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Day 247: NDA Maths

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

  1. Question 1

    Definite Integration. Asked once: NDA 2 2025

    97
    If I1=∫ee2dxln⁡xI_1=\int_e^{e^2}\dfrac{dx}{\ln x} and I2=∫12exx dxI_2=\int_1^2\dfrac{e^x}{x}\,dx, then which one of the following is correct?

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  2. Question 2

    Differential Equations. Asked once: NDA 1 2024

    76
    If dydx=2exy3,  y(0)=12\dfrac{dy}{dx}=2e^x y^3,\;y(0)=\dfrac{1}{2}, then what is 4y2(2−ex)4y^2(2-e^x) equal to?

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  3. Question 3

    Differentiation. Asked once: NDA 2 2026

    91
    Consider the following statements : I. ddxln⁡∣x∣=−1x\frac{d}{dx}\ln|x| = -\frac{1}{x} if x<0x < 0 II. ddxln⁡∣x∣=1x\frac{d}{dx}\ln|x| = \frac{1}{x} if x>0x > 0 Which of the statements given above is/are correct?

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  4. Question 4

    Functions. Asked once: NDA 2 2026

    90
    If f(x)=cos⁡{π3[x]+x}f(x) = \cos\left\{\frac{\pi}{3}[x] + x\right\} for 1<x<21 < x < 2, where [⋅][\cdot] is the greatest integer function, then what is f(π2)f\left(\frac{\pi}{2}\right) equal to?

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  5. Question 5 (case study, 3 parts)

    Height & Distance. Asked once: NDA 2 2022

    Consider the following for the next three (03) items that follow: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x > y). The angles of elevation of the top of the tower from P and Q are 15° and 75° respectively.
    43
    At what height is the top of the tower above the ground level?

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    44
    If θ\theta is the inclination of the tower to the horizontal, then what is cot⁡θ\cot\theta equal to?

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    45
    What is the length of the tower?

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