Question 1 :
State true or false: The product or quotient of a non-zero rational number and an irrational number is irrational.
Question 4 :
A/An ________ is a proven statement used for proving another statement.
Question 6 :
What are the LCM and HCF of 8, 9 and 25?
Question 7 :
Using Euclid’s division lemma can we show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m?
Question 8 :
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 9 :
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 10 :
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 11 :
For any positive integer n, $n^3$– n is divisible by 6. Is it True or False?
Question 14 :
The cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m. Is it true?
Question 15 :
A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?
Question 17 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 17, 23 and 29
Question 18 :
What are the LCM and HCF (by prime factorisation method) of 6, 72 and 120?
Question 20 :
What are the LCM and HCF of 17, 23 and 29?