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Day 265: NDA Maths

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

  1. Question 1

    Height & Distance. Asked once: NDA 1 2019

    97
    In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord?

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  2. Question 2 (case study, 2 parts)

    Indefinite Integration. Asked once: NDA 1 2024

    Let ∫dxx+1−x−1=α(x+1)3/2+β(x−1)3/2+c\displaystyle\int\dfrac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{3/2}+\beta(x-1)^{3/2}+c.
    95
    What is the value of α\alpha?

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    96
    What is the value of β\beta?

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  3. Question 3

    Inverse Trigonometry. Asked once: NDA 1 2024

    44
    What is tan⁡−1 ⁣ab−tan⁡−1 ⁣a−ba+b\tan^{-1}\!\dfrac{a}{b}-\tan^{-1}\!\dfrac{a-b}{a+b} equal to?

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  4. Question 4

    Limits & Continuity. Asked once: NDA 1 2026

    71
    If f(x)f(x) is differentiable at x=ax=a, then consider the following statements: I. f(x)f(x) is continuous at x=ax=a. II. lim⁡x→af(x)=f(a)\lim_{x\to a}f(x)=f(a). Which of the statements given above is/are correct?

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  5. Question 5

    Lines. Asked once: NDA 2 2026

    59
    ABCABC is a triangle, where the vertices AA and BB are fixed points both lying on the xx-axis. Let AB=10AB = 10 cm. The vertex CC moves such that 1tan⁡A+1tan⁡B=1k\frac{1}{\tan A} + \frac{1}{\tan B} = \frac{1}{k}, where k≠0k \ne 0. What is the equation of the locus of the point CC?

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