PYQ Vault

Day 32: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Matrices & Determinants. This type asked 3 times: NDA 1 2019, NDA 1 2020, NDA 1 2025. This one: NDA 1 2025

    10
    If ∣23+i−13−i0i−1−1−1−i1∣=A+iB\begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i-1 \\ -1 & -1-i & 1 \end{vmatrix} = A + iB where i=−1i=\sqrt{-1}, then what is A+BA+B equal to?

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  2. Question 2

    Matrices & Determinants. This type asked 3 times: NDA 2 2018, NDA 2 2019, NDA 1 2025. This one: NDA 1 2025

    12
    If ω\omega is a non-real cube root of unity, then what is a root of the following equation? ∣x+1ωω2ωx+ω21ω21x+ω∣=0\begin{vmatrix} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{vmatrix} = 0

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  3. Question 3

    Sequence & Series. This type asked 3 times: NDA 1 2018, NDA 1 2024, NDA 1 2025. This one: NDA 1 2025

    6
    If p,1,qp, 1, q are in AP and p,2,qp, 2, q are in GP, then which of the following statements is/are correct? I. p,4,qp, 4, q are in HP. II. 1p,14,1q\frac{1}{p}, \frac{1}{4}, \frac{1}{q} are in AP. Select the answer using the code given below.

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  4. Question 4

    Statistics. This type asked 3 times: NDA 2 2022, NDA 2 2024, NDA 1 2025. This one: NDA 1 2025

    120
    What is the arithmetic mean of 82,92,102,…,1528^2, 9^2, 10^2, \ldots, 15^2?

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  5. Question 5 (case study, 3 parts)

    Trigonometric Identities. This type asked 3 times: NDA 2 2019, NDA 1 2024, NDA 1 2025. This one: NDA 1 2025

    Consider the following for the three (03) items that follow: Let p=sin⁡35°, q=sin⁡25°p = \sin 35°,\ q = \sin 25° and r=sin⁡(−95°)r = \sin(-95°).
    31
    What is (p+q+r)(p + q + r) equal to?

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    32
    What is (pq+qr+rp)(pq + qr + rp) equal to?

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    33
    What is p2+q2+r2p^2 + q^2 + r^2 equal to?

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