Quantitative Aptitude Quiz on Trigonometry for MBA Entrance Exams: 14th Dec, 2017 for CAT & MBA Exams

Question 1

A person is standing at a distance of 1800 meters facing a giant clock at the top of a tower. At 5.00 p.m., he can see the tip of the minute hand of the clock at 30 degree elevation from his eye-level. Immediately, the person starts walking towards the tower. At 5.10 pm., the person noticed that the tip of the minute hand made an angle of 60 degrees with respect to his eye-level. Using three-dimensional vision, find the speed at which the person is walking. The length of the minutes hand is $Description: E:\CAT\XAT\XAT_2015_Question_Paper_and_Ans_Key_files\image207.png$ meters $Description: E:\CAT\XAT\XAT_2015_Question_Paper_and_Ans_Key_files\image208.png$

Question 2

There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and Bis

Question 3

A police inspector spots a thief standing 7 km away from him on a straight road aligned in East-West direction. The inspector is standing on the eastern side while the thief is on the western side of the road. On spotting the inspector the thief takes his bicycle and tries to cut across the adjoining field by riding away with a uniform speed of 9√2 km/hour in a direction making an angle of 45 ° with the road towards North-East. The inspector starts with his scooter at the same instance to move with a uniform velocity15 km/hour and catches the thief.

Time taken by the inspector to catch the thief is:

Question 4

A police inspector spots a thief standing 7 km away from him on a straight road aligned in East-West direction. The inspector is standing on the eastern side while the thief is on the western side of the road. On spotting the inspector the thief takes his bicycle and tries to cut across the adjoining field by riding away with a uniform speed of 9√2 km/hour in a direction making an angle of 45 ° with the road towards North-East. The inspector starts with his scooter at the same instance to move with a uniform velocity15 km/hour and catches the thief.

The distance the inspector has to travel is: