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Day 287: 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 2 2025

    For the following two (02) items: Consider the function f(x)={4(5x),x<08k+x,x≥0f(x)=\begin{cases}4(5^x), & x<0\\ 8k+x, & x\geq0\end{cases}.
    83
    If the function is continuous, then what is the value of kk?

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    84
    What is f′(−1)f'(-1) equal to?

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  2. Question 2

    Lines. Asked once: NDA 2 2025

    62
    If the vertices BB and DD of a square ABCDABCD are (2,3)(2,3) and (4,1)(4,1) respectively, then what is the area of the square?

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  3. Question 3

    Logarithms. Asked once: NDA 1 2023

    114
    If GG is the geometric mean of numbers 1,2,22,23,…,2n−11,2,2^{2},2^{3},\ldots,2^{n-1}, then what is the value of 1+2log⁡2G1+2\log_{2}G?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2026

    21
    If MTM^T is the transpose of a 2×22\times2 matrix M, then which of the following is/are correct? I. ∣M+MT∣=∣M∣+∣MT∣|M+M^T|=|M|+|M^T| if M is symmetric. II. ∣M+MT∣=0|M+M^T|=0 if M is anti-symmetric. Select the answer using the code given below.

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  5. Question 5

    Permutation & Combination. Asked once: NDA 1 2023

    19
    Consider the following statements: 1. (25)!+1(25)!+1 is divisible by 26 2. (6)!+1(6)!+1 is divisible by 7 Which of the above statements is/are correct?

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