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Day 293: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Permutation & Combination. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: Consider the sum S=0!+1!+2!+3!+4!+…+100!S=0!+1!+2!+3!+4!+\ldots+100!.
    43
    If the sum SS is divided by 8, what is the remainder?

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    44
    If the sum SS is divided by 60, what is the remainder?

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  2. Question 2

    Probability. Asked once: NDA 2 2025

    110
    Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the first, second and third tosses respectively?

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  3. Question 3 (case study, 2 parts)

    Properties of Triangle. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: In the triangle ABCABC, a2+b2+c2=ac+3 bca^{2}+b^{2}+c^{2}=ac+\sqrt{3}\,bc.
    39
    What is the nature of the triangle?

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    40
    If c=8c=8, what is the area of the triangle?

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  4. Question 4

    Quadratic Equations. Asked once: NDA 2 2024

    39
    What is the number of real roots of the equation (x−1)2+(x−3)2+(x−5)2=0(x-1)^2+(x-3)^2+(x-5)^2=0?

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  5. Question 5

    Sequence & Series. Asked once: NDA 2 2023

    113
    If HH is the Harmonic Mean of (104)\binom{10}{4}, (105)\binom{10}{5}, and (106)\binom{10}{6}, then what is the value of 270H\frac{270}{H}?

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