PYQ Vault

Day 74: NDA Maths

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

  1. Question 1 (case study, 2 parts)

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

    Consider the following for the next two (02) items that follow: Consider the function f(x)=∣x−2∣+∣3−x∣+∣4−x∣f(x)=|x-2|+|3-x|+|4-x|, where x∈Rx\in R.
    41
    At what value of xx does the function attain minimum value?

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    42
    What is the minimum value of the function?

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  2. Question 2

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

    22
    A mapping f:A→Bf:A\to B defined as f(x)=2x+33x+5f(x)=\dfrac{2x+3}{3x+5}, x∈Ax\in A. If ff is to be onto, then what are AA and BB equal to?

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  3. Question 3 (case study, 2 parts)

    Height & Distance. 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: A flagstaff 20 m long standing on a pillar 10 m high subtends an angle tan⁡−1(0.5)\tan^{-1}(0.5) at a point PP on the ground. Let θ\theta be the angle subtended by the pillar at this point PP.
    33
    If xx is the distance of PP from bottom of the pillar, then consider the following statements: 1. xx can take two values which are in the ratio 1:31:3 2. xx can be equal to height of the flagstaff Which of the statements given above is/are correct?

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    34
    What is a possible value of tan⁡θ\tan\theta?

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  4. Question 4

    Matrices & Determinants. This type asked 2 times: NDA 1 2017, NDA 1 2023. This one: NDA 1 2023

    10
    What is the sum of the roots of the equation ∣0x−ax−b00x−cx+bx+c1∣=0\begin{vmatrix}0&x-a&x-b\\0&0&x-c\\x+b&x+c&1\end{vmatrix}=0?

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  5. Question 5

    Permutation & Combination. This type asked 2 times: NDA 2 2017, NDA 1 2023. This one: NDA 1 2023

    29
    Let xx be the number of permutations of the word 'PERMUTATIONS' and yy be the number of permutations of the word 'COMBINATIONS'. Which one of the following is correct?

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