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Day 336: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 2 2022

    13
    Let A={7,8,9,10,11,12,13,14,15,16}A = \{7, 8, 9, 10, 11, 12, 13, 14, 15, 16\} and let f:A→Nf: A \to N be defined by f(x)=f(x) = the highest prime factor of xx. How many elements are there in the range of ff?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2020

    75
    What is lim⁡x→0sin⁡xlog⁡(1−x)x2\lim_{x\to0}\frac{\sin x\log(1-x)}{x^2} equal to?

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  3. Question 3

    Lines. Asked once: NDA 2 2022

    56
    Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis: 1. The line passes through the point (1,12−3)\left(1, \frac{1}{2-\sqrt{3}}\right). 2. The line entirely lies in first and third quadrants. Which of the statements given above is/are correct?

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  4. Question 4 (case study, 2 parts)

    Matrices & Determinants. Asked once: NDA 2 2024

    Let A=(3−342−340−11)A=\begin{pmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{pmatrix}.
    49
    What is A(adj A)A(\text{adj}\,A) equal to?

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    50
    What is A−1A^{-1} equal to?

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  5. Question 5

    Permutation & Combination. Asked once: NDA 2 2019

    23
    If P(n,r)=2520P(n, r) = 2520 and C(n,r)=21C(n, r) = 21, then what is the value of C(n+1,r+1)C(n+1, r+1) ?

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