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Day 112: NDA Maths

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

  1. Question 1

    Inverse Trigonometry. Asked once: NDA 2 2024 (same type asked 3 times)

    22
    What is cot⁡2 ⁣(sec⁡−12)+tan⁡2 ⁣(cosec⁡−13)\cot^2\!\left(\sec^{-1}2\right)+\tan^2\!\left(\operatorname{cosec}^{-1}3\right) equal to?

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  2. Question 2

    Linear Inequalities. Asked once: NDA 1 2022 (same type asked 3 times)

    55
    Consider the inequations 5x−4y+12<05x-4y+12<0, x+y<2x+y<2, x<0x<0 and y>0y>0. Which one of the following points lies in the common region?

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  3. Question 3

    Lines. Asked once: NDA 2 2022 (same type asked 3 times)

    57
    If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

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  4. Question 4

    Lines. Asked once: NDA 1 2021 (same type asked 3 times)

    63
    The point of intersection of diagonals of a square ABCDABCD is at the origin and one of its vertices is at A(4,2)A(4, 2). What is the equation of the diagonal BDBD?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2022 (same type asked 3 times)

    5
    If A=(2sin⁡θcos⁡θ0−2cos⁡θsin⁡θ0−111)A = \begin{pmatrix}2\sin\theta & \cos\theta & 0\\-2\cos\theta & \sin\theta & 0\\-1 & 1 & 1\end{pmatrix}, then what is A(adjA)A(\text{adj}A) equal to?

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