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Geometry PrevQ - Set 0001

  • The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

    (1) remain the same

    (2) decrease by 13.64%

    (3) decrease by 15%

    (4) decrease by 18.75%

    (5) decrease by 30%            (CAT 2006)

  • An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?

    (1) 75

    (2) 90

    (3) 120

    (4) 135

    (5) 150           (CAT 2006)   

  • A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm.) will be:

    (1) 32π

    (2) 50π

    (3) 40.5π

    (4) 81π

    (5) undeterminable            (CAT 2006)

  • A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

     

    Q1) The proportion of the sheet area that remains after punching is:

    (1) (π + 2)/8

    (2) (6 - π)/8

    (3) (4 - π)/4

    (4) (π - 2)/4

    (5) (14 - 3π)/6                                                    

    Q2) Find the area of the part of the circle (round punch) falling outside the square sheet.

    (1) π /4

    (2) (π -1) /2

    (3) (π -1) /4

    (4) (π -2) /2

    (5) (π -2) /4                                                         (CAT 2006)

  • Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

    (1) Between 0 and 90

    (2) Between 0 and 30

    (3) Between 0 and 60

    (4) Between 0 and 75

    (5) Between 0 and 45         (CAT 2007)

  • Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?

    (1) 5
    (2) 21
    (3) 10
    (4) 15
    (5) 14            (CAT 2008)

  • A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jog along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

    (1) 3.88%

    (2) 4.22%

    (3) 4.44%

    (4) 4.72%        (CAT 2005)

  • What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?

    (1) 1 or 7

    (2) 2 or 14

    (3) 3 or 21

    (4) 4 or 28          (CAT 2005)

  • Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

    (1) 780

    (2) 800

    (3) 820

    (4) 741                            (CAT 2005)

  • Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is

    (1) 3

    (2) 1 + π

    (3) 4π/3

    (4) 5                     (CAT 2005)