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Day 129: NDA Maths

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

  1. Question 1

    Sets & Relations. Asked once: NDA 1 2021 (same type asked 3 times)

    36
    Consider the following statements: 1. The null set is a subset of every set. 2. Every set is a subset of itself. 3. If a set has 10 elements, then its power set will have 1024 elements. Which of the above statements are correct?

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  2. Question 2

    Indefinite Integration. Asked once: NDA 1 2020 (same type asked 3 times)

    83
    What is ∫(elog⁡x+sin⁡x)cos⁡x dx\int(e^{\log x}+\sin x)\cos x\,dx equal to?

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  3. Question 3

    Limits & Continuity. Asked once: NDA 1 2020 (same type asked 3 times)

    71
    What is lim⁡x→1x+x2+x3−3x−1\lim_{x\to1}\frac{x+x^2+x^3-3}{x-1} equal to?

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  4. Question 4

    Quadratic Equations. Asked once: NDA 2 2019 (same type asked 3 times)

    16
    Under which one of the following conditions will the quadratic equation x2+mx+2=0x^{2} + mx + 2 = 0 always have real roots ?

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  5. Question 5

    Vectors. Asked once: NDA 2 2018 (same type asked 3 times)

    63
    Let ∣a⃗∣≠0,∣b⃗∣≠0|\vec{a}|\neq 0, |\vec{b}|\neq 0. (a⃗+b⃗)⋅(a⃗+b⃗)=∣a⃗∣2+∣b⃗∣2(\vec{a}+\vec{b})\cdot(\vec{a}+\vec{b})=|\vec{a}|^2+|\vec{b}|^2 holds if and only if

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