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Day 15: NDA Maths

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

  1. Question 1

    Quadratic Equations. This type asked 4 times: NDA 1 2017, NDA 2 2021, NDA 1 2022, NDA 1 2025. This one: NDA 1 2025

    3
    If one root of the equation x2−kx+k=0x^2 - kx + k = 0 exceeds the other by 232\sqrt{3}, then which one of the following is a value of kk?

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  2. Question 2

    Statistics. This type asked 4 times: NDA 1 2019, NDA 2 2019, NDA 2 2021, NDA 1 2025. This one: NDA 1 2025

    113
    The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?

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  3. Question 3

    Complex Numbers. This type asked 4 times: NDA 1 2017, NDA 1 2018, NDA 2 2021, NDA 2 2024. This one: NDA 2 2024

    10
    What is the value of the sum ∑n=120(in−1+in+in+1)\displaystyle\sum_{n=1}^{20}\left(i^{n-1}+i^{n}+i^{n+1}\right) where i=−1i=\sqrt{-1}?

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  4. Question 4

    Conics. This type asked 4 times: NDA 1 2019, NDA 1 2020, NDA 1 2023, NDA 2 2024. This one: NDA 2 2024

    57
    The foci of the ellipse 4x2+9y2=14x^2+9y^2=1 are at QQ and RR. If P(x,y)P(x,y) is any point on the ellipse, then what is PQ+PRPQ+PR equal to?

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  5. Question 5 (case study, 2 parts)

    Definite Integration. This type asked 4 times: NDA 1 2017, NDA 2 2018, NDA 1 2019, NDA 2 2024. This one: NDA 2 2024

    Let f(x)=∣x2−x−2∣f(x)=|x^2-x-2|.
    91
    What is ∫02f(x) dx\displaystyle\int_0^2 f(x)\,dx equal to?

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    92
    What is ∫13f(x) dx\displaystyle\int_1^3 f(x)\,dx equal to?

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