PYQ Vault

Day 300: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    3D Geometry. Asked once: NDA 2 2019

    59
    A straight line passes through the point (1,1,1)(1, 1, 1) makes an angle 60° with the positive direction of zz-axis, and the cosine of the angles made by it with the positive directions of the yy-axis and the xx-axis are in the ratio 3:1\sqrt{3}:1. What is the acute angle between the two possible positions of the line ?

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  2. Question 2

    Application of Derivatives. Asked once: NDA 2 2022

    93
    Consider the following statements in respect of the function f(x)={∣x∣+1,0<∣x∣≤31,x=0f(x) = \begin{cases}|x|+1, & 0<|x|\leq3\\1, & x=0\end{cases}: 1. The function attains maximum value only at x=3 2. The function attains local minimum only at x=0 Which of the statements given above is/are correct?

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  3. Question 3

    Binomial Theorem. Asked once: NDA 1 2018

    28
    What is C(n,r)+2C(n,r−1)+C(n,r−2)C(n,r) + 2C(n,r-1) + C(n,r-2) equal to?

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  4. Question 4

    Circles. Asked once: NDA 1 2017

    55
    What is the equation of the circle which passes through the points (3,−2)(3, -2) and (−2,0)(-2, 0) and having its centre on the line 2x−y−3=02x - y - 3 = 0?

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  5. Question 5 (case study, 3 parts)

    Complex Numbers. Asked once: NDA 2 2022

    Consider the following for the next three (03) items that follow: Let z=1+isin⁡θ1−isin⁡θz = \frac{1+i\sin\theta}{1-i\sin\theta} where i=−1i = \sqrt{-1}
    16
    What is the modulus of zz?

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    17
    What is angle θ\theta such that zz is purely real?

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    18
    What is angle θ\theta such that zz is purely imaginary?

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