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Day 139: NDA Maths

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

  1. Question 1

    Complex Numbers. Asked once: NDA 1 2021 (same type asked 2 times)

    40
    Consider the following statements in respect of an arbitrary complex number ZZ: 1. The difference of ZZ and its conjugate is an imaginary number. 2. The sum of ZZ and its conjugate is a real number. Which of the above statements is/are correct?

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  2. Question 2

    Conics. Asked once: NDA 1 2021 (same type asked 2 times)

    64
    If any point on a hyperbola is (3tan⁡θ,2sec⁡θ)(3\tan\theta, 2\sec\theta), then what is the eccentricity of the hyperbola?

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  3. Question 3

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

    87
    If xmyn=am+nx^m y^n=a^{m+n}, then what is dydx\frac{dy}{dx} equal to?

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  4. Question 4

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

    80
    Let f(x)f(y)=f(xy)f(x)f(y)=f(xy) for all real x,yx,y. If f(2)=4f(2)=4, then what is the value of f ⁣(12)f\!\left(\dfrac{1}{2}\right)?

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  5. Question 5

    Lines. Asked once: NDA 1 2021 (same type asked 2 times)

    58
    If the lines y+px=1y + px = 1 and y−qx=2y - qx = 2 are perpendicular, then which one of the following is correct?

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