\documentclass[a4paper]{article}

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\usepackage{multicol}
\usepackage{graphicx}

\usepackage{fancybox}

\usepackage{amsmath}

\usepackage{tikz}

\usepackage[box,separateanswersheet]{automultiplechoice}


\AMCboxDimensions{shape=oval,width=1.8ex,height=2.5ex}

\geometry{hmargin=2cm,top=3cm,bottom=2cm}

\begin{document}

\scoringDefaultS{b=3,m=-1,e=-1}

\def\AMCformQuestion#1{\vspace{\AMCformVSpace}\par {\sc\footnotesize  Question #1:} }    
\def\AMCchoiceLabel#1{\tiny\Alph{#1}}


\element{Mathematics}{
\begin{question}{Maths:complexe1}
    $\sqrt{-2}\sqrt{-3}=$
    \begin{choiceshoriz}
        \wrongchoice{$\sqrt{6}$}
        \correctchoice{$-\sqrt{6}$}
        \wrongchoice{$i\sqrt{6}$}
        \wrongchoice{None of these}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe2}
    If $\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}$ then:
    \begin{choiceshoriz}
        \wrongchoice{x=1,y=-3}
        \wrongchoice{x=-1,y=3}
        \wrongchoice{x=3,y=1}
        \correctchoice{x=-1,y=-3 or x=1,y=3}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe3}
    The least positive 'n' such that $\left(\frac{2i}{1+i}\right)^{n}$is a positive integer is :
    \begin{choiceshoriz}
        \wrongchoice{2}
        \wrongchoice{4}
        \correctchoice{8}
        \wrongchoice{16}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe4}
    If $z+z^{3}=0$ then which of the following must be true on the complex plane?
    \begin{choiceshoriz}
        \wrongchoice{Re(z)<0}
        \correctchoice{Re(z)=0}
        \wrongchoice{Im(z)=0}
        \wrongchoice{$z^{4}=1$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe5}
    If $x=a+bi$ is a complex number such that $x^{2}=3+4i$ and $x^{3}=2+11i$, then $\left(a+b\right)$is equal to: 
    \begin{choiceshoriz}
        \wrongchoice{2}
        \correctchoice{3}
        \wrongchoice{4}
        \wrongchoice{5}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe6}
    If $z=4+i\sqrt{7}$, then the value of $z^{3}-4z^{2}-9z+91$ is equal to:
    \begin{choiceshoriz}
        \wrongchoice{0}
        \wrongchoice{1}
        \correctchoice{-1}
        \wrongchoice{2}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe7}
    The modulus of $-\frac{1}{2}+i\frac{\sqrt{3}}{2}$ is:
    \begin{choiceshoriz}
        \wrongchoice{0}
        \wrongchoice{-1}
        \correctchoice{1}
        \wrongchoice{2}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe8}
    The amplitude of $-\frac{1}{2}+i\frac{\sqrt{3}}{2}$ is:
    \begin{choiceshoriz}
        \correctchoice{$\frac{2\pi}{3}$}
        \wrongchoice{$\frac{\pi}{3}$}
        \wrongchoice{$\frac{\pi}{6}$}
        \wrongchoice{$\frac{\pi}{4}$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe9}
    The conjugate of $\frac{1-i}{1+i}$ is: 
    \begin{choiceshoriz}
        \wrongchoice{$1$}
        \wrongchoice{$-i$}
        \wrongchoice{$-1$}
        \correctchoice{$i$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe10}
    If $z=3+5i$, then $z^{3}+\bar{z}+198=$is:
    \begin{choiceshoriz}
        \wrongchoice{$-3-5i$}
        \wrongchoice{$-3+5i$}
        \wrongchoice{$3+5i$}
        \correctchoice{$3-5i$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe11}
If $z^{2}+z+1=0$, where$z$ is a complex number, then the value of $\left(z+\dfrac{1}{z}\right)^{2}$is:
    \begin{choiceshoriz}
        \correctchoice{$1$}
        \wrongchoice{$2$}
        \wrongchoice{$3$}
        \wrongchoice{$4$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe12}
    The value of $\sqrt{i}$, where$i=\sqrt{-1}$ is:
    \begin{choiceshoriz}
        \wrongchoice{$\pm\left(\dfrac{i-1}{\sqrt{2}}\right)$}
        \wrongchoice{$\pm\left(\dfrac{i-2}{\sqrt{2}}\right)$}
        \correctchoice{$\pm\left(\dfrac{i+1}{\sqrt{2}}\right)$}
        \wrongchoice{$\pm\left(\dfrac{i+2}{\sqrt{2}}\right)$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe13}
    If $\left(x-iy\right)\left(3+5i\right)$ is the conjugate of $-6-24i$, then:
    \begin{choiceshoriz}
        \wrongchoice{$x=3,y=3$}
        \correctchoice{$x=3,y=-3$}
        \wrongchoice{$x=-3,y=3$}
        \wrongchoice{$x=-3,y=-3$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe14}
    The roots of the equation $x^{2}+x+1=0$ are:
    \begin{choiceshoriz}[o]
        \wrongchoice{Real and Equal}
        \wrongchoice{Real and Unequal}
        \correctchoice{Complex and Conjugate}
        \wrongchoice{None of these}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe15}
    If $arg(z)<0$, then $arg(-z)-arg(z)$ is equal to:
    \begin{choiceshoriz}
        \correctchoice{$\pi$}
        \wrongchoice{$0$}
        \wrongchoice{$-\frac{\pi}{2}$}
        \wrongchoice{$\frac{\pi}{2}$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe16}
The value of $1+\omega^{n}+\omega^{2n}$, when $n$ is a multiple of 3 is:
    \begin{choiceshoriz}
        \wrongchoice{$0$}
        \wrongchoice{$1$}
        \wrongchoice{$2$}
        \correctchoice{$3$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe17}
The value of $1+\omega^{n}+\omega^{2n}$, when $n$ is not a multiple of 3 is:
    \begin{choiceshoriz}
        \correctchoice{$0$}
        \wrongchoice{$1$}
        \wrongchoice{$2$}
        \wrongchoice{$3$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe18}
    If $\bar{z}=-z$, then:
    \begin{choiceshoriz}
        \wrongchoice{$Re(z)<0$}
        \wrongchoice{$Re(z)>0$}
        \correctchoice{$Re(z)=0$}
        \wrongchoice{$Re(z)\neq0$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe19}
    Given the complex numbers $\alpha=\frac{-1+\sqrt{3}i}{2}$ and $\beta=\frac{-1-\sqrt{3}i}{2}$, which of the following is correct?
    \begin{choiceshoriz}[o]
        \wrongchoice{$\alpha=\beta^{2}$}
        \wrongchoice{$\beta=\alpha^{2}$}
        \correctchoice{$\alpha\beta=1$}
        \wrongchoice{All are correct}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe20}
    The additive inverse of$\left(3+i\right)^{2}$ is:
    \begin{choiceshoriz}
        \wrongchoice{$8+6i$}
        \wrongchoice{$8-6i$}
        \wrongchoice{$-8+6i$}
        \correctchoice{$-8-6i$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexe21}
    The multiplicative inverse of $\dfrac{i\left(2+3i\right)\left(3+2i\right)}{5+i}$ is:
    \begin{choiceshoriz}
        \wrongchoice{$\dfrac{5+i}{13}$}
        \wrongchoice{$\dfrac{5-i}{13}$}
        \wrongchoice{$\dfrac{-5+i}{13}$}
        \correctchoice{$\dfrac{-5-i}{13}$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexm1}
    If $i^{2}=-1$, then the value of $\overset{200}{\underset{n=1}{\sum}}i^{n}$ is: 
    \begin{choiceshoriz}
        \wrongchoice{$50$}
        \wrongchoice{$-50$}
        \correctchoice{$0$}
        \wrongchoice{$100$}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexm2}
    The complex number $\left(\frac{3+2i}{2-5i}\right)+\left(\frac{3-2i}{2+5i}\right)$ is:
    \begin{choiceshoriz}[o]
        \wrongchoice{Purely Imaginary}
        \correctchoice{Rational}
        \wrongchoice{Irrational}
        \wrongchoice{None of these}
    \end{choiceshoriz}
\end{question}
}

\element{Mathematics}{
\begin{question}{Maths:complexm3}
    The number of solutions of the system of equations: $Re(z^{2})=0$; $|z|=2$ is:
    \begin{choiceshoriz}
        \correctchoice{4}
        \wrongchoice{3}
        \wrongchoice{2}
        \wrongchoice{1}
    \end{choiceshoriz}
\end{question}
}

\onecopy{2}{    

\AMCcodeVspace=0.0em
\AMCcodeHspace=.0em

%%% beginning of the test sheet header:    

\noindent{\bf QCM  \hfill TEST}

\vspace*{.5cm}
\begin{minipage}{.4\linewidth}
  \centering\large\bf Test\\ Examination on April 14, 2013
\end{minipage}

\begin{center}\em

Duration : 1 hour 30 minutes.

    This booklet is your Question Paper containing 24 questions. Each question has 4 choices (A), (B), (C) and(D), for its answer, out of which only one is correct.
    \\
    Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside the examination hall.
    \\
    The answer sheet, a machine-readable Optical mark recognition sheet (OMR Sheet), is provided separately.
    DO NOT TAMPER WITH / MUTILATE THE OMR OR THE BOOKLET.
\end{center}
\vspace{1ex}

%%% end of the header

\shufflegroup{Mathematics}
\insertgroup{Mathematics}

\AMCcleardoublepage    

\AMCformBegin    

%%% beginning of the answer sheet header

{\large\bf OMR Sheet}
\\[-10pt]
{\hspace*{12mm}\bf  }
\hfill \namefield{\doublebox{    
    \begin{minipage}{.5\linewidth}
      Firstname and Lastname:
      
      \vspace*{.5cm}\dotfill
      \vspace*{1mm}
    \end{minipage}
  }}

\begin{center}
  \bf\em Answers must be given exclusively on this sheet
\end{center}

%%% end of the answer sheet header

\begin{multicols}{2}

\AMCform    

\end{multicols}

\begin{multicols}{2}

\hspace*{-4.5mm}
\ovalbox{%

    \begin{minipage}{0.40\linewidth}
      Enter Roll Number:
    \end{minipage}
    }

   
\vspace*{1mm}

\begin{minipage}{1.5\linewidth}

{\def\AMCchoiceLabelFormat#1{{\small #1}}\AMCcode{id}{8}}
%\AMCcode{id}{8}

\end{minipage}

\hfill
\vspace*{10mm}
\hspace*{1mm}

\end{multicols}

\clearpage

}
\end{document}
