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Day 184: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    3D Geometry. Asked once: NDA 2 2019 (same type asked 4 times)

    60
    If the points (x,y,−3)(x, y, -3), (2,0,−1)(2, 0, -1) and (4,2,3)(4, 2, 3) lie on a straight line, then what are the values of xx and yy respectively ?

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  2. Question 2

    Complex Numbers. Asked once: NDA 2 2019 (same type asked 4 times)

    17
    What is the value of [i+32]2019+[i−32]2019\left[\frac{i+\sqrt{3}}{2}\right]^{2019} + \left[\frac{i-\sqrt{3}}{2}\right]^{2019} ?

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2018 (same type asked 4 times)

    4
    What is the principal argument of (−1−i)(-1-i), where i=−1i = \sqrt{-1}?

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  4. Question 4

    Trigonometric Identities. Asked once: NDA 2 2017 (same type asked 4 times)

    32
    The value of tan⁡9°−tan⁡27°−tan⁡63°+tan⁡81°\tan 9° - \tan 27° - \tan 63° + \tan 81° is equal to

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  5. Question 5

    Functions. Asked once: NDA 2 2017 (same type asked 4 times)

    95
    If f(x)=4x+x41+4x3f(x) = \dfrac{4x+x^4}{1+4x^3} and g(x)=ln⁡ ⁣(1+x1−x)g(x) = \ln\!\left(\dfrac{1+x}{1-x}\right), then what is the value of f∘g ⁣(e−1e+1)f \circ g\!\left(\dfrac{e-1}{e+1}\right) equal to?

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