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Day 21: NDA Maths

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

  1. Question 1

    Statistics. This type asked 4 times: NDA 1 2017, NDA 2 2018, NDA 2 2019, NDA 1 2020. This one: NDA 1 2020

    105
    A data set of nn observations has mean 2M2M, while another data set of 2n2n observations has mean MM. What is the mean of the combined data sets?

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  2. Question 2

    Quadratic Equations. This type asked 4 times: NDA 2 2017, NDA 1 2018, NDA 1 2019, NDA 2 2019. This one: NDA 2 2019

    37
    How many real roots does the equation x2+3∣x∣+2=0x^{2} + 3|x| + 2 = 0 have ?

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  3. Question 3

    Permutation & Combination. Asked 3 times: NDA 1 2020, NDA 2 2023*, NDA 1 2026 (* = numbers or wording changed that year)

    8
    What is the maximum number of points of intersection of 5 circles?

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  4. Question 4

    Lines. Asked 3 times: NDA 1 2017*, NDA 1 2021*, NDA 2 2024 (* = numbers or wording changed that year)

    58
    If P(2,4)P(2,4), Q(8,12)Q(8,12), R(10,14)R(10,14) and S(x,y)S(x,y) are vertices of a parallelogram, then what is (x+y)(x+y) equal to?

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  5. Question 5

    Complex Numbers. This type asked 3 times: NDA 2 2019, NDA 1 2024, NDA 2 2026. This one: NDA 2 2026

    34
    If (1+i)n−16=0(1 + i)^n - 16 = 0, where i=−1i = \sqrt{-1} and nn is a positive integer, then what is the least value of nn?

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