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Day 251: NDA Maths

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

  1. Question 1

    Vectors. Asked once: NDA 2 2026

    66
    Let a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} and d⃗\vec{d} be the vectors. Consider the following : I. (a⃗×b⃗)⋅(c⃗×d⃗)(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) II. (a⃗×b⃗)×(c⃗×d⃗)(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) III. (a⃗⋅b⃗)⋅(c⃗⋅d⃗)(\vec{a} \cdot \vec{b}) \cdot (\vec{c} \cdot \vec{d}) IV. (a⃗⋅b⃗)×(c⃗⋅d⃗)(\vec{a} \cdot \vec{b}) \times (\vec{c} \cdot \vec{d}) V. {(a⃗×b⃗)⋅c⃗}×d⃗\{(\vec{a} \times \vec{b}) \cdot \vec{c}\} \times \vec{d} where '⋅\cdot' represents dot product and '×\times' represents cross product of vectors. How many of the above are not well-defined?

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  2. Question 2

    3D Geometry. Asked once: NDA 2 2023

    96
    If LL is the line with direction ratios ⟨3,−2,6⟩\langle3,-2,6\rangle passing through (1,−1,1)(1,-1,1), what are points on LL at distance 2 from (1,−1,1)(1,-1,1)?

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  3. Question 3

    Application of Derivatives. Asked once: NDA 2 2025

    100
    Consider the following statements: Statement-I: The function f(x)=x3+128xf(x)=\dfrac{x^3+128}{x} has a minimum value 48 at x=4x=4. Statement-II: As xx increases through 4, f′(x)f'(x) changes sign from positive to negative. Which one of the following is correct?

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  4. Question 4

    Binary Numbers. Asked once: NDA 2 2025

    9
    What is the remainder when 5995^{99} is divided by 13?

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  5. Question 5

    Binomial Distribution. Asked once: NDA 1 2019

    114
    In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by

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