1.) The decimal expansion of the rational number 33/22.5 will terminate after
(A) one decimal place
(B) two decimal places
(C) three decimal places
(D) more than 3 decimal places
2.) Euclid’s division lemma states that for two positive integers a and 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
3.) For some integer m, every even integer is of the form
(A) m
(B) m + 1
(C) 2m
(D) 2m + 1
4.) For some integer q, every odd integer is of the form
(A) q
(B) q + 1
(C) 2q
(D) 2q + 1
5.) n2 – 1 is divisible by 8, if n is
(A) an integer
(B) a natural number
(C) an odd integer
(D) an even integer
[Hint : zero is divisible by all the numbers]
6.) If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
(A) 4
(B) 2
(C) 1
(D) 3
7.) The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
(A) 13
(B) 65
(C) 875
(D) 1750
8.) If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
(A) xy
(B) xy2
(C) x3y3
(D) x2y2
9.) If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
(A) ab
(B) a2b2
(C) a3b2
(D) a3b3
10.) The product of a non-zero rational and an irrational number is
(A) always irrational
(B) always rational
(C) rational or irrational
(D) one
11.) The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(A) 10 (B) 100 (C) 504 (D) 2520
12.) The decimal expansion of the rational number 14587/1250 will terminate after:
(A) one decimal place
(B) two decimal places
(C) three decimal places
(D) four decimal places
13.) Using Euclid’s division algorithm, find which of the following pairs of numbers are co-prime: (i) 231, 396 (ii) 847, 2160
14.) The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer.
15.) Can the number 6n, n being a natural number, end with the digit 5? Give reasons.
Ans 1.) B 2.) C 3.) C 4.) D 5.) C 6.) B 7.) A 8.)B 9.) C 10.) A 11.) D 12.) D 13) i) 33 ii) 1 14.) No (0,1 and 2) 15.)