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Day 57: NDA Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1

    Matrices & Determinants. This type asked 2 times: NDA 2 2024, NDA 1 2026. This one: NDA 1 2026

    16
    If pp, qq, rr are the cube roots of unity, then what is ∣p2+q2r2r2p2q2+r2p2q2q2r2+p2∣\begin{vmatrix}p^2+q^2 & r^2 & r^2\\p^2 & q^2+r^2 & p^2\\q^2 & q^2 & r^2+p^2\end{vmatrix} equal to?

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  2. Question 2 (case study, 5 parts)

    Probability. This type asked 2 times: NDA 2 2021, NDA 1 2026. This one: NDA 1 2026

    For the next five (05) items that follow: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).
    101
    What is the probability that the number selected is divisible by 2?

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    102
    What is the probability that the number selected is divisible by 3?

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    103
    What is the probability that the number selected is divisible by 4?

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    104
    What is the probability that the number selected is divisible by 6?

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    105
    What is the probability that the number selected does not contain zero at any position?

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  3. Question 3

    Properties of Triangle. This type asked 2 times: NDA 1 2022, NDA 1 2026. This one: NDA 1 2026

    33
    In a triangle ABC, sin⁡A=cos⁡B+cos⁡C\sin A=\cos B+\cos C, then what is tan⁡ ⁣(B2)+cot⁡ ⁣(B2)\tan\!\left(\dfrac{B}{2}\right)+\cot\!\left(\dfrac{B}{2}\right) equal to?

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  4. Question 4

    Quadratic Equations. This type asked 2 times: NDA 2 2018, NDA 1 2026. This one: NDA 1 2026

    42
    For a given kk, what is the minimum value of x2+kx+k2x^2+kx+k^2?

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  5. Question 5

    Sets & Relations. This type asked 2 times: NDA 1 2017, NDA 1 2026. This one: NDA 1 2026

    7
    A set S contains (2n+1)(2n+1) elements. If the number of subsets of S which contain at most nn elements is 1024, then what is the value of nn?

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