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Day 322: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2022

    82
    If f(α)=sec⁡2α−1f(\alpha) = \sqrt{\sec^2\alpha - 1}, then what is f(α)+f(β)1−f(α)f(β)\frac{f(\alpha)+f(\beta)}{1-f(\alpha)f(\beta)} equal to?

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  2. Question 2

    Vectors. Asked once: NDA 2 2023

    94
    The vectors 60i^+3j^60\hat{i}+3\hat{j}, 40i^−8j^40\hat{i}-8\hat{j} and βi^−52j^\beta\hat{i}-52\hat{j} are collinear if:

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  3. Question 3

    3D Geometry. Asked once: NDA 1 2018

    59
    What is the equation of the plane through (-2,6,-6), (-3,10,-9) and (-5,0,-6)?

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  4. Question 4

    Application of Derivatives. Asked once: NDA 2 2021

    36
    For what value of θ\theta, where 0<θ<π20<\theta<\frac{\pi}{2}, does sin⁡θ+sin⁡θcos⁡θ\sin\theta+\sin\theta\cos\theta attain maximum value?

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  5. Question 5

    Differentiation. Asked once: NDA 2 2021

    71
    If y=(1+x)(1+x2)(1+x4)(1+x8)(1+x16)y=(1+x)(1+x^{2})(1+x^{4})(1+x^{8})(1+x^{16}), then what is dydx\frac{dy}{dx} at x=0x=0 equal to?

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