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Day 201: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2017 (same type asked 3 times)

    96
    The value of the determinant ∣1−αα−α2α21−ββ−β2β21−γγ−γ2γ2∣\begin{vmatrix}1-\alpha & \alpha-\alpha^2 & \alpha^2 \\ 1-\beta & \beta-\beta^2 & \beta^2 \\ 1-\gamma & \gamma-\gamma^2 & \gamma^2\end{vmatrix} is equal to

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 2 2018 (same type asked 3 times)

    20
    What should be the value of x so that the matrix (24−8x)\begin{pmatrix} 2 & 4 \\ -8 & x \end{pmatrix} does not\textbf{\text{not}} have an inverse?

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  3. Question 3

    Sequence & Series. Asked once: NDA 2 2019 (same type asked 3 times)

    31
    Let aa, bb, cc be in AP and k≠0k \neq 0 be a real number. Which of the following are correct ? 1. kaka, kbkb, kckc are in AP 2. k−ak-a, k−bk-b, k−ck-c are in AP 3. ak\dfrac{a}{k}, bk\dfrac{b}{k}, ck\dfrac{c}{k} are in AP Select the correct answer using the code given below :

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  4. Question 4

    Differential Equations. Asked once: NDA 2 2018 (same type asked 3 times)

    89
    What is the order of the differential equation whose solution is y=acos⁡x+bsin⁡x+ce−x+dy=a\cos x+b\sin x+ce^{-x}+d, where a, b, c and d are arbitrary constants?

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  5. Question 5

    Functions. Asked once: NDA 1 2018 (same type asked 3 times)

    89
    What is the period of f(x) = sin x?

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