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Day 358: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 1 2020

    86
    If f(x)=2x−x2f(x)=2x-x^2, then what is the value of f(x+2)+f(x−2)f(x+2)+f(x-2) when x=0x=0?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2017

    92
    Let f(x)={2x+1,−3<x<−2x−1,−2≤x<0x+2,0≤x<1f(x)=\begin{cases}2x+1, & -3<x<-2\\x-1, & -2\leq x<0\\x+2, & 0\leq x<1\end{cases}. Which one of the following statements is correct in respect of the above function?

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  3. Question 3

    Lines. Asked once: NDA 1 2019

    59
    The straight lines x+y−4=0x+y-4=0, 3x+y−4=03x+y-4=0 and x+3y−4=0x+3y-4=0 form a triangle, which is

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2023

    9
    If A=(200030004)A = \begin{pmatrix}2&0&0\\0&3&0\\0&0&4\end{pmatrix}, then which of the following statements are correct? (1) AnA^n will always be singular for any positive integer nn. (2) AnA^n will always be a diagonal matrix for any positive integer nn. (3) AnA^n will always be a symmetric matrix for any positive integer nn.

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  5. Question 5

    Probability. Asked once: NDA 2 2022

    113
    A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are

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