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Day 116: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2024 (same type asked 3 times)

    18
    If Dn=∣n2030n24050n36070∣D_n=\begin{vmatrix}n & 20 & 30 \\ n^2 & 40 & 50 \\ n^3 & 60 & 70\end{vmatrix}, then what is the value of ∑n=14Dn\displaystyle\sum_{n=1}^{4}D_n?

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  2. Question 2

    Sequence & Series. Asked once: NDA 1 2025 (same type asked 3 times)

    5
    If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

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  3. Question 3

    Sets & Relations. Asked once: NDA 2 2022 (same type asked 3 times)

    Consider the following: 1. A∩B = A∩C ⟹ B = C 2. A∪B = A∪C ⟹ B = C
    15
    Which of the above is/are correct?

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  4. Question 4

    Trigonometric Identities. Asked once: NDA 2 2024 (same type asked 3 times)

    33
    If ptan⁡(θ−30°)=qtan⁡(θ+120°)p\tan(\theta-30°)=q\tan(\theta+120°), then what is p+qp−q\dfrac{p+q}{p-q} equal to?

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  5. Question 5

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

    63
    The equation of the plane passing through the intersection of the planes 2x+y+2z=92x+y+2z=9, 4x−5y−4z=14x-5y-4z=1 and the point (3,2,1)(3,2,1) is

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