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CDS - Elementary Mathematics Test 1189
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CDS - Elementary Mathematics Test 1189
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  • Question 1/5
    1 / -0.33
    Two trains running at 45 kmph and 54 kmph cross each other in 12 seconds when they run in opposite direction. When they run in same direction a person in the faster train observes that he crossed the other train in 32 seconds .Find the lengths of the slower trains.
    Solutions

    Let be the lengths of the slow and faster trains respectively.

    When trains are travelling in the opposite directions ,their relative speed

    Distance covered= Sum of length of 2 trains

    Then according to the given condition we have

    When trains are travelling in the same direction, since we are given the time noted by a person in the faster train as 32 seconds the distance covered is equal to the length of the slower train.

    So, distance covered = p

    Relative speed

    p=(2.5)(32)=80 m

    q= 250 m

    The length of the slower train=80m.

  • Question 2/5
    1 / -0.33
    A man rows a distance of 4 km in 1 hour in still water and in 45 minutes with the current. Find the time taken by him to row 10 km with the current and return to the starting point.
    Solutions

    Speed in still water

    Speed with the stream

    Speed of water current=

    Speed against the stream=

    Hence time taken to travel 10 km and back

    = 5 hr 37.5 min.

  • Question 3/5
    1 / -0.33
    In the figure two circles intersect at two points M and N. Through M two line segments AMD and PMQ are drawn to intersect the circles at A , D and P , Q respectively. If  then what is the value of ?
    Solutions

    We know inscribed angle by the same arc are equal.

    ⇒  are made by the same arc AP.

    Hence,

    Also,

    We know inscribed angle by the same arc are equal.

    ⇒  are made by the same arc DQ.

    Hence,

  • Question 4/5
    1 / -0.33
    In the given figure , AB is the diameter of circle with centre at O. OS is perpendicular to AC and BC= 10 cm. Then, OS equal to

    Solutions

    As, O is mid-point of diameter AB and (angle in semi-circle)

    So, OS is parallel to CB and

    Hence,

    ⇒

    ⇒

  • Question 5/5
    1 / -0.33
    Three equal circle of unit radius touch each other .Then , the area of the circle circumscribing the three circle is :
    Solutions

     Here AB=BC=CA= 2 units

    Radius of each circle be 1 units

    OA=

    OP=OA +AP=

    Area of circumscribing circle=

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