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WorksheetsNumber Theory - 1
Total questions: 15
Worksheet time: 29mins
Name
Class
Date
1.
Given a0=1, an=2an-1 (when n is odd) and an=an-1 (when n is even), then what is the value of a100-a97-a96 ?
a)
0
b)
247
c)
248
d)
249
2.
If both 117 and 88 are factors of number (a*47*64*1313) then what is the smallest possible value of a?
a)
10296
b)
429
c)
99
d)
9
3.
The series of differences between consecutive prime numbers is represented as dp1, dp2, dp3, .... dpn .Whare dp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ?
a)
81
b)
82
c)
83
d)
87
4.
How many pairs of positive integers m, n satisfy 1/m+4/n=1/12, where n is an odd integer less than 60 ?
a)
6
b)
4
c)
7
d)
3
5.
A natural number has exactly 10 divisors including 1 and itself. How many distinct prime factors can this natural number have?
a)
Either 1 or 2
b)
Either 1 or 3
c)
Either 2 or 3
d)
Either 1,2 or 3
6.
what is the sum of these 1230 sequences such as 1,2,1,2,2,1,2,2,2,1,2,2,2,2.....
a)
2411
b)
2412
c)
2413
d)
2414
7.
Find the remainder when 987987....(upto 123 digits) is divided by 1001?
a)
987
b)
986
c)
985
d)
984
8.
Number 81A84B6C, where each of the letters A,B,C respresents a distinct digits. The number is divisible by each of the 5,8,9. Find the value of A+B?
a)
9
b)
10
c)
11
d)
12
9.
A seven-digit number comprises of only 2's and 3's. How many of these are multiples `of 12?
a)
1
b)
11
c)
21
d)
44
10.
If a number x100 have 31 digit then how many digits are there in x1000? Given log2=0.3010, log3=0.4771
a)
301
b)
302
c)
303
d)
304
11.
How many three digit numbers are there in which product of their digit is 36.
a)
21
b)
22
c)
23
d)
24
12.
What is the number of odd factors of 49000000?
a)
21
b)
22
c)
23
d)
24
13.
A man ate 100 apple in five days daily he ate more than 6 apples when compare to previous day how many apples he ate in first day?
a)
9
b)
8
c)
7
d)
6
14.
How many numbers in between the 1 to 100 whose factors will be prime. ie like 3= 1, 3
a)
21
b)
22
c)
24
d)
25
15.
What will be the remainder when a four digit prime no. is divided by 12.
a)
1,5,7,11
b)
1,5,7
c)
1,5
d)
1
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