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Day 10: NDA Maths

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

  1. Question 1

    Functions. This type asked 4 times: NDA 2 2018, NDA 2 2022, NDA 2 2023, NDA 2 2026. This one: NDA 2 2026

    44
    Consider the following relations from AA to BB, where A={1,3,5}A = \{1, 3, 5\} and B={2,4,6,8}B = \{2, 4, 6, 8\} : I. {(1,2),(3,2),(3,6),(5,8)}\{(1, 2), (3, 2), (3, 6), (5, 8)\} II. {(3,4),(5,8),(1,6),(3,2)}\{(3, 4), (5, 8), (1, 6), (3, 2)\} III. {(1,2),(3,6)}\{(1, 2), (3, 6)\} IV. {(1,6),(3,2),(5,2)}\{(1, 6), (3, 2), (5, 2)\} Which of the above is/are function(s) from AA to BB?

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  2. Question 2

    Limits & Continuity. This type asked 4 times: NDA 2 2022, NDA 1 2023, NDA 2 2024, NDA 2 2026. This one: NDA 2 2026

    84
    What is lim⁡x→0sin⁡2xx∣x∣\lim_{x \to 0} \frac{\sin^2 x}{x|x|} equal to?

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  3. Question 3

    Matrices & Determinants. This type asked 4 times: NDA 1 2022, NDA 1 2023, NDA 2 2024, NDA 2 2026. This one: NDA 2 2026

    19
    Let AA, BB and CC be the square matrices of order 2 such that AB=ACAB = AC. Which of the statements given below is/are correct? I. BB and CC are not necessarily equal if AA is a singular matrix. II. BB and CC are equal if AA is a non-singular matrix. Select the answer using the code given below.

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  4. Question 4

    Probability. This type asked 4 times: NDA 2 2022, NDA 2 2023, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    105
    Four dice are rolled. What is the probability of getting a total of the numbers on the dice as 7?

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  5. Question 5 (case study, 2 parts)

    Properties of Triangle. This type asked 4 times: NDA 1 2019, NDA 2 2023, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    For the next two (02) items that follow : The angles AA, BB and CC of a triangle ABCABC are in the ratio 1:2:71 : 2 : 7.
    3
    What is the ratio of the side of greatest length to the side of least length?

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    4
    What is sin⁡A⋅cos⁡B\sin A \cdot \cos B equal to?

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