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Day 19: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    3D Geometry. This type asked 4 times: NDA 1 2017, NDA 2 2019, NDA 1 2021, NDA 1 2023. This one: NDA 1 2023

    Consider the following for the next two (02) items that follow: The position vectors of two points AA and BB are i^−j^\hat{i}-\hat{j} and j^+k^\hat{j}+\hat{k} respectively.
    69
    Consider the following points: 1. (−1,−3,1)(-1,-3,1) 2. (−1,3,2)(-1,3,2) 3. (−2,5,3)(-2,5,3) Which of the above points lie on the line joining AA and BB?

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    70
    What is the magnitude of AB→\overrightarrow{AB}?

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  2. Question 2

    Complex Numbers. This type asked 4 times: NDA 1 2017, NDA 2 2018, NDA 2 2019, NDA 1 2023. This one: NDA 1 2023

    5
    If α\alpha and β\beta are the distinct roots of equation x2−x+1=0x^{2}-x+1=0, then what is the value of ∣α100+β100α100−β100∣\left|\frac{\alpha^{100}+\beta^{100}}{\alpha^{100}-\beta^{100}}\right|?

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  3. Question 3

    Complex Numbers. This type asked 4 times: NDA 1 2018, NDA 1 2020, NDA 1 2022, NDA 1 2023. This one: NDA 1 2023

    12
    If z=1+i31−i3z=\dfrac{1+i\sqrt{3}}{1-i\sqrt{3}} where i=−1i=\sqrt{-1}, then what is the argument of zz?

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  4. Question 4

    Statistics. This type asked 4 times: NDA 1 2017, NDA 1 2018, NDA 1 2021, NDA 1 2023. This one: NDA 1 2023

    107
    The central angles pp, qq, rr and ss (in degrees) of four sectors in a Pie Chart satisfy the relation 9p=3q=2r=6s9p=3q=2r=6s. What is the value of 4p−q4p-q?

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  5. Question 5

    Trigonometric Identities. This type asked 4 times: NDA 2 2017, NDA 1 2019, NDA 1 2022, NDA 2 2022. This one: NDA 2 2022

    53
    What is the value of tan⁡2165°+cot⁡2165°\tan^2 165° + \cot^2 165°?

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