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Day 245: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Vectors. Asked once: NDA 2 2026

    68
    How much angle does r⃗=(cos⁡θ)i^+(sin⁡θ)j^+k^\vec{r} = (\cos\theta)\hat{i} + (\sin\theta)\hat{j} + \hat{k} make with the positive direction of zz-axis?

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  2. Question 2 (case study, 2 parts)

    3D Geometry. Asked once: NDA 2 2025

    For the following two (02) items: Suppose SS is the sphere with the smallest radius that passes through the points A(1,0,0)A(1,0,0), B(0,1,0)B(0,1,0) and C(0,0,1)C(0,0,1).
    53
    What is the radius of SS?

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    54
    On which one of the following planes does the centre of SS lie?

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  3. Question 3

    Application of Derivatives. Asked once: NDA 2 2026

    95
    ABCABC is a triangle right angled at BB. If AC=8AC = 8 units, then what is the area of the triangle of maximum area?

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  4. Question 4

    Applications of Integration. Asked once: NDA 2 2021

    99
    What is the area bounded by y=[x]y=[x], where [⋅][\cdot] is the greatest integer function, the xx-axis and the lines x=−1.5x=-1.5 and x=−1.8x=-1.8?

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  5. Question 5

    Binary Numbers. Asked once: NDA 2 2025

    6
    How many terms of the series 1+3+5+7+…1+3+5+7+\ldots amount to a sum equal to 1234567898765432112345678987654321?

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