If two positive integers p and q can expressed as p = ab^ 2 \ and\ q = a^3b where a and b being prime numbers, then LCM (p, q) is
If two positive integers a and b are written as a = x^3y ^2 \ and \ b = cy^3 ; x, y are prime numbers then HCF (a, b) is
State whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false?
“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false?
State whether the square of any positive integer can be of the form 3m + 2, where m is a natural number.
A positive integer is of the form 3q + 1, q being a natural number. In which of the following can you write its square other than 3m + 1?
Find if 987/10500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.
A rational number in its decimal expansion is 327.7081. What can be concluded about the prime factors of q, when this number is expressed in the form p/q? Give reasons.
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75, what is HCF of (3000, 525)? Justify your answer.
If x and y are both odd positive integers, then x² + y²
is even but not divisible by 4. State whether true or false.
State wether the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
State whether the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.
State whether the cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.
State whether the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 1562 8 leaving remainders, 1, 2, and 3 respectively.
On a morning walk, three persons, step off together and their steps measure 40cm, 42 cm and 45cm respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?
One and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer. State whether true or false.
The cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r. State whether the statment is true or false. Justify.
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