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Day 1: NDA Maths

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

  1. Question 1

    Lines. This type asked 8 times: NDA 1 2017, NDA 2 2017, NDA 1 2018, NDA 2 2018, NDA 2 2019, NDA 1 2020, NDA 1 2021, NDA 2 2025. This one: NDA 2 2025

    63
    What is the value of sin⁡θ\sin\theta if θ\theta is the acute angle between the lines whose equations are px+qy=p+qpx+qy=p+q and p(x−y)+q(x+y)=2qp(x-y)+q(x+y)=2q?

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  2. Question 2

    Matrices & Determinants. This type asked 8 times: NDA 1 2017, NDA 2 2017, NDA 1 2018, NDA 2 2019, NDA 1 2020, NDA 1 2021, NDA 2 2022, NDA 2 2024. This one: NDA 2 2024

    1
    Let XX be a matrix of order 3×33 \times 3, YY be a matrix of order 2×32 \times 3 and ZZ be a matrix of order 3×23 \times 2. Which of the following statements are correct? A. (ZY)X(ZY)X is defined and is a square matrix of order 3. B. Y(XZ)Y(XZ) is defined and is a square matrix of order 2. C. X(YZ)X(YZ) is not defined. Select the answer using the code given below.

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  3. Question 3

    Probability. This type asked 7 times: NDA 2 2017, NDA 2 2018, NDA 2 2019, NDA 1 2020, NDA 2 2023, NDA 1 2025, NDA 1 2026. This one: NDA 1 2026

    113
    In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then what is the probability that he was guessing?

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  4. Question 4

    Sequence & Series. This type asked 7 times: NDA 1 2017, NDA 2 2017, NDA 1 2019, NDA 2 2019, NDA 2 2024, NDA 1 2025, NDA 1 2026. This one: NDA 1 2026

    6
    The sum of the first nn terms of an AP is 3n2+5n3n^2+5n. If the mthm^{\text{th}} term of the AP is 68, then what is the value of mm?

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  5. Question 5

    Application of Derivatives. This type asked 7 times: NDA 1 2017, NDA 2 2017, NDA 2 2018, NDA 1 2021, NDA 1 2023, NDA 1 2024, NDA 2 2025. This one: NDA 2 2025

    99
    Consider the following statements regarding the function f(x)=1x−5f(x)=\dfrac{1}{x-5}: Statement-I: f(x)f(x) is decreasing on the intervals x<5x<5 and x>5x>5. Statement-II: f′(x)>0f'(x)>0 for all x≠5x\neq5. Which one of the following is correct?

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