What is the remainder when 2P - 1 is divided by p, where p > 5 is a prime number?
3
By applying the properties of powers and remainders, the remainder is 3. Hence, the correct answer is (c) 3.
Two towers \(A\) and \(B\) of height 23 m and 11 m respectively, stand 9 m apart. A straight rod is joined to the two tops of the towers. A monkey sitting on the top of \(A\), climbs the rod to reach the top of \(B\). If the monkey takes 5 minutes to reach the other end, what is the average speed of the monkey?
If sin a + cos a = √2, where 0 < a < π/2, then what is sin³ a cos³ a equal to?
Had I walked 0.5 km/hr faster, I would have taken 8 minutes less to walk 2 km. What is my original speed?
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
A car travels from a place X to place Y at an average speed of v km/hr from y to X at an average speed of 2v km/hr, again from X to y at an average speed of 3v km/hr and again from y to x at an average speed of 4v km/hr. Then the average speed of the car for the entire journey