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Day 80: NDA Maths

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

  1. Question 1 (case study, 3 parts)

    Statistics. This type asked 2 times: NDA 1 2020, NDA 1 2022. This one: NDA 1 2022

    Consider the following frequency distribution for the next three (03) items that follow: Class: 0-20, 20-40, 40-60, 60-80, 80-100; Frequency: 17, p+qp+q, 32, p−3qp-3q, 19. The total frequency is 120. The mean is 50.
    118
    What is the value of pp?

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    119
    What is the value of qq?

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    120
    If the frequency of each class is doubled, then what would be the mean?

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  2. Question 2

    Vectors. This type asked 2 times: NDA 2 2019, NDA 1 2022. This one: NDA 1 2022

    100
    Let a⃗\vec{a} and b⃗\vec{b} be two unit vectors such that ∣a⃗−b⃗∣<2|\vec{a}-\vec{b}|<2. If 2θ2\theta is the angle between a⃗\vec{a} and b⃗\vec{b}, then which one of the following is correct?

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  3. Question 3

    3D Geometry. This type asked 2 times: NDA 1 2020, NDA 2 2021. This one: NDA 2 2021

    61
    The locus of a point P(x,y,z)P(x,y,z) which moves in such a way that z=7z=7 is a

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  4. Question 4

    Application of Derivatives. This type asked 2 times: NDA 2 2017, NDA 2 2021. This one: NDA 2 2021

    91
    Consider the following statements in respect of the function f(x)=x+1xf(x)=x+\frac{1}{x}: 1. The local maximum value of f(x)f(x) is less than its local minimum value. 2. The local maximum value of f(x)f(x) occurs at x=1x=1. Which of the above statements is/are correct?

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  5. Question 5

    Application of Derivatives. This type asked 2 times: NDA 1 2017, NDA 2 2021. This one: NDA 2 2021

    92
    What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?

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