**1**. **REAL NUMBERS**

**MAX MARKS: – 15 **

**TIME- 45 MIN. **

**1. Check whether 6**^{n}** can end with the digit 0 for any natural number ***n***.** **[2]**

**2. Prove that √5 is irrational.** ** [3] **

**3. Prove that 3+√5 is irrational.** ** [2]**

**4. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.** ** [4]**

**(i) 510 and 92 (ii) 336 and 54**

**5. 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?** **[2]**

**6.Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.** ** [2]**