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Day 28: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 3 times: NDA 1 2022, NDA 2 2022, NDA 1 2026. This one: NDA 1 2026

    25
    Let A and B be two sets. For some set C, both A∩CA\cap C and B∩CB\cap C are empty sets and A∪C=B∪CA\cup C=B\cup C. Which of the following is/are true? I. C=φC=\varphi II. A=BA=B III. A∪B=CA\cup B=C. Select the answer using the code given below.

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  2. Question 2

    Trigonometric Identities. This type asked 3 times: NDA 1 2018, NDA 2 2024, NDA 1 2026. This one: NDA 1 2026

    27
    If α\alpha and β\beta are complementary angles such that α−β=π6\alpha-\beta=\dfrac{\pi}{6} and mtan⁡β=ntan⁡αm\tan\beta=n\tan\alpha, then what is (m+nm−n)\left(\dfrac{m+n}{m-n}\right) equal to?

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  3. Question 3 (case study, 2 parts)

    3D Geometry. This type asked 3 times: NDA 2 2017, NDA 1 2019, NDA 2 2025. This one: NDA 2 2025

    For the following two (02) items: A plane PP is parallel to the line having direction ratios ⟨1,3,2⟩\langle1,3,2\rangle and contains the line of intersection of the planes 6x+4y−5z=26x+4y-5z=2 and x−2y+3z=0x-2y+3z=0.
    51
    Which of the following are the direction ratios of the line of intersection of the given planes?

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    52
    What is the equation of the plane PP?

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  4. Question 4

    Application of Derivatives. This type asked 3 times: NDA 1 2020, NDA 1 2021, NDA 2 2025. This one: NDA 2 2025

    96
    A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct? I. The rectangle of the largest area is the square. II. It is possible to form a rectangle of an area of 27 cm2^2. Select the answer using the code given below.

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  5. Question 5

    Binomial Distribution. This type asked 3 times: NDA 2 2023, NDA 1 2025, NDA 2 2025. This one: NDA 2 2025

    116
    Let XX be a random variable following binomial distribution with parameters n=5n=5 and p=kp=k. Further, P(X=1)=0.4096P(X=1)=0.4096 and P(X=2)=0.2048P(X=2)=0.2048. What is the value of kk?

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