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Day 229: NDA Maths

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

  1. Question 1

    Definite Integration. Asked once: NDA 1 2018 (same type asked 5 times)

    82
    What is ∫02[x2] dx\int_{0}^{\sqrt{2}}[x^2]\,dx equal to (where [.] is greatest integer function)?

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  2. Question 2

    Differential Equations. Asked once: NDA 1 2020 (same type asked 5 times)

    74
    The order and degree of the differential equation kdydx=∫[1+(dydx)2]23dxk\frac{dy}{dx}=\int\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{2}{3}}dx are respectively

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  3. Question 3

    Sequence & Series. Asked once: NDA 2 2021 (same type asked 5 times)

    2
    If xx, yy, zz are in GP, then which of the following is/are correct? 1. ln⁡(3x)\ln(3x), ln⁡(3y)\ln(3y), ln⁡(3z)\ln(3z) are in AP 2. xyz+ln⁡(x)xyz + \ln(x), xyz+ln⁡(y)xyz + \ln(y), xyz+ln⁡(z)xyz + \ln(z) are in HP Select the correct answer using the code given below.

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  4. Question 4

    3D Geometry. Asked once: NDA 2 2019 (same type asked 5 times)

    56
    A point on a line has coordinates (p+1, p−3, 2p)(p+1,\, p-3,\, \sqrt{2}p) where pp is any real number. What are the direction cosines of the line ?

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  5. Question 5

    Binomial Distribution. Asked once: NDA 2 2018 (same type asked 5 times)

    107
    8 coins are tossed simultaneously. The probability of getting at least 6 heads is

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