PYQ Vault

Day 9: NDA Maths

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

  1. Question 1

    3D Geometry. This type asked 4 times: NDA 2 2017, NDA 1 2020, NDA 1 2025, NDA 2 2026. This one: NDA 2 2026

    62
    A line makes angles α\alpha, β\beta and γ\gamma with the positive directions of xx-axis, yy-axis and zz-axis respectively such that α+β=90∘\alpha + \beta = 90^\circ. Which of the following statements is/are correct? I. The maximum value of cos⁡α+cos⁡β\cos \alpha + \cos \beta is 2\sqrt{2}. II. The minimum value of cos⁡α+cos⁡β+cos⁡γ\cos \alpha + \cos \beta + \cos \gamma is 1. Select the answer using the code given below.

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  2. Question 2

    Complex Numbers. This type asked 4 times: NDA 2 2017, NDA 2 2021, NDA 2 2023, NDA 2 2026. This one: NDA 2 2026

    36
    If z=x+iyz = x + iy be such that ∣z+λiz−λi∣=1\left| \frac{z + \lambda i}{z - \lambda i} \right| = 1, where i=−1i = \sqrt{-1} and λ\lambda is a positive real number, then which of the following statements is/are correct? I. zz lies on the line y=xy = x. II. The amplitude of zz is π4\frac{\pi}{4}. Select the answer using the code given below.

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  3. Question 3

    Differential Equations. This type asked 4 times: NDA 1 2019, NDA 1 2022, NDA 2 2022, NDA 2 2026. This one: NDA 2 2026

    79
    What is the differential equation of the family of straight lines passing through the origin?

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  4. Question 4

    Differential Equations. This type asked 4 times: NDA 1 2018, NDA 2 2021, NDA 1 2023, NDA 2 2026. This one: NDA 2 2026

    80
    What is the degree of the differential equation representing the family of curves y2=c xy^2 = \sqrt{c}\,x, where cc is a positive parameter?

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  5. Question 5

    Differential Equations. This type asked 4 times: NDA 2 2018, NDA 1 2019, NDA 2 2025, NDA 2 2026. This one: NDA 2 2026

    98
    What is the solution of the differential equation dydx=1+xcot⁡(y−x)\frac{dy}{dx} = 1 + x \cot(y - x)?

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