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Day 35: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Applications of Integration. This type asked 3 times: NDA 1 2021, NDA 2 2022, NDA 1 2024. This one: NDA 1 2024

    The circle x2+y2−2x=0x^2+y^2-2x=0 is partitioned by line y=xy=x in two segments. Let A1,A2A_1,A_2 be the areas of major and minor segments respectively.
    97
    What is the value of A1A_1?

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    98
    What is the value of 2(A1+A2)A1−3A2\dfrac{2(A_1+A_2)}{A_1-3A_2}?

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  2. Question 2

    Binomial Theorem. This type asked 3 times: NDA 2 2019, NDA 1 2023, NDA 1 2024. This one: NDA 1 2024

    31
    If the 4th term in the expansion of (mx+1x)n\left(mx+\dfrac{1}{x}\right)^n is 52\dfrac{5}{2}, then what is the value of mnmn?

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  3. Question 3 (case study, 2 parts)

    Definite Integration. This type asked 3 times: NDA 2 2022, NDA 2 2023, NDA 1 2024. This one: NDA 1 2024

    Let ϕ(a)=∫aa+100π∣sin⁡x∣ dx\phi(a)=\displaystyle\int_a^{a+100\pi}|\sin x|\,dx.
    89
    What is ϕ(a)\phi(a) equal to?

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    90
    What is ϕ′(a)\phi'(a) equal to?

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  4. Question 4

    Functions. This type asked 3 times: NDA 1 2017, NDA 1 2021, NDA 1 2024. This one: NDA 1 2024

    22
    Let A={x∈R:−1<x<1}A=\{x\in\mathbb{R}:-1<x<1\}. Which of the following is/are bijective functions from AA to itself? (A) f(x)=x∣x∣f(x)=x|x| (B) g(x)=cos⁡(πx)g(x)=\cos(\pi x) Select the correct answer using the code given below:

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  5. Question 5

    Lines. This type asked 3 times: NDA 1 2017, NDA 1 2019, NDA 1 2024. This one: NDA 1 2024

    59
    What is the equation of the straight line passing through the point (−sin⁡θ,cos⁡θ)(-\sin\theta,\cos\theta) and perpendicular to the line xcos⁡θ+ysin⁡θ=9x\cos\theta+y\sin\theta=9?

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