Question 3 :
Without actually performing the long division, state whether $\frac{15}{1600}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 5 :
What are the LCM and HCF (by prime factorisation method) of 96 and 404?

Question 7 :
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 8 :
A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m?

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

Question 10 :
Use Euclid's division algorithm to find the HCF of : 867 and 255

Question 11 :
State true or false: The square of an odd positive integer is of the form 8m + 1, for some whole number m.

Question 13 :
“The product of three consecutive positive integers is divisible by 6'. Is this statement true or false ?

Question 16 :
Using Euclid’s division algorithm, find if this pair of numbers is co-prime: 847, 2160.

Question 18 :
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 19 :
Without actually performing the long division, state whether $\frac{23}{2^35^2}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 20 :
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 22 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers, write its decimal expansion, without actual division.

Question 23 :
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 24 :
What are the LCM and HCF of 6 and 20 by prime factorisation method?

Question 25 :
How is 156 expressed as a product of its prime factors?

Question 26 :
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 28 :
The decimal expansion of the rational number $\dfrac{33}{2^{2}\cdot 5}$ will terminate after ______.

Question 30 :
Choose the correct answer from the given four options in the question: The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is__________.

Question 31 :
State true or false: The square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

Question 32 :
What are the LCM and HCF of 17, 23 and 29?

Question 33 :
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is _____ .

Question 34 :
The prime factorisation of a ___________ is unique, except for the order of its factors.

Question 35 :
Choose the correct answer from the given four options in the question: If two positive integers p and q can be expressed as $p = ab^2$ and $ q = a^3$ b; a, b being prime numbers, then LCM (p, q) is _____ .

Question 37 :
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 39 :
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 40 :
The square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m. Is it true?

Question 41 :
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 42 :
Without actually performing the long division, state whether $\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 43 :
Use Euclid's division algorithm to find the HCF of : 196 and 38220

Question 44 :
Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion.

Question 45 :
The product or quotient of a non-zero rational number and an irrational number is ___________.

Question 46 :
Using Euclid’s division algorithm, find if this pair of number is co-prime: 231, 396 .

Question 47 :
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 50 :
(7 × 11 × 13 + 13) and (7 × 6 × 5 × 4 × 3 × 2 × 1 + 5) are composite numbers. TRUE or FALSE ?