The number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor. If the first floor has `x` rooms, how many rooms does the ground floor has?

In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. "^8P_6-2(6!) b. "^8P_6 c. "^8P_5(6!) d. none of these

The perimeter of a floor of a room is 30m and its height is 3m. Find the area of four walls of the room.

Five persons entered the lift cabin on the ground floor of an 8-floor building. If each of them can leave the cabin independently at any floor beginning with the first; find the probability of 5 persons leaving at different floor.

An accurate pendulum clock is mounted on ground floor of a high building. How much time will it lose or gain in one day if its is transferred to top storey of a building which is h = 200m higher than the ground floor? Radius of earth is 6.4 xx 10^(6)

A home designer will carpet n rooms with the same dimensions in a house using a specific type of carpeting. The designer charges using the expressions nClw, where n is the number of rooms, C is a constant with units of dollars per square meter. L is the length of the each room in meters, and w is the width of each room in meter. If a customer asks the designer to use a less expansive type oof carpating, which of the following factors in the expressions would change?

Water drops fall from the roof a building 20 m high at regular time intervals. If the first drop strikes the floor when the sixth drop begins to fall, the heights of the second and fourth drops from the ground at that instant are (g = 10 ms^(-2))

The use of calculator is not permitted. The Boulevard Hotel has a peculiar way of numbering its rooms. The first room on each floor is numbered as the product of all floor number below it starting from floor number on ( the ground floor is not counted). For example , the first room on the fourth floor would be numbered as 1 xx 2 xx 3 = 6 . All successive room numbers would be numbered three more than the previous room number. Thus , on the fourth floor, rooms are numbered as 6,6+3 = 9,6 + 2 xx 3 = 12, 6+3 xx 3 = 15 etc. If it is known that there are six rooms on each floor, how many numbers on the fifteenth floor are prime numbers ?

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00. What should be the initial downward speed of the rocketeer so that he catches the student at the top of 100 the floor for safe landing ?

The floor of a room measures 12 feet by 9 feet. Find the length of the largest rod that can be placed on the floor of the room.

There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrically situated (that is each room is exactly opposite to one other room). Four guests have to be accommodated in four of the eight rooms (that is, one in each) such that no two guests are in adjacent rooms or in opposite rooms. in how many ways can the guests be accommodated?