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Day 73: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Binomial Distribution. This type asked 2 times: NDA 1 2020, NDA 1 2023. This one: NDA 1 2023

    105
    Let XX and YY be two random variables such that X+Y=100X+Y=100. If XX follows Binomial distribution with parameters n=100n=100 and p=45p=\frac{4}{5}, what is the variance of YY?

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  2. Question 2

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

    1
    If ω\omega is a non-real cube root of 1, then what is the value of ∣1−ωω+ω2∣\left|\frac{1-\omega}{\omega+\omega^{2}}\right|?

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  3. Question 3

    Complex Numbers. This type asked 2 times: NDA 1 2018, NDA 1 2023. This one: NDA 1 2023

    11
    If 2−i32-i\sqrt{3} where i=−1i=\sqrt{-1} is a root of the equation x2+ax+b=0x^{2}+ax+b=0, then what is the value of (a+b)(a+b)?

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  4. Question 4 (case study, 3 parts)

    Definite Integration. This type asked 2 times: NDA 2 2019, NDA 1 2023. This one: NDA 1 2023

    Consider the following for the next three (03) items that follow: Let I1=∫0πx1+cos⁡2x dxI_{1}=\int_{0}^{\pi}\dfrac{x}{1+\cos^{2}x}\,dx and I2=∫0π11+sin⁡2x dxI_{2}=\int_{0}^{\pi}\dfrac{1}{1+\sin^{2}x}\,dx.
    81
    What is the value of I1+I2I1−I2\dfrac{I_{1}+I_{2}}{I_{1}-I_{2}}?

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    82
    What is the value of 8I128I_{1}^{2}?

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    83
    What is the value of I2I_{2}?

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  5. Question 5 (case study, 2 parts)

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

    Consider the following for the next two (02) items that follow: Let I=∫ab∣x∣x dxI=\int_{a}^{b}\dfrac{|x|}{x}\,dx, a<ba<b.
    84
    What is II equal to when a<0<ba<0<b?

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    85
    What is II equal to when a<b<0a<b<0?

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