Question 1 :
The square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m. Is it true?

Question 2 :
State True or False, Let p be a prime number. If p divides $a^2$ , then p divides a, where a is a positive integer.

Question 4 :
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

Question 6 :
Choose the correct answer from the given four options in the question: If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ________ .

Question 7 :
The square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q. Is it true?

Question 8 :
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Question 10 :
How is 3825 expressed as a product of its prime factors?

Question 12 :
Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion.

Question 13 :
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)?

Question 14 :
How is 5005 expressed as a product of its prime factors?

Question 16 :
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after _______.

Question 18 :
Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

Question 19 :
Given that HCF (306, 657) = 9, find LCM (306, 657).

Question 20 :
Without actually performing the long division, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 21 :
Can $6^n$ end with the digit 0 for any natural number n ?

Question 22 :
State True or False, Let x = $\frac{p}{q}$ be a rational number, such that the prime factorisation of q is of the form $2^n5^m$, where n, m are non-negative integers. Then x has a decimal expansion which terminates.

Question 23 :
A trader was moving along a road selling eggs. An idler who didn’t have much work to do, started to get the trader into a wordy duel. This grew into a fight, he pulled the basket with eggs and dashed it on the floor. The eggs broke.The trader requested the Panchayat to ask the idler to pay for the broken eggs. The Panchayat asked the trader how many eggs were broken. He gave the following response: If counted in pairs, one will remain; If counted in threes, two will remain; If counted in fours, three will remain; If counted in fives, four will remain; If counted in sixes, five will remain; If counted in sevens, nothing will remain; My basket cannot accomodate more than 150 eggs. How many eggs were there in total?

Question 26 :
Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 27 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 8, 9 and 25

Question 28 :
Every ______________can be expressed ( factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

Question 29 :
Use Euclid’s division algorithm to find the HCF of 441, 567, 693.

Question 30 :
Can $12^n$ end with the digit 0 or 5 for any natural number n?

Question 31 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 17, 23 and 29

Question 32 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 12, 15 and 21

Question 33 :
Choose the correct answer from the given four options in the question: For some integer q, every odd integer is of the form.

Question 34 :
If x and y are both odd positive integers, then $x^2+ y^2$ is even but not divisible by 4. Is it true?

Question 38 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Question 40 :
How is 156 expressed as a product of its prime factors?

Question 42 :
Any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer. TRUE or FALSE ?

Question 43 :
“The product of two consecutive positive integers is divisible by 2'. Is this statement true or false?