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Day 189: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 1 2020 (same type asked 3 times)

    25
    What is sin⁡3x+cos⁡3x+4sin⁡3x−3sin⁡x+3cos⁡x−4cos⁡3x\sin 3x + \cos 3x + 4\sin^3 x - 3\sin x + 3\cos x - 4\cos^3 x equal to?

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  2. Question 2

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

    46
    What is the value of csc⁡ ⁣(−73π3)\csc\!\left(-\frac{73\pi}{3}\right)?

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  3. Question 3

    Vectors. Asked once: NDA 2 2018 (same type asked 3 times)

    68
    What is (a⃗−b⃗)×(a⃗+b⃗)(\vec{a}-\vec{b})\times(\vec{a}+\vec{b}) equal to?

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  4. Question 4

    Vectors. Asked once: NDA 2 2021 (same type asked 3 times)

    66
    Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be unit vectors such that a⃗×b⃗\vec{a}\times\vec{b} is perpendicular to c⃗\vec{c}. If θ\theta is the angle between a⃗\vec{a} and b⃗\vec{b}, then which of the following is/are correct? 1. a⃗×b⃗=sin⁡θ c⃗\vec{a}\times\vec{b}=\sin\theta\,\vec{c} 2. a⃗⋅(b⃗×c⃗)=0\vec{a}\cdot(\vec{b}\times\vec{c})=0 Select the correct answer using the code given below.

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  5. Question 5

    3D Geometry. Asked once: NDA 2 2019 (same type asked 3 times)

    58
    If the line x−41=y−21=z−k2\dfrac{x-4}{1} = \dfrac{y-2}{1} = \dfrac{z-k}{2} lies on the plane 2x−4y+z=72x - 4y + z = 7, then what is the value of kk ?

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