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Day 114: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2022 (same type asked 3 times)

    79
    What is the maximum value of 3(sin⁡x−cos⁡x)+4(cos⁡3x−sin⁡3x)3(\sin x - \cos x) + 4(\cos^3 x - \sin^3 x)?

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  2. Question 2

    Trigonometric Identities. Asked once: NDA 2 2022 (same type asked 3 times)

    54
    What is the value of sin⁡ ⁣(2nπ+5π6)sin⁡ ⁣(2nπ−5π6)\sin\!\left(2n\pi+\frac{5\pi}{6}\right)\sin\!\left(2n\pi-\frac{5\pi}{6}\right), where n∈Zn \in Z?

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  3. Question 3

    Vectors. Asked once: NDA 2 2025 (same type asked 3 times)

    66
    Let p⃗=a⃗−b⃗\vec{p}=\vec{a}-\vec{b}, q⃗=a⃗+b⃗\vec{q}=\vec{a}+\vec{b}. If ∣a⃗∣=∣b⃗∣=2|\vec{a}|=|\vec{b}|=2 and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2, then what is the value of ∣p⃗×q⃗∣|\vec{p}\times\vec{q}|?

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  4. Question 4

    Vectors. Asked once: NDA 1 2025 (same type asked 3 times)

    70
    Let a⃗,b⃗,(a⃗×b⃗)\vec{a}, \vec{b}, (\vec{a}\times\vec{b}) be unit vectors. What is (a⃗⋅b⃗)(\vec{a}\cdot\vec{b}) equal to?

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  5. Question 5

    3D Geometry. Asked once: NDA 2 2023 (same type asked 3 times)

    97
    Which one of the planes is parallel to the line x−23=y−34=z−45\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}?

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