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Day 314: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Trigonometric Identities. Asked once: NDA 2 2023

    Let sin⁡x+sin⁡y=3(cos⁡y−cos⁡x)\sin x+\sin y=\sqrt{3}(\cos y-\cos x); x+y=π2x+y=\frac{\pi}{2}, 0<x,y<π20<x,y<\frac{\pi}{2}.
    77
    What is a value of sin⁡3x+sin⁡3y\sin3x+\sin3y?

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    78
    What is a value of cos⁡3x+cos⁡3y\cos^3x+\cos^3y?

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  2. Question 2

    Vectors. Asked once: NDA 2 2023

    95
    Consider vectors a⃗=(0,1,1)\vec{a}=(0,1,1) and b⃗=(1,0,1)\vec{b}=(1,0,1). (1) Number of unit vectors perpendicular to both is only one. (2) Angle between them is π/3\pi/3. Which is/are correct?

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  3. Question 3

    3D Geometry. Asked once: NDA 2 2018

    57
    Coordinates of the points O, P, Q and R are respectively (0,0,0)(0,0,0), (4,6,2m)(4,6,2m), (2,0,2n)(2,0,2n) and (2,4,6)(2,4,6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length 2\sqrt{2}. What are the values of m and n respectively?

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  4. Question 4

    Application of Derivatives. Asked once: NDA 1 2022

    77
    If the derivative of the function f(x)=mx+2nx+1f(x)=\frac{m}{x}+2nx+1 vanishes at x=2x=2, then what is the value of m+8nm+8n?

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  5. Question 5

    Complex Numbers. Asked once: NDA 1 2018

    8
    The number of non-zero integral solutions of the equation ∣1−2i∣x=5x|1-2i|^x = 5^x is

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