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Day 198: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 1 2017 (same type asked 3 times)

    81
    Let f(x)={x,x is rational0,x is irrationalf(x)=\begin{cases}x, & x\text{ is rational}\\0, & x\text{ is irrational}\end{cases} and g(x)={0,x is rationalx,x is irrationalg(x)=\begin{cases}0, & x\text{ is rational}\\x, & x\text{ is irrational}\end{cases}. If f:R→Rf:\mathbb{R}\to\mathbb{R} and g:R→Rg:\mathbb{R}\to\mathbb{R}, then (f−g)(f-g) is

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  2. Question 2

    Lines. Asked once: NDA 1 2017 (same type asked 3 times)

    58
    What is the equation of the straight line parallel to 2x+3y+1=02x+3y+1=0 and passes through the point (−1,2)(-1, 2)?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2020 (same type asked 3 times)

    50
    Consider the following in respect of a non-singular matrix of order 3: 1. A(adj A)=(adj A)AA(\text{adj }A)=(\text{adj }A)A 2. ∣adj A∣=∣A∣|\text{adj }A|=|A|. Which of the above statements is/are correct?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2021 (same type asked 3 times)

    12
    How many matrices of different orders are possible with elements comprising all prime numbers less than 30?

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  5. Question 5

    Properties of Triangle. Asked once: NDA 2 2017 (same type asked 3 times)

    39
    In triangle ABCABC, if sin⁡2A+sin⁡2B+sin⁡2Ccos⁡2A+cos⁡2B+cos⁡2C=2\dfrac{\sin^2 A + \sin^2 B + \sin^2 C}{\cos^2 A + \cos^2 B + \cos^2 C} = 2, then the triangle is

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