Q 1. HCF of 8, 9, 25 is
(a) 8
(b) 9
(c) 25
(d) 1
(d) 1
Q 2. The values of x and y in the given figure are
(a) x + 10, y = 14
(b) x = 21, y = 84
(c) x = 21, y = 25
(d) x = 10, y = 40
(b) x = 21, y = 84
Q 3. The product of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
b) irrational
Q 4. If HCF (a, b) = 12 and a × b = 1800 then LCM (a, b) is
(a) 3600
(b) 900
(c) 150
(d) 90
(c) 150
Q 5. The sum of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
b) irrational
Q 6. If mn = 32, where m and n are positive integers, then the value of (n)mn is
(a) 9765625
(b) 9775625
(c) 9785625
(d) 9865625
(a) 9765625
Q 7. The product of two different irrational numbers is always
(a) rational
(b) irrational
(c) both of above
(d) none of above
(b) irrational
Q 8. The decimal expansion of 178 will terminate after how many places of decimals?
(a) 1
(b) 2
(c) 3
(d) will not terminate
(c) 3
Q 9. The sum of two irrational numbers is always
(a) irrational
(b) rational
(c) rational or irrational
(d) one
(a) irrational
Q 10. If HCF of 55 and 99 is expressible in form 55 m – 99, then the value of m:
(a) 4
(b) 2
(c) 1
(d) 3
(b) 2
Q 11. 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
(a) 3q, 3q+ 1, 3q + 2
Q 12. Given that LCM of (91, 26) = 182 then HCF (91, 26) is
(a) 13
(b) 26
(c) 7
(d) 9
(a) 13
Q 13. Which number is divisible by 11?
(a) 1516
(b) 1452
(c) 1011
(d) 1121
(b) 1452
Q 14. 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
2
Q 15. If A = 2n + 13, B = n + 7 where n is a natural number then HCF of A and B
(a) 2
(b) 1
(c) 3
(d) 4
(b) 1
Q 16. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(b) y
Q 17. There are 312, 260, and 156 students in classes 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 an equal number of students
(a) 52
(b) 56
(c) 48
(d) 63
(a) 52
Q 18. (–1)n + (–1)8n = 0 when n is
(a) any positive integer
(b) any odd natural number
(c) any even numeral number
(d) any negative integer
(b) any odd natural number
Q 19. 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
(d) 0 ≤ r < b
Q 20. (n² – 1) is divisible by 8, if n is
(a) an integer
(b) a natural number
(c) an odd natural number
(d) an even natural number
. (c) an odd natural number
Q 21. The number ‘π’ is
(a) natural number
(b) rational number
(c) irrational number
(d) rational or irrational
(c) irrational number
Q 22. If 112 = q×6+r, then the possible values of r are:
(a) 2, 3, 5
(b) 0, 1, 2, 3, 4, 5
(c) 1, 2, 3, 4
(d) 0, 1, 2, 3
(b) 0, 1, 2, 3, 4, 5
Q 23. (6 + 5 √3) – (4 – 3 √3) is
(a) a rational number
(b) an irrational number
(c) a natural number
(d) an integer
(b) an irrational number
Q 24. The LCM of 2.5, 0.5 and 0.175 is
(a) 2.5
(b) 5
(c) 7.5
(d) 0.875
(d) 0.875
Q 25. 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
(c) less than 7
Q 26. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then LCM(a, b) is
(a) xy
(b) xy2
(c) x3y3
(d) x2y2
c) x3y3
Q 27. 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
(b) – 5
Q 28. The decimal expansion of the rational number 14587250 will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places
(c) three decimal places
Q 29. Every positive odd integer is of the form ________ where ‘q’ is some integer.
(a) 3q + 1
(b) 5q + 1
(c) 2q + 1
(d) 2q + 2
(c) 2q + 1
Q 30. The product of a non-zero rational and an irrational number is
(a) always rational
(b) rational or irrational
(c) always irrational
(d) zero
(c) always irrational