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Day 71: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Differential Equations. This type asked 2 times: NDA 2 2021, NDA 2 2023. This one: NDA 2 2023

    70
    What is the differential equation of all parabolas of the type y2=4a(x−b)y^2=4a(x-b)?

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  2. Question 2

    Differentiation. This type asked 2 times: NDA 1 2023, NDA 2 2023. This one: NDA 2 2023

    65
    If f(x)=∣ln⁡∣x∣∣f(x)=|\ln|x|| where 0<x<10<x<1, then what is f′(0.5)f'(0.5) equal to?

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  3. Question 3

    Functions. This type asked 2 times: NDA 2 2022, NDA 2 2023. This one: NDA 2 2023

    25
    A function satisfies f(x−y)=f(x)f(y)f(x-y)=\frac{f(x)}{f(y)}, where f(y)≠0f(y)\neq0. If f(1)=0.5f(1)=0.5, then what is f(2)+f(3)+f(4)+f(5)+f(6)f(2)+f(3)+f(4)+f(5)+f(6) equal to?

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  4. Question 4

    Lines. This type asked 2 times: NDA 1 2022, NDA 2 2023. This one: NDA 2 2023

    88
    For what values of kk is the line (k−3)x−(5−k2)y+(k2−7k+6)=0(k-3)x-(5-k^2)y+(k^2-7k+6)=0 parallel to the line x+y=1x+y=1?

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  5. Question 5

    Lines. This type asked 2 times: NDA 1 2017, NDA 2 2023. This one: NDA 2 2023

    89
    The line x+y=4x+y=4 cuts the line joining P(−1,1)P(-1,1) and Q(5,7)Q(5,7) at RR. What is PR:RQPR:RQ equal to?

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