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Day 360: NDA Maths

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

  1. Question 1 (case study, 3 parts)

    Functions. Asked once: NDA 2 2019

    Directions for the following three (03) items : Read the following information and answer the three items that follow : Let f(x)=x2+2x−5f(x) = x^{2} + 2x - 5 and g(x)=5x+30g(x) = 5x + 30.
    91
    What are the roots of the equation g[f(x)]=0g[f(x)] = 0 ?

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    92
    Consider the following statements : 1. f[g(x)]f[g(x)] is a polynomial of degree 3. 2. g[g(x)]g[g(x)] is a polynomial of degree 2. Which of the above statements is/are correct ?

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    93
    If h(x)=5f(x)−xg(x)h(x) = 5f(x) - xg(x), then what is the derivative of h(x)h(x) ?

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  2. Question 2

    Lines. Asked once: NDA 1 2019

    56
    The points (1,3)(1,3) and (5,1)(5,1) are two opposite vertices of a rectangle. The other two vertices lie on the line y=2x+cy=2x+c. What is the value of c?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2023

    13
    If aa, bb, cc are in AP, then what is ∣x+1x+2x+3x+2x+3x+4x+ax+bx+3∣\begin{vmatrix}x+1&x+2&x+3\\x+2&x+3&x+4\\x+a&x+b&x+3\end{vmatrix} equal to?

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  4. Question 4

    Probability. Asked once: NDA 2 2022

    103
    If n>7n > 7, then what is the probability that C(n,7)C(n, 7) is a multiple of 7?

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2017

    22
    The sum of the first nn terms of the series 12+34+78+1516+…\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{7}{8}+\dfrac{15}{16}+\ldots is equal to

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