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Day 373: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 2 2017

    87
    Let f(n)=[14+n1000]f(n) = \left[\dfrac{1}{4} + \dfrac{n}{1000}\right], where [x][x] denotes the integral part of xx. Then the value of ∑n=11000f(n)\displaystyle\sum_{n=1}^{1000} f(n) is

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 2 2021

    12
    If ∣a−ba−b−c−ab−a+b−c−a−b−a−b+c∣−kabc=0\begin{vmatrix}a&-b&a-b-c\\-a&b&-a+b-c\\-a&-b&-a-b+c\end{vmatrix}-kabc=0 (a≠0,b≠0,c≠0)(a\ne0,b\ne0,c\ne0), then what is the value of kk?

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  3. Question 3

    Probability. Asked once: NDA 2 2019

    101
    A coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails ?

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  4. Question 4

    Statistics. Asked once: NDA 2 2017

    107
    Which one of the following can be considered as appropriate pair of values of regression coefficient of yy on xx and regression coefficient of xx on yy?

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  5. Question 5

    Trigonometric Identities. Asked once: NDA 1 2019

    31
    What is the value of sin⁡34°cos⁡236°−sin⁡56°sin⁡124°cos⁡28°cos⁡88°+cos⁡178°sin⁡208°\dfrac{\sin 34° \cos 236° - \sin 56° \sin 124°}{\cos 28° \cos 88° + \cos 178° \sin 208°}?

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