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Day 350: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 1 2024

    19
    For what value of nn is the determinant ∣(94)(93)(10n−2)(116)(115)(12n)(m7)(m6)(m+1n+1)∣=0\begin{vmatrix}\binom{9}{4}&\binom{9}{3}&\binom{10}{n-2}\\\binom{11}{6}&\binom{11}{5}&\binom{12}{n}\\\binom{m}{7}&\binom{m}{6}&\binom{m+1}{n+1}\end{vmatrix}=0 for every m>nm>n?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2017

    19
    The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word 'EQUATION' is

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  3. Question 3

    Probability. Asked once: NDA 1 2023

    118
    Three dice are thrown. What is the probability that each face shows only multiples of 3?

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  4. Question 4

    Sequence & Series. Asked once: NDA 1 2018

    22
    What is the greatest integer among the following by which 55+755^5 + 7^5 is divisible?

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  5. Question 5

    Statistics. Asked once: NDA 2 2019

    103
    The median of the observations 22, 24, 33, 37, x+1x+1, x+3x+3, 46, 47, 57, 58 in ascending order is 42. What are the values of 5th and 6th observations respectively ?

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