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Day 248: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Indefinite Integration. Asked once: NDA 1 2026

    For the next two (02) items that follow: Let ∫sin⁡θ dθ(2+cos⁡θ)(3+4cos⁡θ)=Aln⁡∣2+cos⁡θ∣+Bln⁡∣3+4cos⁡θ∣\int\dfrac{\sin\theta\,d\theta}{(2+\cos\theta)(3+4\cos\theta)}=A\ln|2+\cos\theta|+B\ln|3+4\cos\theta|.
    91
    What is the value of A?

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    92
    What is the value of B?

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  2. Question 2

    Inverse Trigonometry. Asked once: NDA 1 2025

    49
    If kk is a root of x2−4x+1=0x^2 - 4x + 1 = 0, then what is tan⁡−1k+tan⁡−11k\tan^{-1}k + \tan^{-1}\frac{1}{k} equal to?

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  3. Question 3

    Limits & Continuity. Asked once: NDA 2 2026

    87
    What is lim⁡x→∞(x+x−x)\lim_{x \to \infty} (\sqrt{x + \sqrt{x}} - \sqrt{x}) equal to?

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  4. Question 4

    Lines. Asked once: NDA 2 2026

    52
    A line (sin⁡θ)x+(cos⁡θ)y=sin⁡2θ(\sin \theta) x + (\cos \theta) y = \sin 2\theta cuts the coordinate axes at points PP and QQ. Let MM be the midpoint of the line segment PQPQ. What is the distance of MM from the origin?

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  5. Question 5 (case study, 2 parts)

    Logarithms. Asked once: NDA 2 2025

    For the following two (02) items: Let p=∑j=1nlog⁡102jp=\sum_{j=1}^{n}\log_{10}2^j and q=∑j=1nlog⁡105jq=\sum_{j=1}^{n}\log_{10}5^j.
    23
    If p+q=66p+q=66, then which one of the following is correct?

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    24
    If p+q=15p+q=15, then what is q−pq-p equal to?

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