Real Number
Xth Mathematics
MULTIPLE
CHOICE QUESTIONS
1 Euclid’s division algorithm
can be applied to :
(a) only positive integers
(b) only negative integers
(c) all integers
(d) all integers except 0.
2. For some integer m, every even integer is of the
form :
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
3. If the HCF of 65 and 117 is
expressible in the form 65m – 117, then the value of m is :
(a) 1
(b) 2
(c) 3
(d) 4
4. 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
5. 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
6. 7 × 11 × 13 × 15 + 15 is :
(a) composite number
(b) prime number
(c) neither composite nor
prime
(d) none of these
7. 1.2348 is :
(a) an integer
(b) an
irrational number
(c) a rational number
(d) none of these
8. 2.35 is :
(a) a terminating decimal
(b) a rational number
(c) an irrational number
(d) both (a) and (c)
9. 3.24636363... is :
(a) a terminating decimal
number
(b) a non-terminating
repeating decimal number
(c) a rational number
(d) both (b) and (c)
10. For some integer q, every
odd integer is of the form :
(a) 2q
(b) 2q + 1
(c) q
(d) q + 1
11. If the HCF of 85 and 153 is
expressible in the form 85m – 153, then the value of m is :
(a) 1
(b) 4
(c) 3
(d) 2
12. The decimal expansion of the
rational number 47 / 22.5. will terminate after :
(a) one decimal place
(b)
three decimal places
(c) two decimal places
(d) more than 3 decimal places
13. If two positive integers p
and q can be expressed as p = ab2 and q = a2b;
a, b being prime numbers, then LCM (p, q) is :
(a) ab
(b) a2b2
(c) a3b2
(b) a3b3
14. 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 :
(a) 0 < r ≤ b
(b)
1 < r < b
(c) 0 < r < b
(d) 0 ≤ r < b
15. Following are the steps in
finding the GCD of 21 and 333 :
333 = 21 × m + 18
21 = 18 × 1 + 3
n = 3 × 6 + 0
The integers m and n
are :
(a) m = 15, n = 15
(b) m = 15, n = 18
(c) m = 15, n = 16
(d) m = 18,
n = 15
16. HCF and LCM of a and b
are 19 and 152 respectively. If a = 38, then b is equal to :
(a) 152
(b) 19
(c) 38
(d) 76
17. (n + 1)2 – 1 is divisible by 8, if n is
:
(a) an odd integer
(b) an
even integer
(c) a natural number
(d) an
integer
18. The largest number which
divides 71 and 126, leaving remainders 6 and 9 respectively is :
(a) 1750
(b) 13
(c) 65
(d)
875
19. If two integers a and
b are written as a = x3y2
and b = xy4;
x, y are prime numbers, then H.C.F. (a, b) is :
(a) x3y3
(b) x2y2
(c) xy
(d) xy2
20. The decimal expansion of the
rational number 145171250 will terminate after :
(a) 4 decimal places
(b) 3 decimal places
(c) 2 decimal places
(d) 1 decimal
place