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Day 26: NDA Maths

5 questions (11 parts). Try each one first, then open its answer.

  1. Question 1

    Vectors. This type asked 3 times: NDA 2 2019, NDA 2 2023, NDA 2 2026. This one: NDA 2 2026

    67
    The scalar projection of a⃗=λi^+j^−2k^\vec{a} = \lambda\hat{i} + \hat{j} - 2\hat{k} on b⃗=2i^−j^−λk^\vec{b} = 2\hat{i} - \hat{j} - \lambda\hat{k} is 7/37/3. What is the value of λ\lambda?

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  2. Question 2

    Vectors. This type asked 3 times: NDA 2 2021, NDA 1 2025, NDA 2 2026. This one: NDA 2 2026

    70
    Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be unit vectors such that a⃗⋅b⃗=a⃗⋅c⃗=0\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0. If the angle between b⃗\vec{b} and c⃗\vec{c} is π/6\pi/6, then what is a⃗\vec{a} equal to?

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  3. Question 3 (case study, 2 parts)

    3D Geometry. This type asked 3 times: NDA 2 2019, NDA 2 2023, NDA 1 2026. This one: NDA 1 2026

    For the next two (02) items that follow: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0.
    55
    What is the equation of the line L?

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    56
    What are the direction ratios of a line M parallel to the plane P?

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  4. Question 4 (case study, 5 parts)

    Binomial Theorem. This type asked 3 times: NDA 2 2024, NDA 1 2025, NDA 1 2026. This one: NDA 1 2026

    For the next five (05) items that follow: Let u be a positive integer and f be a real number lying between 0 and 1. Further, (2+1)10=u+f(\sqrt{2}+1)^{10}=u+f and (2−1)10=v(\sqrt{2}-1)^{10}=v.
    46
    Consider the following statements: I. (u+v+f)(u+v+f) is an integer. II. (f+v)(f+v) is an integer. Which of the statements given above is/are correct?

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    47
    What is the multiplicative inverse of (2+1)20(\sqrt{2}+1)^{20}?

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    48
    What is the value of (v+f)(v+f)?

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    49
    What is the value of u?

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    50
    What is the value of uv?

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  5. Question 5 (case study, 2 parts)

    Circles. This type asked 3 times: NDA 2 2017, NDA 2 2021, NDA 1 2026. This one: NDA 1 2026

    For the next two (02) items that follow: Consider the points A(0,2), B(2,3), C(4,5) and D(0,k).
    59
    If the points lie on a circle, then what is/are the possible value(s) of k?

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    60
    If a circle is drawn through A, B and D, then what is the diameter of the circle?

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