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Day 151: NDA Maths

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

  1. Question 1 (case study, 2 parts)

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

    Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the integrals I1=∫0πx dx1+sin⁡xI_{1} = \displaystyle\int_{0}^{\pi} \dfrac{x\,dx}{1+\sin x} and I2=∫0π(π−x) dx1−sin⁡(π+x)I_{2} = \displaystyle\int_{0}^{\pi} \dfrac{(\pi-x)\,dx}{1-\sin(\pi+x)}.
    94
    What is the value of I1I_{1} ?

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    95
    What is the value of I1+I2I_{1} + I_{2} ?

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  2. Question 2

    Definite Integration. Asked once: NDA 1 2022 (same type asked 2 times)

    64
    What is ∫−2−1x∣x∣ dx\int_{-2}^{-1}\frac{x}{|x|}\,dx equal to?

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  3. Question 3

    Functions. Asked once: NDA 1 2020 (same type asked 2 times)

    89
    What is the minimum value of ∣x−1∣|x-1|, where x∈Rx\in\mathbb{R}?

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  4. Question 4

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

    74
    The function f:X→Yf:X\to Y defined by f(x)=cos⁡xf(x)=\cos x, where x∈Xx\in X, is one-one and onto if XX and YY are respectively equal to

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  5. Question 5

    Height & Distance. Asked once: NDA 1 2022 (same type asked 2 times)

    34
    A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height hh. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ\theta and 2θ2\theta respectively. What is the height of the tower?

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