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Day 194: NDA Maths

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

  1. Question 1

    Vectors. Asked once: NDA 1 2018 (same type asked 3 times)

    68
    What is the moment about i^+2j^−k^\hat{i}+2\hat{j}-\hat{k} of force 3i^+k^3\hat{i}+\hat{k} through 2i^−j^+3k^2\hat{i}-\hat{j}+3\hat{k}?

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  2. Question 2

    Vectors. Asked once: NDA 2 2017 (same type asked 3 times)

    45
    Let α⃗=i^+2j^−k^\vec{\alpha} = \hat{i}+2\hat{j}-\hat{k}, β⃗=2i^−j^+3k^\vec{\beta} = 2\hat{i}-\hat{j}+3\hat{k} and γ⃗=2i^+j^+6k^\vec{\gamma} = 2\hat{i}+\hat{j}+6\hat{k} be three vectors. If α⃗\vec{\alpha} and β⃗\vec{\beta} are both perpendicular to the vector δ⃗\vec{\delta} and δ⃗⋅γ⃗=10\vec{\delta}\cdot\vec{\gamma} = 10, then what is the magnitude of δ⃗\vec{\delta}?

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  3. Question 3

    3D Geometry. Asked once: NDA 1 2018 (same type asked 3 times)

    61
    Vertices P=(1,-1,1), Q=(3,-2,2), R=(0,2,6). If angle RQP = theta, then angle PRQ equals?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2019 (same type asked 3 times)

    10
    If ∣x−3i1y1i02i−i∣=6+11i\begin{vmatrix} x & -3i & 1 \\ y & 1 & i \\ 0 & 2i & -i \end{vmatrix} = 6 + 11i, then what are the values of x and y respectively?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 2 2018 (same type asked 3 times)

    19
    If a+b+c=0a + b + c = 0, then one of the solutions of ∣a−xcbcb−xabac−x∣=0\begin{vmatrix} a-x & c & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix} = 0 is

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