find the highest power 6 which can divide LCM of first 200 natural numbers ?
Find the number of ways in which 3465 can be written as product of two coprimes.
Select one:
a. 2
b. 4
c. 8
d. 16
e. 32
Given that a pair of natural numbers have their product (10!), how many distinct values can HCF of the two number take?
Select one:
a. 30
b. 40
c. 60
d. 64
e. None of the above
Find the smallest four-digit number which when divided by 9 and 8 give a remainder of 8 and 7 respectively ?
Select one or more:
a. 1097
b. 1151
c. 1223
d. 1245
e. None of the above
Hw to tackle these type of questions??
Sn = 1/2 + 1/6 + 1/12 + 1/20 + ..........
Now this expression either tends to infinity or sometimes for a definite finite value.In any case the sum is asked. but getting to an answer is seemingly difficult. Help!
Set A is formed by selecting some of the numbers from the first 100 natural numbers such that the HCF of any two numbers in the set is the same.
The HCF of any two numbers in set A is h, and the maximum possible number of elements in set A is 4. What is the maximum possible value of h?
Select one:
a. 13
b. 18
c. 19
d. 20
e. 21
When all numbers which leave 47 as a remainder divided by 779 are contined in a set; then how many different remainders are possible when all possible numbers of that set are divided by 95 ?
Select one:
a. 1
b. 4
c. 5
d. 19
e. 95
A*B*C = 100How many positive integral solutions are there
A*B*C
How many 3-digit numbers leave same remainder when divided by 18, 12 and 9 but no remainder by 3? Note: No remainder is also remainder 0.
Select one:
a. 25
b. 50
c. 75
d. 100
e. None of the above
If a = b2 – b, b >3, where a, b are Natural numbers. Then a2 – 2a is always divisible by?
Select one:
a. 12
b. 15
c. 20
d. 24
e. None of the above
Find the least difference between two numbers which when divided by 5, 6, 7 and 8 leaves a remainder 3, 4, 5, 6 respectively but when divided by 9 leaves no remainder.
Select one:
a. 2520
b. 5040
c. 7560
d. 15120
e. None of the above
Z is family of all such numbers which are 4 more than a multiple of 9 and also 10 more than a multiple of 12. By which largest number any member of Z can be divided giving same remainder every time?
Select one:
a. 18
b. 24
c. 36
d. 48
e. 72
Z is a number which is 4 more than a multiple of 9 and also 10 more than a multiple of 12. If I divide Z by 18, what remainder would I expect?
Select one:
a. 1
b. 4
c. 12
d. Data Inconsistent
e. None of the above
A number when divided by a divisor gave 33 as the remainder. When the square of the number is divided by the same divisor, the remainder is 9. Find the total number of such divisors possible.
Select one:
a. 15
b. 16
c. 17
d. 18
e. 32
On dividing a number by 5, 7 and 8 successively the remainders are respectively 2, 3 and 4. What will be the remainder if the order of division is reversed?
Select one:
a. 2, 5, 5
b. 5, 5, 2
c. 2, 2, 5
d. 5, 2, 2
e. None of the above
Which of the following statements is always true about the sum of the squares of three consecutive positive integers?
Select one:
a. When divided by 11, it leaves a remainder of 1
b. When divided by 3, it always leaves a remainder of 2
c. When divided by 5, it leaves 0 or an even remainder
d. Two or more of the above statements
e. All of the above
Let A denote the set of all prime numbers, B the set of all prime numbers and the number 4, and C the set of all prime numbers and their squares. Let D be the set of positive integers k, for which (k-1)!/k is not an integer. Then
Select one:
a. D is equal to A
b. D is equal to B
c. D is a subset of C
d. D is a superset of C
e. None of the above
The remainder when 300^3000 - 1 is divided by 1001 is
Select one:
a. 1
b. 2
c. 3
d. 1000
e. None of the above
N is a positive integer, which when divided by 16, 17 and 18 leaves remainders of 6, 7 and 8 respectively. Find the remainder when N2 + 5N + 6 is divided by 12.
Select one:
a. 2
b. 4
c. 6
d. 8
e. None of the above
What is the remainder when 128^2000 is divided by 153?
Select one:
a. 16
b. 37
c. 39
d. 64
e. None of the above