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Day 96: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Definite Integration. Asked once: NDA 1 2025 (same type asked 5 times)

    Let f(x)=[x2]f(x)=[x^2], where [⋅][\cdot] is the greatest integer function.
    99
    What is ∫23f(x) dx\int_{\sqrt{2}}^{\sqrt{3}} f(x)\,dx equal to?

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    100
    What is ∫22f(x) dx\int_{\sqrt{2}}^{2} f(x)\,dx equal to?

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  2. Question 2

    Differential Equations. Asked once: NDA 1 2024 (same type asked 5 times)

    75
    What are the order and degree respectively of the differential equation (2−(dydx)2)0.6=d2ydx2\left(2-\left(\dfrac{dy}{dx}\right)^2\right)^{0.6}=\dfrac{d^2y}{dx^2}?

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  3. Question 3

    Sequence & Series. Asked once: NDA 2 2025 (same type asked 5 times)

    5
    If (10+log⁡10x)(10 + \log_{10} x), (10+log⁡10y)(10 + \log_{10} y) and (10+log⁡10z)(10 + \log_{10} z) are in AP, then consider the following statements: I. The GM of xx and zz is y2y^2. II. The AM of log⁡10x\log_{10} x and log⁡10z\log_{10} z is log⁡10y\log_{10} y. Which of the statements given above is/are correct?

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  4. Question 4

    3D Geometry. Asked once: NDA 1 2024 (same type asked 5 times)

    54
    If ⟨l,m,n⟩\langle l,m,n\rangle are the direction cosines of a normal to the plane 2x−3y+6z+4=02x-3y+6z+4=0, then what is the value of 49(7l2+m2−n2)49(7l^2+m^2-n^2)?

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  5. Question 5

    Binomial Distribution. Asked once: NDA 2 2024 (same type asked 5 times)

    117
    The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?

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