Class 10 Maths – Real Numbers Quiz

Which of the following is an irrational number?

Which of the following statements about numbers is correct?

An irrational number \(\sqrt{5}\) lies between which two consecutive integers?

Which of the following is a prime number?

How many prime numbers are there between 30 and 40?

Which statement about the number 1 is correct?

The prime factorisation of 108 is:

Which number has the prime factorisation \(2^3 \times 5 \times 11\)?

In the prime factorisation of 180, how many prime factors are there in total when each repeated prime is counted with its multiplicity?

If \(3^a \times 5^2 = 3^4 \times 5^b\), where \(a\) and \(b\) are positive integers, then the value of \(a + b\) is:

The HCF of 12 and 18 is:

The LCM of 8 and 12 is:

The HCF of 15, 25 and 45 is:

The HCF of the numbers 24 and 36 is 12. Their LCM is:

If HCF(14, 42) = 14, then LCM(14, 42) is equal to:

The HCF and LCM of two numbers are 4 and 84. If one of the numbers is 12, the other number is:

Two bells ring at intervals of 15 minutes and 20 minutes. If they ring together at 10:00 a.m., at what time will they ring together next?

A shopkeeper has 42 pens and 63 pencils. He wants to make identical packets, each containing the same number of pens and the same number of pencils, with nothing left over. What is the maximum number of packets he can make?

Which is the correct first step in proving that \(\sqrt{3}\) is irrational by the method of contradiction?

In the proof that \(\sqrt{5}\) is irrational, we assume \(\sqrt{5} = \frac{p}{q}\) with coprime integers \(p, q\) and \(q \neq 0\). Squaring gives \(p^2 = 5q^2\). Since \(5\) divides \(p^2\), which conclusion follows directly?