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Engineering
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 If  0 ≤ x < 2 π, then the number of real values of x, which satisfy the equation

cos x + cos 2x + cos 3x + cos 4x = 0, is :

  • Option 1)

    3

  • Option 2)

    5

  • Option 3)

    7

  • Option 4)

    9

 
As we learnt in in General Solution of Trigonometric Ratios - - wherein  is the given angle     Thus,                           Hence, there are a total number of 7 solutions.   Option 1) 3 This option is incorrect. Option 2) 5 This option is incorrect. Option 3) 7 This option is correct. Option 4) 9 This option is incorrect.
Engineering
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A man is walking towards a vertical pillar in a straight path, at a uniform speed.  At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 300.  After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 600. Then the time taken (in minutes) by him, from B to reach the pillar, is :

  • Option 1)

    6

  • Option 2)

    10

  • Option 3)

    20

  • Option 4)

    5

 
As we learnt in Height and Distances - The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios. -  Let PQ represent pillar. Say height = h In  ,   In      Now, the person is walking at a uniform speed, hence time taken will be proportional to distance travelled. Thus,  Hence, time required is 5...
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