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Day 145: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    3D Geometry. Asked once: NDA 1 2023 (same type asked 2 times)

    Consider the following for the next two (02) items that follow: Let A(1,−1,2)A(1,-1,2) and B(2,1,−1)B(2,1,-1) be the end points of the diameter of the sphere x2+y2+z2+2ux+2vy+2wz−1=0x^{2}+y^{2}+z^{2}+2ux+2vy+2wz-1=0.
    61
    What is u+v+wu+v+w equal to?

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    62
    If P(x,y,z)P(x,y,z) is any point on the sphere, then what is PA2+PB2PA^{2}+PB^{2} equal to?

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  2. Question 2

    Application of Derivatives. Asked once: NDA 2 2021 (same type asked 2 times)

    95
    What is the condition that f(x)=x3+x2+kxf(x)=x^{3}+x^{2}+kx has no local extremum?

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  3. Question 3

    Binomial Theorem. Asked once: NDA 1 2017 (same type asked 2 times)

    26
    The expansion of (x−y)n(x-y)^n, n≥5n \geq 5 is done in descending powers of xx. If the sum of the fifth and sixth terms is zero, then xy\dfrac{x}{y} is equal to

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  4. Question 4

    Circles. Asked once: NDA 1 2021 (same type asked 2 times)

    56
    What is the radius of the circle 4x2+4y2−20x+12y−15=04x^2+4y^2-20x+12y-15=0?

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  5. Question 5

    Conics. Asked once: NDA 2 2019 (same type asked 2 times)

    55
    If the angle between the lines joining the end points of minor axis of the ellipse x2a2+y2b2=1\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 with one of its foci is π2\dfrac{\pi}{2}, then what is the eccentricity of the ellipse ?

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