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Day 128: NDA Maths

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

  1. Question 1

    Differential Equations. Asked once: NDA 1 2021 (same type asked 3 times)

    96
    If the general solution of a differential equation is y2+2cy−cx+c2=0y^2+2cy-cx+c^2=0, where cc is an arbitrary constant, then what is the order of the differential equation?

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  2. Question 2 (case study, 3 parts)

    Functions. Asked once: NDA 2 2019 (same type asked 3 times)

    Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function f(x)=g(x)+h(x)f(x) = g(x) + h(x) where g(x)=sin⁡(x4)g(x) = \sin\left(\dfrac{x}{4}\right) and h(x)=cos⁡(4x5)h(x) = \cos\left(\dfrac{4x}{5}\right).
    86
    What is the period of the function g(x)g(x) ?

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    87
    What is the period of the function h(x)h(x) ?

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    88
    What is the period of the function f(x)f(x) ?

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  3. Question 3

    Functions. Asked once: NDA 1 2020 (same type asked 3 times)

    26
    The value of ordinate of the graph of y=2+cos⁡xy = 2 + \cos x lies in the interval

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  4. Question 4

    Indefinite Integration. Asked once: NDA 1 2020 (same type asked 3 times)

    88
    What is ∫dxx(xn+1)\int\frac{dx}{x(x^n+1)} equal to?

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  5. Question 5

    Limits & Continuity. Asked once: NDA 2 2019 (same type asked 3 times)

    72
    Consider the following statements in respect of the function f(x)=sin⁡(1x)f(x) = \sin\left(\dfrac{1}{x}\right) for x≠0x \neq 0 and f(0)=0f(0) = 0 : 1. lim⁡x→0f(x)\lim_{x \to 0} f(x) exists. 2. f(x)f(x) is continuous at x=0x = 0. Which of the above statements is/are correct ?

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