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Day 121: NDA Maths

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

  1. Question 1

    Statistics. Asked once: NDA 2 2024 (same type asked 3 times)

    102
    The mean of nn observations 1,4,9,16,…,n21,4,9,16,\ldots,n^2 is 130. What is the value of nn?

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  2. Question 2

    Trigonometric Identities. Asked once: NDA 1 2024 (same type asked 3 times)

    43
    What is sin⁡10°⋅sin⁡50°+sin⁡50°⋅sin⁡250°+sin⁡250°⋅sin⁡10°\sin10°\cdot\sin50°+\sin50°\cdot\sin250°+\sin250°\cdot\sin10° equal to?

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  3. Question 3

    Application of Derivatives. Asked once: NDA 1 2018 (same type asked 3 times)

    50
    The maximum value of sin⁡(x+π/5)+cos⁡(x+π/5)\sin(x+\pi/5) + \cos(x+\pi/5), where x∈(0,π/2)x \in (0, \pi/2), is attained at

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  4. Question 4

    Circles. Asked once: NDA 1 2020 (same type asked 3 times)

    51
    The center of the circle (x−2a)(x−2b)+(y−2c)(y−2d)=0(x-2a)(x-2b)+(y-2c)(y-2d)=0 is

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  5. Question 5 (case study, 2 parts)

    Functions. Asked once: NDA 1 2024 (same type asked 3 times)

    Let f(x)f(x) and g(x)g(x) be two functions such that g(x)=x−1xg(x)=x-\dfrac{1}{x} and f ⁣∘ ⁣g(x)=x3−1x3f\!\circ\! g(x)=x^3-\dfrac{1}{x^3}.
    85
    What is g[f(x)−3x]g[f(x)-3x] equal to?

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    86
    What is f′′(x)f''(x) equal to?

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