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Day 81: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Complex Numbers. This type asked 2 times: NDA 2 2018, NDA 2 2021. This one: NDA 2 2021

    34
    Consider the following statements in respect of the roots of the equation x3−8=0x^{3}-8=0: 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?

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  2. Question 2 (case study, 2 parts)

    Lines. This type asked 2 times: NDA 2 2019, NDA 2 2021. This one: NDA 2 2021

    Direction: Consider the following for the next two (02) items that follow. The two vertices of an equilateral triangle are (0, 0) and (2, 2).
    53
    Consider the following statements: 1. The third vertex has at least one irrational coordinate. 2. The area is irrational. Which of the above statements is/are correct?

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    54
    The difference of coordinates of the third vertex is

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  3. Question 3

    Matrices & Determinants. This type asked 2 times: NDA 1 2018, NDA 2 2021. This one: NDA 2 2021

    30
    Let A=(02−20)A=\begin{pmatrix}0&2\\-2&0\end{pmatrix} and (mI+nA)2=A(mI+nA)^{2}=A where mm, nn are positive real numbers and II is the identity matrix. What is (m+n)(m+n) equal to?

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  4. Question 4

    Matrices & Determinants. This type asked 2 times: NDA 2 2017, NDA 2 2021. This one: NDA 2 2021

    21
    For what values of kk is the system of equations 2k2x+3y−1=02k^{2}x+3y-1=0, 7x−2y+3=07x-2y+3=0, 6kx+y+1=06kx+y+1=0 consistent?

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  5. Question 5

    Permutation & Combination. This type asked 2 times: NDA 1 2019, NDA 2 2021. This one: NDA 2 2021

    19
    Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two of these points is 380. 2. The number of triangles that can be drawn by joining any three of these points is 1140. Select the correct answer using the code given below.

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