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Day 260: 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 2026

    For the next two (02) items that follow: Let f(x)={ax(x−1),x<1x−1,1≤x≤3px2+qx+2,x>3f(x)=\begin{cases}ax(x-1), & x<1\\ x-1, & 1\leq x\leq3\\ px^2+qx+2, & x>3\end{cases}. Given that f(x)f(x) is continuous for all x but not differentiable at x=1. Further f′(x)f'(x) is continuous at x=3.
    95
    What is the value of p?

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    96
    What is the value of q?

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  2. Question 2

    Lines. Asked once: NDA 2 2026

    55
    A ray of light passing through the point P(1,2)P(1, 2) reflects on the xx-axis at point NN and the reflected ray passes through the point Q(5,3)Q(5, 3). What is the distance of the point NN from the origin?

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  3. Question 3

    Logarithms. Asked once: NDA 2 2024

    8
    Let p=ln⁡xp=\ln x, q=ln⁡x3q=\ln x^3 and r=ln⁡x5r=\ln x^5, where x>1x>1. Which of the following statements is/are correct? A. p,qp,q and rr are in AP. B. p,qp,q and rr can never be in GP. Select the answer using the code given below.

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2026

    16
    If AA is a square matrix of order 3 and ∣A∣=2|A| = 2, then what is adj(adjA)\text{adj}(\text{adj} A) equal to?

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  5. Question 5

    Permutation & Combination. Asked once: NDA 2 2025

    3
    Let y=x!y = x! and z=(2x)!z = (2x)!. If (z/y)=120(z/y) = 120, then what is the value of (3x)!(3x)!?

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