PYQ Vault

Day 385: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2018

    33
    What is the determinant of the matrix (xyy+zzxz+xyzx+y)\begin{pmatrix} x & y & y+z \\ z & x & z+x \\ y & z & x+y \end{pmatrix}?

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  2. Question 2

    Probability. Asked once: NDA 2 2017

    102
    Let a die be loaded in such a way that even faces are twice as likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

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  3. Question 3

    Trigonometric Identities. Asked once: NDA 1 2017

    46
    What is the value of tan⁡18°\tan 18°?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2017

    16
    The value of the determinant ∣cos⁡2θ2sin⁡2θ2sin⁡2θ2cos⁡2θ2∣\begin{vmatrix}\cos^2\dfrac{\theta}{2} & \sin^2\dfrac{\theta}{2} \\ \sin^2\dfrac{\theta}{2} & \cos^2\dfrac{\theta}{2}\end{vmatrix} for all values of θ\theta is

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  5. Question 5

    Probability. Asked once: NDA 2 2017

    119
    Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?

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