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Day 146: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 1 2018 (same type asked 2 times)

    85
    For f(x)=1∣x∣−xf(x)=\frac{1}{\sqrt{|x|-x}}, what is the domain of f?

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  2. Question 2

    Lines. Asked once: NDA 1 2022 (same type asked 2 times)

    89
    What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x+y=px+y=p (where pp is a real number) by the coordinate axes?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2022 (same type asked 2 times)

    Consider the following for the next three (03) items that follow: If A=(1000cos⁡θsin⁡θ0sin⁡θ−cos⁡θ)A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos\theta & \sin\theta \\ 0 & \sin\theta & -\cos\theta \end{pmatrix}, which of the following are correct? 1. A+adjAA + adjA is a null matrix 2. A−1+adjAA^{-1} + adjA is a null matrix 3. A−A−1A - A^{-1} is a null matrix
    6
    Select the correct answer using the code given below:

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2021 (same type asked 2 times)

    42
    What is the value of the following determinant? ∣cos⁡Ctan⁡A0sin⁡B0−tan⁡A0sin⁡Bcos⁡C∣\begin{vmatrix}\cos C&\tan A&0\\\sin B&0&-\tan A\\0&\sin B&\cos C\end{vmatrix}

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  5. Question 5 (case study, 2 parts)

    Probability. Asked once: NDA 1 2024 (same type asked 2 times)

    Events A,B,CA,B,C: P(A)=0.6,P(B)=0.4,P(C)=0.5,P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2P(A)=0.6,P(B)=0.4,P(C)=0.5,P(A\cup B)=0.8,P(A\cap C)=0.3,P(A\cap B\cap C)=0.2 and P(A∪B∪C)≥0.85P(A\cup B\cup C)\geq0.85.
    113
    What is the minimum value of P(B∩C)P(B\cap C)?

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    114
    What is the maximum value of P(B∩C)P(B\cap C)?

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