UPSC 2006 › CSAT

A watch showed a time of fourteen minutes past nine (9 hrs 14 minutes). The positions of the hour-hand and the minute-hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following?

Each of 8 identical balls is to be placed in the squares shown in the figure given above in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls. In how many maximum different ways can this be done?

In a tournament each of the participants was to play one match against each of the other participants. 3 players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75 ?

P, Q, R, S and T reside in a 5-storeyed (Ground + 4) building, and each of them resides on a separate floor. Further,

1. T does not reside on the topmost floor.
2. Q does not reside on the ground floor.
3. S resides on one storey above that of P and one storey below that of R. To know as to which of the 5 persons resides on the ground floor which of the above statements are sufficient / insufficient?

A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed?

3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

Refer to the three figures I, II and III in which numbers are arranged in squares. What is the value of X in figure III?

Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV. Consider the following statements:

1. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6.
2. Figures II and III are sufficient to know as to which face is opposite to the face numbered 4.
3. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 4.

Which of the statements given above are correct? The original figure is not available for this question.

In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

Each of the persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E possess 7 items in all. How many items do A and B possess in all?

There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line, and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. Consider the following statements:

1. The minimum number of triangles that can be formed by joining these points is zero.
2. The maximum number of triangles that can be formed by joining these points is twenty.

Which of the statements given above is/are correct?

A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea. Consider the following statements:

1. The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.
2. The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both coffee and tea.

Which of the statements given above is/are correct?

How many numbers are there in all 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?