Q1. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
Q2. If $n$ is any natural number, then $12^n$ cannot end with the digit:
Q3. Two numbers are in the ratio 3:4 and their LCM is 120. The sum of the numbers is:
Q4. Assertion (A): $\sqrt{x}$ is an irrational number, where $x$ is a prime number. Reason (R): Square root of any prime number is an irrational number.
Q5. Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Solve on white paper.
Q6. Can two numbers have 18 as their HCF and 380 as their LCM? Justify your answer.
Q7. Prove that $2 - 3\sqrt{5}$ is an irrational number, given that $\sqrt{5}$ is irrational.
Q8. Prove that $\sqrt{2} + \sqrt{3}$ is an irrational number.
Q9. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together?
Q10. Prove that $\sqrt{3}$ is an irrational number. Hence, show that $\frac{1}{2 - \sqrt{3}}$ is an irrational number.
Q11. Case Study:
A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft by 8 ft.
(i) What should be the size (side length) of the tile in feet?
(ii) How many such tiles are required?
(iii) If the size of the bathroom was 10 ft by 15 ft, what would be the size of the largest square tile?