PYQ Vault

Day 330: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 1 2023

    98
    If f(x)=x(4x2−3)f(x)=x(4x^{2}-3), then what is f(sin⁡θ)f(\sin\theta) equal to?

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  2. Question 2

    Indefinite Integration. Asked once: NDA 1 2017

    85
    Let f(x)f(x) be an indefinite integral of sin⁡2x\sin^2 x. Consider the following statements: Statement 1: The function f(x)f(x) satisfies f(x+π)=f(x)f(x+\pi)=f(x) for all real xx. Statement 2: sin⁡2(x+π)=sin⁡2x\sin^2(x+\pi)=\sin^2 x for all real xx. Which one of the following is correct in respect of the above statements?

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  3. Question 3

    Limits & Continuity. Asked once: NDA 1 2021

    76
    If lim⁡x→aax−xaxa−aa=−1\lim_{x\to a}\frac{a^x-x^a}{x^a-a^a}=-1, then what is the value of aa?

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  4. Question 4

    Lines. Asked once: NDA 2 2023

    90
    What is the sum of intercepts of the line whose perpendicular distance from origin is 4 units and the normal makes 15°15° with positive xx-axis?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2025

    30
    If A=(xyzyzxzxy)A = \begin{pmatrix} x & y & z \\ y & z & x \\ z & x & y \end{pmatrix} where x,y,zx, y, z are integers, is an orthogonal matrix, then what is A2A^2 equal to?

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