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WorksheetsReal Numbers
Total questions: 40
Worksheet time: 21mins
Name
Class
Date
1.
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
2.
For some integer m, every even integer is of the form
a)
m
b)
m + 1
c)
2m
d)
2m + 1
3.
For some integer m, every odd integer is of the form
a)
m
b)
m + 1
c)
2m
d)
2m + 1
4.
Euclid’s Division Lemma Represents The Pair Of Integers 25 & 7.
a)
25 = 25 x 1 + 0
b)
25 = 7 x 3 + 4
c)
25 = 7 x 2 + 11
d)
25 = 7 x 4 - 3
5.
The Number In The Form Of 4p +3, Where 'p' Is a Whole Number, Will Always Be
a)
Even
b)
Odd
c)
Even or Odd
d)
Multiple of 3
6.
(6 + 5 √3) – (4 – 3 √3 ) is a . . .
a)
Natural number
b)
Irrational number
c)
Integer
d)
Whole Number
7.
HCF of 418 and 33 is . . . .
a)
33
b)
22
c)
11
d)
1
8.
HCF of 4052 and 12576 is . . .
a)
4
b)
24
c)
124
d)
6
9.
Find the HCF of 1848 and 3058
a)
2
b)
22
c)
11
d)
44
10.
HCF of 56 and 96
a)
2
b)
8
c)
16
d)
0
11.
LCM of 12 and 18
a)
6
b)
12
c)
18
d)
36
12.
For any value of n, the numbers of the form 4ⁿ where n is a natural number end with. . .
a)
4
b)
6
c)
4 or 6
d)
0
13.
For any value of n, the numbers of the form 6ⁿ where n is a natural number end with. . .
a)
3
b)
6
c)
3 or 6
d)
0
14.
log 1 = . . .
a)
0
b)
1
c)
10
d)
None
15.
Prime factorization of 140
a)
2 x 2 x 35
b)
4 x 5 x 7
c)
2 x 2 x 5 x 7
d)
2 x 5 x 14
16.
Express 5³ = 125 in logarithm form.
a)
Log₅125 = 3
b)
Log5³ = 125
c)
5³ = Log 125
d)
Log₃125 = 5
17.
Find the log of 32 to the base 4.
a)
2/5
b)
5/2
c)
5
d)
8
18.
Find x if log₅(x-7)=1.
a)
5
b)
7
c)
12
d)
6
19.
Express log(75/16)-2log(5/9)+log(32/243) in terms of log 2 and log 3.
a)
log2
b)
log3
c)
log2 + log3
d)
log(2/3)
20.
The logarithms having base ‘10’ are called
a)
pure logarithms
b)
common logarithms/Briggesian logarithms
c)
natural logarithms
d)
infinite logarithms
21.
Log (mn) = . . .
a)
log m + log n
b)
log m - log n
c)
n log m
d)
log n × log m
22.
A concise, precise and convenient method to write very small or large numbers is called
a)
equation
b)
scientific notation
c)
matrix
d)
iota
23.
10 ‾³ = 0.001 can be written in the form of logarithm as
a)
log 1 = −3
b)
log 0.001 = 3
c)
log 3 = − 0.001
d)
log 0.001 = −3
24.
Log(m/n) =
a)
log m + log n
b)
log m - log n
c)
n log m
d)
log n × log m
25.
The logarithms having base ‘e’ are called
a)
pure logarithms
b)
common logarithms
c)
natural logarithms
d)
infinite logarithms
26.
log 1000 = . . .
a)
0
b)
1
c)
2
d)
3
27.
Log2 is . . . . .
a)
rational
b)
irrational
c)
Integer
d)
None
28.
Determine the value of the following
a)
7
b)
5
c)
12
d)
8
29.
16/125 is a . . .
a)
terminating decimal
b)
non-terminating, repeating decimal
30.
25/32 is a . . .
a)
terminating decimal
b)
non-terminating, repeating decimal
31.
100/81 is a . . .
a)
terminating decimal
b)
non-terminating, repeating decimal
32.
41/75 is a . . . .
a)
terminating decimal
b)
non-terminating, repeating decimal
33.
Express 0.375 in the form of p/q
a)
8/3
b)
8/7
c)
3/8
d)
3/7
34.
Express 1.04 in the form of p/q
a)
7/8
b)
8/7
c)
25/26
d)
26/25
35.
0.63 can be expressed in the form of p/q as . . .
a)
31/30
b)
31/33
c)
7/11
d)
21/30
36.
If log 2 = 0.30103 then log 32 =
a)
4.81648
b)
1.50515
c)
9.63296
d)
9.0309
37.
if n² - 1 is divisible by 8 then ' n ' is . . .
a)
odd number
b)
even number
c)
prime number
d)
integer
38.
3 x 5 x 7 x 11 + 35 is . . . . . .
a)
prime number
b)
composite number
c)
even number
d)
Negative number
39.
log x³ y²z =
a)
3log x + 2log y + log z
b)
log x +log y +log z
c)
log x³ +log y² - log z
d)
2log x +3 log y - log z
40.
HCF of n, n +1 where n∈N
a)
1
b)
n
c)
n +1
d)
n (n +1 )
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