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Day 257: NDA Maths

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

  1. Question 1

    3D Geometry. Asked once: NDA 2 2022

    62
    Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4) and D(8, 14, 12). Which of the following statements is/are correct? 1. The points are the vertices of a rectangle ABCD. 2. The mid-point of AC is the same as that of BD. Select the correct answer using the code given below:

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  2. Question 2 (case study, 2 parts)

    Application of Derivatives. Asked once: NDA 1 2025

    Let ABC be a triangle right-angled at B and AB + AC = 3 units.
    73
    What is ∠A\angle A equal to if the area of the triangle is maximum?

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    74
    What is the maximum area of the triangle?

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  3. Question 3

    Binary Numbers. Asked once: NDA 1 2025

    7
    If x=(1111)2, y=(1001)2x=(1111)_2,\ y=(1001)_2 and z=(110)2z=(110)_2, then what is x3−y3−z3−3xyzx^3-y^3-z^3-3xyz equal to?

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  4. Question 4

    Binomial Distribution. Asked once: NDA 2 2017

    115
    If a variable takes values 0,1,2,3,…,n0, 1, 2, 3, \ldots, n with frequencies 1,C(n,1),C(n,2),C(n,3),…,C(n,n)1, C(n,1), C(n,2), C(n,3), \ldots, C(n,n) respectively, then the arithmetic mean is

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  5. Question 5

    Binomial Theorem. Asked once: NDA 1 2024

    10
    If 26!=n⋅8k26!=n\cdot 8^k, where kk and nn are positive integers, then what is the maximum value of kk?

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