PYQ Vault

Day 263: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Application of Derivatives. Asked once: NDA 2 2024

    Let f(x)=cos⁡2x+xf(x)=\cos 2x+x on [−π2,π2]\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right].
    85
    What is the greatest value of f(x)f(x)?

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    86
    Let f(x)=cos⁡2x+xf(x) = \cos 2x + x on [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]. What is the least value of f(x)f(x)?

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  2. Question 2

    Binary Numbers. Asked once: NDA 1 2022

    54
    If x3+y3=(100010111)2x^3+y^3=(100010111)_2 and x+y=(11111)2x+y=(11111)_2, then what is (x−y)2+xy(x-y)^2+xy equal to?

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  3. Question 3

    Binomial Theorem. Asked once: NDA 1 2024

    30
    What is the coefficient of x10x^{10} in the expansion of (1−x220)−1(x2−1x2)−5\left(1-\dfrac{x^2}{20}\right)^{-1}\left(x^2-\dfrac{1}{x^2}\right)^{-5}?

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  4. Question 4

    Circles. Asked once: NDA 2 2023

    84
    If 3x+y−5=03x+y-5=0 is the equation of a chord of the circle x2+y2−25=0x^2+y^2-25=0, then what are the coordinates of the mid-point of the chord?

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  5. Question 5

    Complex Numbers. Asked once: NDA 2 2025

    17
    Let 1,ω,ω21,\omega,\omega^2 be three cube roots of unity. If x=a+bx=a+b, y=aω+bω2y=a\omega+b\omega^2, z=aω2+bωz=a\omega^2+b\omega, then what is x2+y2+z2x^2+y^2+z^2 equal to?

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