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Day 284: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Trigonometric Equations. Asked once: NDA 1 2022

    29
    If tan⁡(45°+θ)=1+sin⁡2θ\tan(45°+\theta)=1+\sin2\theta, where −π4<θ<π4-\frac{\pi}{4}<\theta<\frac{\pi}{4}, then what is the value of cos⁡2θ\cos2\theta?

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  2. Question 2 (case study, 2 parts)

    Trigonometric Identities. Asked once: NDA 1 2025

    Let p=∣sin⁡α−sin⁡(α−90∘)∣p = |\sin\alpha - \sin(\alpha - 90^\circ)|.
    34
    What is the minimum value of pp?

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    35
    What is the maximum value of pp?

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  3. Question 3

    Vectors. Asked once: NDA 1 2025

    68
    The position vectors of three points A, B and C are a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c} respectively such that 3a⃗−4b⃗+c⃗=0⃗3\vec{a} - 4\vec{b} + \vec{c} = \vec{0}. What is AB : BC equal to?

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  4. Question 4

    3D Geometry. Asked once: NDA 1 2020

    64
    Into how many compartments do the coordinate planes divide the space?

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  5. Question 5 (case study, 2 parts)

    Application of Derivatives. Asked once: NDA 2 2023

    Given that 4x2+y2=94x^2+y^2=9.
    47
    What is the maximum value of yy?

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    48
    What is the maximum value of xyxy?

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