UPSC 2007 › CSAT

(Each small circle represents a different station) Refer to the figure showing a network between station A and station B. What is the maximum number of different paths that exist between station A and station B?

In how many maximum different ways can 3 identical balls be placed in 12 squares (each ball is placed in the exact centre of a square) shown in the figure above such that they do not lie along the same straight line? The original figure is not available for this question.

In the figure shown above, what is the maximum number of different ways in which 8 identical balls can be placed in small triangles 1, 2, 3 and 4 such that each triangle contains at least one ball?

Amit has five friends: 3 girls and 2 boys. Amit’s wife also has five friends: 3 boys and 2 girls. In how many maximum different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s friends?

Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done?

All six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as a dictionary. What will be the position of the word SACHIN in that sequence?

Three dice (each having six faces with each face showing one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows the number 2?

Groups, each containing 3 boys, are to be formed out of 5 boys – A, B, C, D and E – such that no one group contains both C and D together. What is the maximum number of different groups?

Six faces of a cube are numbered from 1 to 6, each face carrying one different number. Further,

1. The face 2 is opposite to the face 6.
2. The face 1 is opposite to the face 5.
3. The face 3 is between the face 1 and face 5.
4. The face 4 is adjacent to the face 2.

Which one of the following is correct?

Each of the 3 persons is to be given some identical items such that the product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?

Six equidistant vertical lines are drawn on a board. Six equidistant horizontal lines are also drawn on the board cutting the six vertical lines and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?

A person has to completely put each of three liquids – 403 litres of petrol, 465 litres of diesel and 496 litres of mobile oil – in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?

If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears?

Amit starts from a point A, walks to another point B and then returns from B to A by his car, taking a total time of 6 hours 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways?