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Day 318: NDA Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: NDA 2 2019

    65
    If 2tan⁡A=3tan⁡B=12\tan A = 3\tan B = 1, then what is tan⁡(A−B)\tan(A-B) equal to ?

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  2. Question 2 (case study, 2 parts)

    Trigonometric Identities. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: Let x=sin⁡2A+sin⁡A+1sin⁡Ax=\dfrac{\sin^{2}A+\sin A+1}{\sin A} where 0<A≤π20<A\leq\dfrac{\pi}{2}.
    37
    What is the minimum value of xx?

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    38
    At what value of AA does xx attain the minimum value?

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  3. Question 3

    Vectors. Asked once: NDA 2 2023

    93
    If θ\theta is the angle between a⃗\vec{a} and b⃗\vec{b} such that a⃗⋅b⃗≥0\vec{a}\cdot\vec{b}\geq0, then which one is correct?

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  4. Question 4

    3D Geometry. Asked once: NDA 1 2018

    58
    Let A=(1,8,4), B=(0,-11,4), C=(2,-3,1). What are the coordinates of D, foot of perpendicular from A to BC?

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  5. Question 5

    Application of Derivatives. Asked once: NDA 2 2021

    98
    If the function f(x)=x2−kxf(x)=x^{2}-kx is monotonically increasing in the interval (1,∞)(1,\infty), then which one of the following is correct?

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