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Day 186: NDA Maths

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

  1. Question 1

    Definite Integration. Asked once: NDA 2 2021 (same type asked 3 times)

    96
    If f(x)=2xf(x)=2^{x}, then what is ∫210f′(x)f(x) dx\int_{2}^{10}\frac{f'(x)}{f(x)}\,dx equal to?

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  2. Question 2

    Differential Equations. Asked once: NDA 1 2017 (same type asked 3 times)

    83
    If x dy=y(dx+y dy)x\,dy = y(dx + y\,dy); y(1)=1y(1) = 1 and y(x)>0y(x) > 0, then what is y(−3)y(-3) equal to?

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  3. Question 3 (case study, 2 parts)

    Differentiation. Asked once: NDA 2 2025 (same type asked 3 times)

    For the following two (02) items: Let the function f(x)=∣x−3∣+∣x−4∣f(x)=|x-3|+|x-4| be defined on the interval [0,5][0,5].
    87
    What is dydx\dfrac{dy}{dx} at x=3.5x=3.5 equal to?

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    88
    Consider the following statements: I. The function is differentiable at x=3x=3. II. The function is differentiable at x=4x=4. Which of the statements given above is/are correct?

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  4. Question 4

    Functions. Asked once: NDA 2 2017 (same type asked 3 times)

    61
    The inverse of the function y=5ln⁡xy = 5^{\ln x} is

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  5. Question 5

    Height & Distance. Asked once: NDA 2 2017 (same type asked 3 times)

    36
    The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30° and 45°. If hTh_T is the height of the tower and hPh_P is the height of the pole, then which of the following are correct? 1. 2hPhT3+3=hP2\dfrac{2h_P h_T}{3+\sqrt{3}} = h_P^2 2. hT−hP3+1=hP2\dfrac{h_T - h_P}{\sqrt{3}+1} = \dfrac{h_P}{2} 3. 2(hP+hT)hP=4+3\dfrac{2(h_P + h_T)}{h_P} = 4+\sqrt{3} Select the correct answer using the code given below.

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