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Number System
Total Time: 60 mins
1.
2.
Practise Exercise no. 2
The product of any two irrational numbers is
a) always an irrational number
b) always a rational number
c) always an integer
d) sometimes rational, sometimes irrational
If 2 = 1.4142, then
2− 1
2 +1
is equal to
a) 2.4142
c) 0.4142
3.
The number 0.5646464… is equivalent to
a)
c)
4.
5.
b) 5.8282
d) 0.1718
564
990
564
999
b)
d)
559
999
559
990
3.36 – 2.05 + 1.33 is equal to
a) 2.60
b) 2.64
c) 2.61
d) 2.64
The square root of 0.4
a) 0.6
b) 0.7
c) 0.8
d) 0.2
12. If n = 23, then nn =
a) 26
c) 218
Total no. Of Qs:40
b) 211
d) 224
13. A number when divided by 899 gives a remainder 63. If
the same number is divided by 29, the remainder will be:
a) 3
b) 4
c) 5
d) 6
14. A number when divided by 6 leaves the remainder 3.
When the square of the same number is divided by 6, the
remainder is:
a) 0
b) 1
c) 2
d) 3
15. When the positive integer n is divided by 3, the
remainder is 2 and when n is divided by 5, the remainder
is 1. What is the least possible value of n?
a) 6
b) 8
c) 11
d) 17
16. The product of three consecutive integers is 210, then
their sum is:
a) 15
b) 17
c) 18
d) 21
17. If the number 357a25b is divisible by both 3 and 5, then
the missing digits in the unit’s place and the thousands’
place respectively are:
a) 0, 6
b) 5, 6
c) 5, 4
d) 0, 7
6.
If a and b are both odd numbers, then which of the
following is even?
a) a + b + 1
b) 2a + b
c) a + b + 3
d) ab + 1
7.
a, b are positive integers and a – b is even and a/b is also
even, which of the following must be odd
a) b/2
b) (a+b)/2
c) (a+2)/2
d) (b+2)/2
18. The number 311311 is:
a) divisible by 3 but not by 11
b) divisible by 11 but not by 3
c) divisible by both 3 & 11
d) neither divisible by 3 nor by 11
8.
If multiplication of two numbers a & b is greater than
zero (ab > 0) and a is less than zero (a < 0), then which of
the following must be negative?
a) b
b) –b
c) –a
d) –(a + b)
19. What should be subtracted from 345670 to make it
divisible by 11?
a) 16
b) 17
c) 18
d) 19
9.
A natural number is multiplied by a prime number. The
product is always a
a) Prime number
b) Composite number
c) Whole number
d) Irrational number
10. There are four prime numbers written in ascending order.
The product of first three is 385 and that of last three is
1001. The last number is
a) 11
b) 13
c) 17
d) 19
11. 2x-1 + 2x+1 = 1280, then find the value of x.
a) 9
b) 10
c) 11
d) 12
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20. Which of the following has most number of divisors?
a) 99
b) 101
c) 176
d) 182
21. A girl wrote all the numbers from 100 to 200. Then she
started counting the number of one's that has been used
while writing all these numbers. What is the number that
she got?
a) 111
b) 119
c) 120
d) 121
22. If each of the three nonzero numbers a, b and c is
divisible by 3, then abc must be divisible by which one
of the following the numbers?
a) 8
b) 27
c) 81
d) 121
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23. When a particular positive number is divided by 5, the
remainder is 2. If the same number is divided by 6, the
remainder is 1. If the difference between the quotients of
division is 3, then find the number.
a) 37
b) 97
c) 67
d) 87
24. The number obtained by interchanging the two digits of a
two digit number is less than the original number by 27.
If the difference between the two digits of the number is
3, what is the original number?
a) 74
b) 63
c) 85
d) Cannot be determined
25. The number obtained by interchanging the two digits of a
two digit number is less than the original number by 27.
If the difference between the two digits of the number is
3, what is the original number?
a) 13
b) 59
c) 35
d) 37
c) 529
d) 624
35. Find the smallest number which, when divided by 5
leaves the remainder 3 and when divided by 9 will leave
the remainder 6.
a) 51
b) 33
c) 47
d) 60
36. Find the greatest number which will divide 410, 751 and
1030 so as to leave remainder 7 in each case.
a) 72
b) 29
c) 45
d) 31
37. What is the highest power of 2 that divides 20!
completely?
a) 18
b) 20
c) 10
d) 40
38. How many trialing zeros are there in 100! ?
a) 100
b) 25
c) 24
d) 20
26. The number obtained by interchanging the two digits of a
two digit number is less than the original number by 27.
If the difference between the two digits of the number is
3, what is the original number?
a) 5
b) 9
c) 4
d) 0
39. If N = 123  34  52, then find the total number of factors
of N
a) 60
b) 168
c) 160
d) 144
27. The LCM of two numbers is 120 and HCF is 7. If one of
the numbers is 12, find the other number.
a) 30
b) 40
c) 70
d) Data Inconsistent
40. Three runners running around a circular track, can
complete one revolution in 15, 18 and 21 min
respectively. After how much time will they meet at the
starting point?
a) 6.5 hours
b) 10.5 hours
c) 12.5 hours
d) None of these
28. The HCF of two number is 8. Which one of the
following can never be their LCM?
a) 24
b) 48
c) 56
d) 60
29. Ramon wants to cut a rectangular board into identical
square pieces. If the board is 18 inches by 30 inches,
what is the least number of square pieces he can cut
without wasting any of the board.
a) 4
b) 6
c) 9
d) 15
30. LCM and HCF of 3/2, 10/6 and 15/4 is:
a) 10 and 1/6
b) 15 and 1/12
c) 30 and 1/12
d) 15 and 1/6
31. Which of the following is NOT a factor of 1515 ?
a) 125
b) 225
c) 135
d) 180
32. (15!)/3m is an integer. What is the greatest possible value
of m?
a) 4
b) 5
c) 6
d) 7
33. The number aaaaaa, where a is a single digit natural
number, is divisible by
a) 11
b) 13
c) 143
d) All of above
34. What is the least number which, when divided by 52,
leaves remainder 33, and when divided by 78 leaves
remainder 59, and when divided by 117 leaves remainder
98?
a) 449
b) 379
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Page 2
Number System Practise Exercise 2 (Solutions)
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D
C
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A
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D
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B
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B
C
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C
B
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A
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A
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B
B