Suppose p and q are the LCM and HCF respectively of two positive numbers. If p : q = 14 : 1 and pq = 1134, then what is the difference between the two numbers?
A man walks at an average speed of 3 km/hr from his residence and reaches office 40 minutes early. If he walks at an average speed of 2 km/hr, he reaches 40 minutes late. What is the distance between his residence and office?
What is the value of the following?
\( \frac{1}{5\sqrt{4} + 4\sqrt{5}} + \frac{1}{6\sqrt{5} + 5\sqrt{6}} + \frac{1}{7\sqrt{6} + 6\sqrt{7}} + \frac{1}{8\sqrt{7} + 7\sqrt{8}} + \frac{1}{9\sqrt{8} + 8\sqrt{9}} \)
If \( \left(x + \sqrt{1 + x^{2}}\right)\left(y + \sqrt{1 + y^{2}}\right) = 1 \), where x and y are real numbers, then what is the value of \( (x + y)^{2} \)?
