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Day 375: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 1 2017

    96
    Let f(a)=a−1a+1f(a)=\dfrac{a-1}{a+1}. Consider the following: 1. f(2a)=f(a)+1f(2a)=f(a)+1 2. f ⁣(1a)=−f(a)f\!\left(\dfrac{1}{a}\right)=-f(a) Which of the above is/are correct?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 2 2021

    50
    Consider the following in respect of the matrix A=(111111111)A=\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}: 1. Inverse of AA does not exist 2. A3=AA^{3}=A 3. 3A=A23A=A^{2} Which of the above are correct?

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  3. Question 3

    Probability. Asked once: NDA 1 2019

    106
    If A, B, C are three events, then what is the probability that at least two of these events occur together?

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  4. Question 4

    Statistics. Asked once: NDA 2 2017

    105
    Consider the following statements: 1. Coefficient of variation depends on the unit of measurement of the variable. 2. Range is a measure of dispersion. 3. Mean deviation is least when measured about median. Which of the above statements are correct?

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  5. Question 5

    Trigonometric Identities. Asked once: NDA 1 2019

    98
    If sin⁡θ=−12\sin\theta=-\dfrac{1}{2} and tan⁡θ=13\tan\theta=\dfrac{1}{\sqrt{3}}, then in which quadrant does θ\theta lie?

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