PYQ Vault

Day 254: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Inverse Trigonometry. Asked once: NDA 1 2025

    Let y=sin⁡−1(x−4x327)y = \sin^{-1}\left(\frac{x - 4x^3}{27}\right).
    91
    What is yy equal to?

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    92
    What is dydx\frac{dy}{dx} equal to?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 2 2026

    82
    If f(x)f(x) is the integral of 1+cos⁡2x−2cos⁡xxsin⁡2xtan⁡x\frac{1 + \cos^2 x - 2\cos x}{x\sin^2 x\tan x} then what is lim⁡x→0f′(x)\lim_{x \to 0} f'(x) equal to?

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  3. Question 3

    Lines. Asked once: NDA 2 2026

    56
    A line cuts off intercept pp on the xx-axis and intercept qq on the yy-axis, where p>qp > q. The sum of the intercepts is 2 and the product of the intercepts is −15-15. What is the equation of the line?

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  4. Question 4

    Logarithms. Asked once: NDA 2 2025

    4
    Let nn be a natural number. The number of consecutive zeros at the end of the expansion of n!n! is exactly 2. How many values of nn are possible?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 2 2026

    39
    If x+ay+a2z=1x + ay + a^2 z = 1, x+by+b2z=1x + by + b^2 z = 1, x+cy+c2z=1x + cy + c^2 z = 1 where a≠b≠ca \ne b \ne c, then what is x+y+zx + y + z equal to?

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