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Clock and Calendar Test 1
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Clock and Calendar Test 1
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  • Question 1/10
    1 / -0

    At what time between 5.30 and 6 will the hands of a clock be at right angles?

    Solutions

    At 5 o’clock, the hands are 25 min. spaces apart.
    To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces
    55 min. spaces are gained in 60 min.
    40 min. spaces are gained in 

  • Question 2/10
    1 / -0

    At what approximate time between 4 and 5 am will the hands of a clock be at right angle?

    Solutions

    Here H × 30 = 4 × 30 = 120°.
    (Since initially the hour hand is at 4.∴ H = 4).
    Required angle A = 90° and since, H × 30 > A° so, there will be two timings.
    Required time T = ²⁄₁₁ (H × 30 ± A) minutes past H.
    ∴ One timing = ²⁄₁₁ (4 × 30 + 90) minutes past 4.
    = 38 ²⁄₁₁ minutes past 4.
    Or 4 : 38 approx.

  • Question 3/10
    1 / -0

    At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?

    Solutions

    When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
    At 7 o’clock, they are 25 min. spaces apart.
    ∴ Minute hand will have to gain only 5 in. spaces.
    55 min. spaces are gained in 60 min.
    5 min. spaecs are gained in 

  • Question 4/10
    1 / -0

    If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?

    Solutions

    In order to strike 12, there are 11 intervals of equal time

    Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec.

  • Question 5/10
    1 / -0

    Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.

    Solutions

    Angle traced by the hour hand in 12 hours = 360°
    Angle traced by it in 3 hrs 25 min. i.e.  
    Angle traced by it in 25 min. 
    Required angle 

  • Question 6/10
    1 / -0

    At what angle the hands of a clock are inclined at 15 minutes past 5 ?

    Solutions

    At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.
    Angle through which hour hand shifts in 15 minutes is
    ∴Required angle = 

  • Question 7/10
    1 / -0

    What is the angle between the 2 hands of the clock at 8:24 pm?

    Solutions

    Required angle = 240 – 24 × (11/2) = 240 –132 = 108°.

  • Question 8/10
    1 / -0

    What will be the acute angle between hands of a clock at 2 : 30?

    Solutions

    At 2’O Clock, Minute Hand will be 10 × 6 = 60° behind the Hour Hand.
    In 30 minutes, Minute Hand will gain 5 ½° × 30 = 150 + 15 = 165°
    ∴Angle between Hour Hand and Minute Hand = 165 – 60 = 105°

  • Question 9/10
    1 / -0

    If the two hands in a clock are 3 minutes divisions apart, then the angle between them is

    Solutions

    In a clock, each minute makes 6°
    ∴ 3 minutes will make 6 × 3 = 18°

  • Question 10/10
    1 / -0

    In 16 minutes, the minute hand gains over the hour hand by

    Solutions

    In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand.
    ∴ In 16 minutes, the minute hand gains over the hour hand by 

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