Question 2 :
State true or false: The square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Question 3 :
The square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q. Is it true?
Question 4 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers. Find the value of m.
Question 5 :
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 6 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 8, 9 and 25
Question 9 :
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 10 :
What are the LCM and HCF of 17, 23 and 29?
Question 11 :
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 12 :
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 13 :
Use Euclid’s division algorithm to find the HCF of 441, 567, 693.
Question 14 :
Given that HCF (306, 657) = 9, find LCM (306, 657).
Question 15 :
Is it correct, that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.
Question 16 :
What are the LCM and HCF (by prime factorisation method) of 96 and 404?
Question 17 :
“The product of three consecutive positive integers is divisible by 6'. Is this statement true or false ?
Question 18 :
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is _____ .
Question 19 :
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 20 :
A/An ________ is a proven statement used for proving another statement.