Q1. The HCF of the smallest prime number and the smallest composite number is:
Q2. If HCF(26, 169) = 13, then LCM(26, 169) is:
Q3. The product of a non-zero rational and an irrational number is:
Q4. Assertion (A): The number $6^n$, n being a natural number, ends with the digit 5. Reason (R): The number $9^n$ cannot end with digit 0 for any natural number n.
Q5. Explain why $7 \times 11 \times 13 + 13$ is a composite number.
Solve on white paper.
Q6. Find the LCM and HCF of 6, 72 and 120 using prime factorization method.
Q7. Check whether $6^n$ can end with the digit 0 for any natural number n.
Q8. Prove that $\sqrt{2}$ is an irrational number.
Q9. Find the largest number which divides 70 and 125, leaving remainders 5 and 8 respectively.
Q10. Prove that $\sqrt{5}$ is irrational. Hence, show that $3 + 2\sqrt{5}$ is also an irrational number.
Q11. Case Study:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
(i) In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number of participants that can accommodated in each room are?
(ii) What is the minimum number of rooms required during the event?
(iii) Find the LCM of 60, 84 and 108.