
 It is a power of 2 only.
 It is a power of 5 only.
It may have any factors.
Q29. If the HCF of 85 and 153 is expressible in the form 85n - 153, then value of n is :
3
2
4
1
Q30. For a = n and b = 3, which of the following represents the correct mathematical form of Euclid's division lemma?
n = 3q + r
r = 3q + n
n = q + 3
n = 3q - r
Q31. The L.C.M. of 12, 15 and 21 is
450
420
180
360
Q32. The HCF and LCM of 2 numbers are 4 and 24 respectively .If one number is 8, find the other number.
12
4
24
8
Q33. 1192 - 1112 is:
Prime number
Composite number
An odd prime number
An odd composite number
Q34. Find HCF of 155 and 1385 by using Euclid’s Division Algorithm.
15
10
5
25
Q35. Find HCF of 84, 90 and 120.
6
7
14
20
Q36. H.C.F. of two consecutive even numbers is:
0
1
4
2
Q37. For some integer m, every odd integer is of the form
m
2m
2m + 1
-2m  
Q38. Find HCF of 35, 56 and 91.
7
14
21
35
Q39. Find the HCF of 75 and 243 by Euclid’s division lemma. 
1
3
18
6
Q40. Find HCF of 963 and 657 by using Euclid’s Division Algorithm.
45
36
9
4

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