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Day 302: NDA Maths

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

  1. Question 1

    Indefinite Integration. Asked once: NDA 1 2020

    90
    What is the value of kk such that integration of 3x2+8−4kx\frac{3x^2+8-4k}{x} with respect to xx, may be a rational function?

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  2. Question 2

    Inverse Trigonometry. Asked once: NDA 1 2018

    40
    What is the principal value of sin⁡−1 ⁣(sin⁡2π3)\sin^{-1}\!\left(\sin\frac{2\pi}{3}\right)?

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  3. Question 3 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 1 2025

    Let the function f(x)=x2+9f(x) = x^2 + 9.
    93
    What is lim⁡x→0f(x)−3f(x)+7−4\lim_{x\to 0} \dfrac{\sqrt{f(x)}-3}{\sqrt{f(x)+7}-4} equal to?

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    94
    Consider the following statements: (I). f(x)f(x) is an increasing function. (II). f(x)f(x) has local maximum at x=0x = 0. Which of the statements given above is/are correct?

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  4. Question 4

    Lines. Asked once: NDA 1 2025

    52
    If pp and qq are real numbers between 0 and 1 such that the points (p,1),(1,q)(p, 1), (1, q) and (0,0)(0, 0) form an equilateral triangle, then what is (p+q)(p + q) equal to?

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  5. Question 5

    Logarithms. Asked once: NDA 1 2020

    8
    If x=log⁡c(ab)x = \log_c(ab), y=log⁡a(bc)y = \log_a(bc), z=log⁡b(ca)z = \log_b(ca), then which of the following is correct?

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