PYQ Vault

Day 376: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2021

    49
    If x=ab−cx=\frac{a}{b-c}, y=bc−ay=\frac{b}{c-a}, z=ca−bz=\frac{c}{a-b}, then what is the value of ∣1−xx11−y1z1∣\begin{vmatrix}1&-x&x\\1&1&-y\\1&z&1\end{vmatrix}?

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  2. Question 2

    Probability. Asked once: NDA 1 2019

    112
    There are n socks in a drawer, of which 3 socks are red. If 2 of the socks are chosen randomly and the probability that both selected socks are red is 12\dfrac{1}{2}, then what is the value of n?

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  3. Question 3

    Statistics. Asked once: NDA 1 2017

    110
    Consider the following statements: Statement 1: Range is not a good measure of dispersion. Statement 2: Range is highly affected by the existence of extreme values. Which one of the following is correct in respect of the above statements?

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  4. Question 4 (case study, 2 parts)

    Trigonometric Identities. Asked once: NDA 1 2019

    Consider the following for the next 02 (two) items: It is given that cos⁡(θ−α)=a\cos(\theta-\alpha)=a, cos⁡(θ−β)=b\cos(\theta-\beta)=b.
    36
    What is cos⁡(α−β)\cos(\alpha-\beta) equal to?

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    37
    What is sin⁡2(α−β)+2abcos⁡(α−β)\sin^2(\alpha-\beta)+2ab\cos(\alpha-\beta) equal to?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2021

    55
    With the numbers 2, 4, 6, 8, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?

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