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CDS - Elementary Mathematics Test-75
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CDS - Elementary Mathematics Test-75
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  • Question 1/10
    1 / -0

    Solutions

     

  • Question 2/10
    1 / -0

    Solutions

     

  • Question 3/10
    1 / -0

    The value of (1 + tan2θ) (1 – Sin2θ) is

    Solutions

     

  • Question 4/10
    1 / -0

    Consider the following statements: 

    1) There is only value of x in the first quadrant that satisfies sinx + cosx = 2. 

    2) There is only one value of x in the first quadrant that satisfies sinx–cosx = 0 

    Which of the above is/are correct?

    Solutions

    In statement II, 

    When x=45, sin 45 – cos 45=1 /√2 - 1 /  √2 = 0

     

  • Question 5/10
    1 / -0

    Find the value of: 

    Solutions

     

  • Question 6/10
    1 / -0

    The length of the shadow of a person s cm tall when the angle of elevation of the sun is α is p cm. It is q cm when the angle of elevation of the sun is β. Which one of the following is correct when β = 3α ?

    Solutions

  • Question 7/10
    1 / -0

    If sec x = 13/12, Find the value of : cosec2x (1-tanx)(1+tanx) cos2x

    Solutions

    Sec x = 13/12 

    tan2x = sec2x-1 

    ⇒ =169/144 -1 

    ⇒ =25/144 

    ⇒ tan x = 5/12 

    ⇒ ∴ 

    cosec x = 13/5 

    And cos x = 12/13 

    ∴ cosec2x (1-tanx)(1+tanx) cos2

    ⇒ (169/25) (1-25/144) (144/169) 

    ⇒ (169/25) (119/144)(144/169) 

    ⇒ 119/25

     

  • Question 8/10
    1 / -0

    The angle of elevation of the tip of a tower from a point on the ground is 450 moving 21 m directly towards the base of the tower the angle of elevation changes to 600.what is the height of the tower to the nearest meter?

    Solutions

     

  • Question 9/10
    1 / -0

    Solutions

     

  • Question 10/10
    1 / -0

    If sin 7x = cos 11x, then the value of tan 9x + cot 9x is

    Solutions

    sin7x = cos 11x 

    As sin(90 - x) = cos x 

    Hence sin 7x = sin (90 - 11x) 

    ⇒ 7x = 90 - 11x 

    ⇒ 18x = 90 

    ⇒ x = 5 

    Now tan 9x + cot 9x 

    = tan 9 × 5 + cot 9 × 5 

    = tan 45 + cot 45 = 1 + 1 = 2

     

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