Prelims

In the Cartesian plane four points P, Q, R, S have co-ordinates (1, 1), (4, 2), (4, 4) and (1, 4). The area of the quadrilateral PQRS is

A table has three drawers. It is known that one of the drawers contains two silver coins, another contains two gold coins and the third one contains a silver coin and a gold coin. One of the drawers is opened at random and a coin is drawn. It is found to be a silver coin. What is the probability that the other coin in the drawer is a gold coin ?

Consider the figure given below : PQRS is a square of side 1 unit and Q, S are the centres of the two circles. The area of the shaded portion is

A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 metres ahead of the policeman, then the time required for the policeman to catch the thief will be

A student has 60% chance of passing in English and 54% chance of passing in both English and Mathematics. What is the percentage probability that he will fail in Mathematics ?

A rectangular sump of dimensions 6 m x 5 m x 4 m is to be built by using bricks to make the outer dimension 6.2 m x 5.2 x 4.2 m. Approximately how many bricks of size 20 cm x 10 cm x 5 cm are required to build the sump for storing water ?

The value of (a – m) (b – m) … (y – m) (z – m) is

Seven men, A, B, C, D, E, F and G are standing in a queue in that order. Each one is wearing a cap of a different colour like violet, indigo, blue, green, yellow, orange and red. D is able to see in front of him green and blue but not violet. E can see violet and yellow, but not red. G can see caps of all colours other than orange. If E is wearing an indigo coloured cap, then the colour of the cap worn by F is

In the given diagram, circle A represents teachers who can teach Physics, circle B represents teachers who can teach Chemistry and circle C represents those who can teach Mathematics. Among the regions marked p, q, r …….. the one which represents teachers who can teach Physics and Mathematics but not Chemistry, is

A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed in kilometres/hour during the entire round-trip ?