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Day 327: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Limits & Continuity. Asked once: NDA 2 2021

    74
    What is lim⁡n→∞an+bnan−bn\lim_{n\to\infty}\frac{a^{n}+b^{n}}{a^{n}-b^{n}} where a>b>1a>b>1 equal to?

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  2. Question 2

    Lines. Asked once: NDA 2 2023

    83
    Given that 16p2+49q2−4r2−56pq=016p^2+49q^2-4r^2-56pq=0. Which one of the following is a point on the pair of straight lines (px+qy+r)(px+qy−r)=0(px+qy+r)(px+qy-r)=0?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2025

    9
    Consider the following statements in respect of the determinant Δ=∣k(k+2)2k+112k+1k+21331∣\Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix}: (I). Δ\Delta is positive if k>0k>0. (II). Δ\Delta is negative if k<0k<0. (III). Δ\Delta is zero if k=0k=0. How many of the statements given above are correct?

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  4. Question 4

    Permutation & Combination. Asked once: NDA 2 2021

    18
    How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

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  5. Question 5

    Probability. Asked once: NDA 2 2024

    115
    For two events A and B, P(A)=P(A∣B)=0.25P(A)=P(A|B)=0.25 and P(B∣A)=0.5P(B|A)=0.5. Which of the following are correct? A. A and B are independent. B. P(Ac∪Bc)=0.875P(A^c\cup B^c)=0.875. C. P(Ac∩Bc)=0.375P(A^c\cap B^c)=0.375. Select the answer using the code given below.

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