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Day 222: NDA Maths

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

  1. Question 1

    Complex Numbers. Asked once: NDA 1 2018 (same type asked 4 times)

    20
    The modulus-amplitude form of 3+i\sqrt{3}+i, where i=−1i = \sqrt{-1} is

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  2. Question 2

    Functions. Asked once: NDA 1 2017 (same type asked 4 times)

    77
    Let f:[−6,6]→Rf:[-6,6]\to\mathbb{R} be defined by f(x)=x2−3f(x)=x^2-3. Consider the following: 1. (f∘f∘f)(−1)=(f∘f∘f)(1)(f\circ f\circ f)(-1) = (f\circ f\circ f)(1) 2. (f∘f∘f)(−1)−4(f∘f∘f)(1)=(f∘f)(0)(f\circ f\circ f)(-1) - 4(f\circ f\circ f)(1) = (f\circ f)(0) Which of the above is/are correct?

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  3. Question 3

    Differentiation. Asked once: NDA 2 2018 (same type asked 4 times)

    71
    Let the slope of the curve y=cos⁡−1(sin⁡x)y=\cos^{-1}(\sin x) be tan⁡θ\tan\theta. Then the value of θ\theta in the interval (0,π)(0,\pi) is

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  4. Question 4

    Trigonometric Equations. Asked once: NDA 2 2018 (same type asked 4 times)

    44
    If cos⁡α\cos\alpha and cos⁡β\cos\beta (0<α<β<π)(0 < \alpha < \beta < \pi) are the roots of the quadratic equation 4x2−3=04x^2 - 3 = 0, then what is the value of sec⁡α×sec⁡β\sec\alpha \times \sec\beta?

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  5. Question 5

    Limits & Continuity. Asked once: NDA 1 2018 (same type asked 4 times)

    80
    If f(x)=x2−9x2−2x−3f(x)=\frac{x^2-9}{x^2-2x-3}, x≠3x\ne3 is continuous at x=3, then?

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