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Day 127: NDA Maths

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

  1. Question 1

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

    60
    A sphere of radius r through origin cuts axes at A,B,C. What is the locus of centroid of triangle ABC?

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  2. Question 2

    Functions. Asked once: NDA 1 2019 (same type asked 3 times)

    80
    The domain of the function f(x)=(2−x)(x−3)f(x)=\sqrt{(2-x)(x-3)} is

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  3. Question 3

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

    13
    Which one of the following factors does the expansion of the determinant ∣xy3x25y39x310y527∣\begin{vmatrix} x & y & 3 \\ x^2 & 5y^3 & 9 \\ x^3 & 10y^5 & 27 \end{vmatrix} contain?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2020 (same type asked 3 times)

    5
    For how many values of kk, is the matrix (0k4−k0−5−kk−1)\begin{pmatrix}0 & k & 4 \\ -k & 0 & -5 \\ -k & k & -1\end{pmatrix} singular?

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2021 (same type asked 3 times)

    49
    Consider the following statements: 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP. Which of the above statements is/are correct?

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