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Day 56: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Trigonometric Identities. This type asked 2 times: NDA 1 2017, NDA 2 2026. This one: NDA 2 2026

    For the next two (02) items that follow : Given that tan⁡(A2+B2)=p\tan\left(\frac{A}{2} + \frac{B}{2}\right) = p and tan⁡(A2−B2)=q\tan\left(\frac{A}{2} - \frac{B}{2}\right) = q, where pq≠±1pq \ne \pm 1.
    7
    What is tan⁡A\tan A equal to?

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    8
    What is tan⁡B\tan B equal to?

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  2. Question 2

    Application of Derivatives. This type asked 2 times: NDA 1 2017, NDA 1 2026. This one: NDA 1 2026

    77
    What is the length of the longest interval in which the function f(x)=2cos⁡2x−1f(x)=2\cos^2x-1 is decreasing?

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  3. Question 3

    Application of Derivatives. This type asked 2 times: NDA 2 2021, NDA 1 2026. This one: NDA 1 2026

    75
    Consider the following statements in respect of the function f(x)=xf(x)=x in the interval (−1,1)(-1,1): I. The function attains maximum value. II. The function attains minimum value. Which of the statements given above is/are correct?

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  4. Question 4 (case study, 2 parts)

    Applications of Integration. This type asked 2 times: NDA 1 2019, NDA 1 2026. This one: NDA 1 2026

    For the next two (02) items that follow: Let k be the area between the curve y=sinx and x-axis in the interval [0,π/4][0,\pi/4].
    87
    What is the area between the curve y=sinx and the x-axis in the interval [π/4,π/2][\pi/4,\pi/2]?

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    88
    What is the area between the curve y=cosx and the x-axis in the interval [π/4,π/2][\pi/4,\pi/2]?

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  5. Question 5

    Limits & Continuity. This type asked 2 times: NDA 1 2020, NDA 1 2026. This one: NDA 1 2026

    73
    What is lim⁡x→010sin⁡x−1tan⁡x\lim_{x\to0}\dfrac{10^{\sin x}-1}{\tan x} equal to?

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