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Prelims 2007 – 2005 · page 4 of 11

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  1. A train completes a journey with a few stoppages in between at an average speed of 40 km per hour. If the train had not stopped anywhere, it would have completed the journey at an average speed of 60 km per hour. On an average, how many minutes per hour does the train stop during the journey?

  2. The average salary of 100 employees in an office is Rs. 16,000 per month. The management decided to raise salary of every employee by 5% but stopped a transport allowance of Rs. 800 per month which was paid earlier to every employee. What will be the new average monthly salary?

  3. 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?

  4. 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 ?

  5. 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?

  6. 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?

  7. 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?

  8. 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?

  9. There are 8 equidistant points A, B, C, D, E, F, G and H in the clockwise direction on the periphery of a circle. In a time-interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time-interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start will the two persons meet each other?

  10. 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?

  11. 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?

  12. 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?

  13. 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?

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

  15. 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?

  16. Directions (For the next FOUR items): Based on the information given below, answer the four items which follow it:

    Gopal, Harsh, Inder, Jai and Krishnan have Ahmedabad, Bhopal, Cuttack, Delhi and Ernakulam as their hometowns (not necessarily in that order). They are studying in Engineering, Medical, Commerce, Economics and History Colleges (not necessarily in that order). None of the five boys is studying in his hometown, but each of them studies in one of the cities given above. Further, it is given that:

    (i) Gopal's hometown is Ernakulam.

    (ii) Harsh is not studying in Ahmedabad or Bhopal.

    (iii) Economic college is in Bhopal.

    (iv) Inder's hometown is Cuttack.

    (v) Krishnan is studying in Delhi.

    (vi) Jai is studying in Ernakulam and the History College is in his hometown Ahmedabad.

    (vii) Engineering College is situated in Ernakulam.

    Which is Krishnan's hometown?

  17. Directions (For the next FOUR items): Based on the information given below, answer the four items which follow it:

    Gopal, Harsh, Inder, Jai and Krishnan have Ahmedabad, Bhopal, Cuttack, Delhi and Ernakulam as their hometowns (not necessarily in that order). They are studying in Engineering, Medical, Commerce, Economics and History Colleges (not necessarily in that order). None of the five boys is studying in his hometown, but each of them studies in one of the cities given above. Further, it is given that:

    (i) Gopal's hometown is Ernakulam.

    (ii) Harsh is not studying in Ahmedabad or Bhopal.

    (iii) Economic college is in Bhopal.

    (iv) Inder's hometown is Cuttack.

    (v) Krishnan is studying in Delhi.

    (vi) Jai is studying in Ernakulam and the History College is in his hometown Ahmedabad.

    (vii) Engineering College is situated in Ernakulam.

    Which College is situated in Inder's hometown?

  18. Directions (For the next FOUR items): Based on the information given below, answer the four items which follow it:

    Gopal, Harsh, Inder, Jai and Krishnan have Ahmedabad, Bhopal, Cuttack, Delhi and Ernakulam as their hometowns (not necessarily in that order). They are studying in Engineering, Medical, Commerce, Economics and History Colleges (not necessarily in that order). None of the five boys is studying in his hometown, but each of them studies in one of the cities given above. Further, it is given that:

    (i) Gopal's hometown is Ernakulam.

    (ii) Harsh is not studying in Ahmedabad or Bhopal.

    (iii) Economic college is in Bhopal.

    (iv) Inder's hometown is Cuttack.

    (v) Krishnan is studying in Delhi.

    (vi) Jai is studying in Ernakulam and the History College is in his hometown Ahmedabad.

    (vii) Engineering College is situated in Ernakulam.

    Who studies in Bhopal?

  19. Directions (For the next FOUR items): Based on the information given below, answer the four items which follow it:

    Gopal, Harsh, Inder, Jai and Krishnan have Ahmedabad, Bhopal, Cuttack, Delhi and Ernakulam as their hometowns (not necessarily in that order). They are studying in Engineering, Medical, Commerce, Economics and History Colleges (not necessarily in that order). None of the five boys is studying in his hometown, but each of them studies in one of the cities given above. Further, it is given that:

    (i) Gopal's hometown is Ernakulam.

    (ii) Harsh is not studying in Ahmedabad or Bhopal.

    (iii) Economic college is in Bhopal.

    (iv) Inder's hometown is Cuttack.

    (v) Krishnan is studying in Delhi.

    (vi) Jai is studying in Ernakulam and the History College is in his hometown Ahmedabad.

    (vii) Engineering College is situated in Ernakulam.

    If Inder studies in Ahmedabad, then which one of the following is the correct combination of Person-Hometown-Place of Study?

  20. Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain?

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