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Day 4: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 6 times: NDA 1 2017, NDA 1 2018, NDA 1 2019, NDA 2 2023, NDA 1 2024, NDA 1 2026. This one: NDA 1 2026

    24
    What is (((A∩B)∪(A−B))−((A∩B)∪(B−A)))∪A(((A\cap B)\cup(A-B))-((A\cap B)\cup(B-A)))\cup A equal to?

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  2. Question 2

    Differential Equations. This type asked 6 times: NDA 1 2017, NDA 2 2017, NDA 1 2018, NDA 1 2019, NDA 2 2019, NDA 2 2023. This one: NDA 2 2023

    69
    What are the order and degree respectively of x2 ⁣(d3ydx3)2+(dydx)4+sin⁡x=0x^2\!\left(\frac{d^3y}{dx^3}\right)^2+\left(\frac{dy}{dx}\right)^4+\sin x=0?

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  3. Question 3

    Application of Derivatives. This type asked 5 times: NDA 2 2018, NDA 2 2019, NDA 1 2022, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    97
    Let f(x)=∫xexdxf(x) = \int xe^x dx. Then f(x)f(x) decreases in the interval

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  4. Question 4

    Limits & Continuity. This type asked 5 times: NDA 1 2018, NDA 2 2018, NDA 1 2020, NDA 2 2021, NDA 2 2026. This one: NDA 2 2026

    86
    Consider the following statements in respect of the given function : f(x)={x3∣x∣,x≠00,x=0f(x) = \begin{cases} \frac{x^3}{|x|}, & x \ne 0 \\ 0, & x = 0 \end{cases} I. f(x)f(x) is continuous everywhere. II. f(x)f(x) is differentiable everywhere. Which of the statements given above is/are correct?

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  5. Question 5

    Matrices & Determinants. This type asked 5 times: NDA 1 2023, NDA 2 2023, NDA 1 2024, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    20
    If AA is a square matrix of order 3 and ∣A∣=4|A| = 4, then what is ∣adjA∣|\text{adj} A| equal to?

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