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Day 275: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Conics. Asked once: NDA 2 2022

    61
    An equilateral triangle is inscribed in a parabola x2=3yx^2 = \sqrt{3}y where one vertex of the triangle is at the vertex of the parabola. If p is the length of side of the triangle and q is the length of the latus rectum, then which one of the following is correct?

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  2. Question 2

    Definite Integration. Asked once: NDA 2 2021

    97
    If ∫−20f(x) dx=k\int_{-2}^{0}f(x)\,dx=k, then ∫−20∣f(x)∣ dx\int_{-2}^{0}|f(x)|\,dx is

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  3. Question 3

    Differential Equations. Asked once: NDA 1 2020

    82
    The solution of the differential equation dy=(1+y2) dxdy=(1+y^2)\,dx is

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  4. Question 4 (case study, 2 parts)

    Differentiation. Asked once: NDA 1 2025

    The slope of the tangent to the curve y=f(x)y = f(x) at (x,f(x))(x, f(x)) is 4 for every real number xx and the curve passes through the origin.
    77
    What is the nature of the curve?

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    78
    What is the area bounded by the curve, the xx-axis and the line x=4x = 4?

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  5. Question 5 (case study, 2 parts)

    Functions. Asked once: NDA 1 2025

    Let f={(1,1),(2,4),(3,7),(4,10)}f = \{(1,1),(2,4),(3,7),(4,10)\}.
    87
    If f(x)=px+qf(x) = px + q, then what is the value of (p+q)(p + q)?

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    88
    Consider the following statements: (I). ff is one-one function. (II). ff is onto function if the codomain is the set of natural numbers. Which of the statements given above is/are correct?

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