Chapter 1 – Real Numbers

In a seminar, the number of participants in English, German and Sanskrit are 45,75 and 135. Find the number of rooms required to house them, if in each room, the same number of participants are to be accommodated and they should be of the same language.

If p = HCF (100,190) and q = LCM (100, 190); then p2q2 is :

A number \(\frac{p}{q}\), when expressed in decimal form, terminates after 7 digits, then factors of q are of the form xm x yn; the value of x + y should be :

The condition to be satisfied by q, so that the rational number \(\frac{p}{q}\) has a non terminating decimal expansion is:

If – 2 ≤ x ≤ 2, which of the following is not true for x:

The largest positive integer which divides 434 and 539 leaving remainders 9 and 12 respectively is:

There is a circular path around a field. Reema takes 22 minutes to complete one round while her friend Saina takes 20 minutes to complete the same. If they both start at the same time and move in the same direction, after how many minutes will they meet again at the starting

If HCF (306, 657) = 9, then LCM of 306 and 657 is:

Euclid’s Lemma states that, for given positive integers a and b, there exist unique integers q and r, such that a = bq + r, where :

A number which can be expressed in the form \(\frac{p}{q}\) where q ≠ 0 is a rational number is:

In decimal expansion and representation, which of the following is not a rational numbers:

If a positive integer ‘a’ is divided by 2, what can be the remainder ?

For some positive integer q, every even integer is of the form:

If a non-zero rational number is multiplied to an irrational number, we always get:

HCF and LCM of two positive integers a and b satisfy a relationship, that:

If we write 0.9 as a rational number, we get:

Write an irrational number between 2 and 3.

Which of the following are irrational whose sum and product are both rationals :

Find the value of x from the following such that x2 is irrational but x4 is rational:

A rational number between 72 and 73 is:

The rational number that corresponds to 0.6+0.\(\bar{7}\)+0.4\(\bar{7}\) is :

The greatest number which divides 87 and 97, leaving 7 as remainder is :

The least number, which when divided by 10,14 and 18, leaves remainder 4, is :

The greatest number which divides 17, 28 and 34 leaving remainders 2, 3 and 4 respectively is:

72 litres of liquid A and 108 litres of liquid B are to be packed in containers of the same size. The minimum number of containers required are:

he HCF of two consecutive rational numbers x and x +1 is :

The HCF of a number which is neither prime nor composite and any other number x is:

Find q and r, if 12560 = 215 q + r.

Using Euclid’s Lemma, if d is the HCF of 1155 and 506, find ‘d’

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