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Prelims 1997 – 1996 · page 10 of 11

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  1. The number of students in two sections, A and B, having different heights is shown in the following table:

    Height (in metres)Number of students in Section ANumber of students in Section B
    1.5532
    1.6073
    1.621214
    1.651514
    1.6889
    1.7165
    1.7534

    The ratio of the number of students of a particular height in Section A to that in Section B is the maximum for the height of

  2. The following table shows the per cent change in the number of sales (in rupees) at different retail stores in a given neighbourhood market in the period 1993 to 1995:

    Retail Store — Percent Change 1993 to 1994 — 1994 to 1995

    Anshu: +10, -10 Borna: -20, +9

    Calpo: +5, +12 Dilip: -7, -15

    Elegant: +17, -8 If the sales at Anshu store amounted to Rs. 8 lakhs in 1993, then the number of sales (in lakhs of rupees) at that store in 1995 was

  3. If the number representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be

  4. The length, breadth and height of a room are l, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls is

  5. Seven persons P, Q, R, S, T, U and V participate in and finish all the events of a series of swimming races. There are no ties at the finish of any of the events. V always finishes somewhere ahead of P. P always finishes somewhere ahead of Q. Either R finishes first and T finishes last or S finishes first and U or Q finishes last. If in a particular race V finished fifth, then which one of the following would be true?

  6. Consider the following:

    I.Saxena, David, Jain and Kumar were District Collectors at places P, Q, R and S respectively in 1970.
    II.In 1972 they were transferred. Saxena and Jain interchanged places. Kumar and David also interchanged places.
    III.One year later in 1973 they were again transferred such that David and Jain interchanged places and Saxena and Kumar were also interchanged.

    What should be the next round of transfers so that all the four persons could have been posted at all the four places?

  7. In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?

  8. Examine the following statements regarding a set of balls:

    I.All balls are black.
    II.All balls are white.
    III.Only some balls are black.
    IV.No balls are black.

    Assuming that the balls can only be black or white, which two statements given above can both be true, but cannot both be false?

    Choose the correct answer from the codes given below:

  9. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

  10. The number of times in a day the Hour hand and the Minute hand of a clock at right angles is

  11. Examine the following statements:

    I.George attends Music classes on Monday.
    II.He attends Mathematics classes on Wednesday.
    III.His Literature classes are not on Friday.
    IV.He attends History classes on the day following the day of his Mathematics classes.
    V.On Tuesday, he attends his Sports classes.

    If he attends just one subject in a day and his Sunday is free, then he is also free on

  12. Consider the following figures:

    (i) a rectangle 4 cm × 9 cm

    (ii) a square of side 6 cm

    (iii) a right-angled triangle with base 8 cm and height 9 cm

    Which one of the following conclusions can be drawn from these figures?

  13. In an accurate clock, over a period of 2 hours 20 minutes, the minute hand will move over

  14. Two important characteristics of a hypothesis are that it should be testable and that it should be stated in a manner that it can be refuted.

    Which one of the following hypotheses fulfils these characteristics?

  15. If the price of a television set is increased by 25%, then by what percentage should the new price be reduced to bring the price back to the original level?

  16. If A = x² − y², B = 20 and x + y = 10, then

  17. Six roads lead to a country. They may be indicated by letters X, Y, Z and digits 1, 2,

    3.When there is storm, Y is blocked. When there are floods X, 1 and 2 will be affected. When road 1 is blocked, Z also is blocked. At a time when there are floods and a storm also blows, which road(s) can be used?
  18. When the frequency distribution is normal

  19. The next pair of letters in the series AZ, CX, FU, ...... is

  20. Mouse is to cat as fly is to

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