PYQ Vault

Day 41: NDA Maths

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

  1. Question 1

    Indefinite Integration. This type asked 3 times: NDA 1 2017, NDA 1 2020, NDA 2 2021. This one: NDA 2 2021

    93
    What is ∫dxx(x2+1)\int\frac{dx}{x(x^{2}+1)} equal to?

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  2. Question 2

    Limits & Continuity. This type asked 3 times: NDA 2 2017, NDA 2 2019, NDA 2 2021. This one: NDA 2 2021

    78
    Consider the following statements in respect of the function f(x)=sin⁡ ⁣(1x2)f(x)=\sin\!\left(\frac{1}{x^{2}}\right), x≠0x\ne0: 1. It is continuous at x=0x=0, if f(0)=0f(0)=0. 2. It is continuous at x=2πx=\frac{2}{\sqrt{\pi}}. Which of the above statements is/are correct?

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  3. Question 3

    Sets & Relations. This type asked 3 times: NDA 2 2019, NDA 1 2021, NDA 2 2021. This one: NDA 2 2021

    38
    Consider three sets XX, YY and ZZ having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S=(X−Y)∪ZS=(X-Y)\cup Z. How many proper subsets does SS have?

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  4. Question 4

    Indefinite Integration. This type asked 3 times: NDA 2 2018, NDA 1 2020, NDA 1 2021. This one: NDA 1 2021

    100
    What is ∫e(2ln⁡x+ln⁡x2) dx\int e^{(2\ln x+\ln x^2)}\,dx equal to?

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  5. Question 5

    Limits & Continuity. This type asked 3 times: NDA 2 2018, NDA 1 2020, NDA 1 2021. This one: NDA 1 2021

    79
    What is lim⁡x→−1x3+x2x2+3x+2\lim_{x\to -1}\frac{x^3+x^2}{x^2+3x+2} equal to?

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