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Day 357: NDA Maths

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

  1. Question 1

    Sequence & Series. Asked once: NDA 2 2017

    20
    A person is to count 4500 notes. Let ana_n denote the number of notes he counts in the nnth minute. If a1=a2=a3=…=a10=150a_1 = a_2 = a_3 = \ldots = a_{10} = 150, and a10,a11,a12,…a_{10}, a_{11}, a_{12}, \ldots are in AP with the common difference −2-2, then the time taken by him to count all the notes is

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  2. Question 2

    Statistics. Asked once: NDA 2 2018

    119
    In any discrete series (when all values are not same), if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct?

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  3. Question 3

    Trigonometric Identities. Asked once: NDA 1 2021

    25
    What is 1+tan⁡2θ1+cot⁡2θ−(1−tan⁡θ1−cot⁡θ)2\frac{1+\tan^2\theta}{1+\cot^2\theta} - \left(\frac{1-\tan\theta}{1-\cot\theta}\right)^2 equal to?

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  4. Question 4

    Vectors. Asked once: NDA 1 2019

    68
    If in a right-angled triangle ABC, hypotenuse AC=pAC=p, then what is AB→⋅AC→+BC→⋅BA→+CA→⋅CB→\overrightarrow{AB}\cdot\overrightarrow{AC}+\overrightarrow{BC}\cdot\overrightarrow{BA}+\overrightarrow{CA}\cdot\overrightarrow{CB} equal to?

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  5. Question 5

    Differentiation. Asked once: NDA 1 2018

    87
    What is the derivative of f(x)=etan⁡x+ln⁡(sec⁡x)−eln⁡xf(x)=e^{\tan x}+\ln(\sec x)-e^{\ln x} at x=π/4x=\pi/4?

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