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Day 94: NDA Maths

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

  1. Question 1

    Limits & Continuity. Asked once: NDA 2 2021 (same type asked 5 times)

    76
    Consider the following statements in respect of f(x)=∣x∣−1f(x)=|x|-1: 1. f(x)f(x) is continuous at x=1x=1. 2. f(x)f(x) is differentiable at x=0x=0. Which of the above statements is/are correct?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 1 2026 (same type asked 5 times)

    19
    If M=(200020002)M=\begin{pmatrix}2&0&0\\0&2&0\\0&0&2\end{pmatrix}, then what is the value of ∣M∣⋅∣adjM∣|M|\cdot|\text{adj}M|?

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  3. Question 3 (case study, 3 parts)

    Probability. Asked once: NDA 1 2026 (same type asked 5 times)

    For the next three (03) items that follow: Let A, B, C and D be mutually exclusive and exhaustive events and P(A)2=P(B)3=P(C)5=P(D)8\dfrac{P(A)}{2}=\dfrac{P(B)}{3}=\dfrac{P(C)}{5}=\dfrac{P(D)}{8}.
    106
    What is P(A)+P(B)+P(C) equal to?

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    107
    What is [2P(A)+3P(B)][4P(C)+5P(D)]\dfrac{[2P(A)+3P(B)]}{[4P(C)+5P(D)]} equal to?

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    108
    If G is the geometric mean of P(A), P(B), P(C) and P(D), then what is 9G equal to?

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  4. Question 4

    Sequence & Series. Asked once: NDA 1 2024 (same type asked 5 times)

    106
    If a,b,ca,b,c are in HP, then what is 1b−a+1b−c\dfrac{1}{b-a}+\dfrac{1}{b-c} equal to?

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  5. Question 5

    Trigonometric Equations. Asked once: NDA 2 2025 (same type asked 5 times)

    49
    If 0≤x≤π20\leq x\leq\dfrac{\pi}{2}, then what is the number of values of xx satisfying the equation tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x?

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