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Day 316: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: Let f(x)=sin⁡[π2]x+cos⁡[−π2]xf(x)=\sin[\pi^{2}]x+\cos[-\pi^{2}]x where [⋅][\cdot] is a greatest integer function.
    79
    What is f ⁣(π2)f\!\left(\dfrac{\pi}{2}\right) equal to?

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    80
    What is f ⁣(π4)f\!\left(\dfrac{\pi}{4}\right) equal to?

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  2. Question 2

    Lines. Asked once: NDA 2 2024

    56
    The diagonals of a quadrilateral ABCDABCD are along the lines x−2y=1x-2y=1 and 4x+2y=34x+2y=3. The quadrilateral ABCDABCD may be a

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  3. Question 3

    Logarithms. Asked once: NDA 2 2018

    1
    What is the value of log⁡7log⁡7777\log_7 \log_7 \sqrt{7\sqrt{7\sqrt{7}}} equal to?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2025

    11
    If A2+B2+C2=0A^2 + B^2 + C^2 = 0, then what is the value of ∣1cos⁡Ccos⁡Bcos⁡C1cos⁡Acos⁡Bcos⁡A1∣\begin{vmatrix} 1 & \cos C & \cos B \\ \cos C & 1 & \cos A \\ \cos B & \cos A & 1 \end{vmatrix}?

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  5. Question 5

    Permutation & Combination. Asked once: NDA 1 2022

    48
    Consider the following statements: 1. n!3!\frac{n!}{3!} is divisible by 6, where n>3n>3 2. n!3!+3\frac{n!}{3!}+3 is divisible by 7, where n>3n>3 Which of the above statements is/are correct?

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