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Day 224: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Applications of Integration. Asked once: NDA 1 2021 (same type asked 3 times)

    81
    What is the area bounded by y=16−x2y=\sqrt{16-x^2}, y≥0y\geq0 and the xx-axis?

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  2. Question 2

    Definite Integration. Asked once: NDA 2 2022 (same type asked 3 times)

    95
    If ∫0π/2(sin⁡4x+cos⁡4x) dx=k\int_0^{\pi/2}(\sin^4x+\cos^4x)\,dx = k, then what is the value of ∫020π(sin⁡4x+cos⁡4x) dx\int_0^{20\pi}(\sin^4x+\cos^4x)\,dx?

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  3. Question 3

    Sequence & Series. Asked once: NDA 1 2018 (same type asked 3 times)

    23
    If x=1−y+y2−y3+…x = 1 - y + y^2 - y^3 + \ldots where ∣y∣<1|y| < 1, then which is correct?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2018 (same type asked 2 times)

    28
    Consider the following in respect of matrices A, B and C of same order: 1. (A+B+C)′=A′+B′+C′(A+B+C)' = A' + B' + C' 2. (AB)′=A′B′(AB)' = A'B' 3. (ABC)′=C′B′A′(ABC)' = C'B'A' where A' is the transpose of the matrix A. Which of the above are correct?

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  5. Question 5

    Lines. Asked once: NDA 2 2018 (same type asked 8 times)

    53
    The angle between the two lines lx+my+n=0lx + my + n = 0 and l′x+m′y+n′=0l'x + m'y + n' = 0 is given by tan⁡−1θ\tan^{-1}\theta. What is θ\theta equal to?

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