Build a question paper in 60 seconds.

1. A
   $\begin{pmatrix}\cos3\theta & \sin3\theta \\ -\sin3\theta & \cos3\theta\end{pmatrix}$
2. B
   $\begin{pmatrix}\cos^3\theta & \sin^3\theta \\ -\sin^3\theta & \cos^3\theta\end{pmatrix}$
3. C
   $\begin{pmatrix}\cos3\theta & -\sin3\theta \\ \sin3\theta & \cos3\theta\end{pmatrix}$
4. D
   $\begin{pmatrix}\cos^3\theta & -\sin^3\theta \\ \sin^3\theta & \cos^3\theta\end{pmatrix}$

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1. A
   $3\times1$
2. B
   $1\times1$
3. C
   $1\times3$
4. D
   $3\times3$

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1. A
   $\begin{pmatrix}1&0\\0&1\end{pmatrix}$
2. B
   $\begin{pmatrix}1&1\\0&0\end{pmatrix}$
3. C
   $\begin{pmatrix}0&0\\1&1\end{pmatrix}$
4. D
   $\begin{pmatrix}0&1\\1&0\end{pmatrix}$

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1. A
   $\dfrac{1}{\sqrt{10}}$
2. B
   $-\sqrt{\dfrac{3}{10}}$
3. C
   $\dfrac{\sqrt{3}}{\sqrt{10}}$
4. D
   None of the above

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1. A
   0
2. B
   1
3. C
   2
4. D
   4

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1. A
   120 m
2. B
   180 m
3. C
   240 m
4. D
   360 m

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1. A
   $\dfrac{\pi}{12}$
2. B
   $\dfrac{\pi}{6}$
3. C
   $\dfrac{\pi}{3}$
4. D
   $\dfrac{\pi}{2}$

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1. A
   $\dfrac{1}{2}$
2. B
   $\dfrac{1}{4}$
3. C
   $\dfrac{1}{8}$
4. D
   $\dfrac{1}{16}$

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1. A
   $\tan\!\left(\dfrac{\alpha+\beta}{2}\right)$
2. B
   $\cot\!\left(\dfrac{\alpha+\beta}{2}\right)$
3. C
   $\sin\!\left(\dfrac{\alpha+\beta}{2}\right)$
4. D
   $\cos\!\left(\dfrac{\alpha+\beta}{2}\right)$

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1. A
   $-1$
2. B
   $0$
3. C
   $1$
4. D
   $2$

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1. A
   $\dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$
2. B
   $\dfrac{\sqrt{5}-1}{\sqrt{10+\sqrt{5}}}$
3. C
   $\dfrac{\sqrt{10+2\sqrt{5}}}{\sqrt{5}-1}$
4. D
   $\dfrac{\sqrt{10+\sqrt{5}}}{\sqrt{5}-1}$

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1. A
   $x=y=z$
2. B
   $xz=1$
3. C
   $x\neq y$ and $y=z$
4. D
   $x=y$ and $y\neq z$

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1. A
   $-3$
2. B
   $-2$
3. C
   $-\dfrac{1}{3}$
4. D
   $1$

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1. A
   1 and 3
2. B
   1 and 2
3. C
   1 and 4
4. D
   2 and 3

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1. A
   $-2$ only
2. B
   $\dfrac{1}{2}$ only
3. C
   Both $-2$ and $\dfrac{1}{2}$
4. D
   Neither $\dfrac{1}{2}$ nor $-2$

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1. A
   $\left(-\dfrac{1}{3}, \dfrac{7}{3}\right)$
2. B
   $\left(-1, \dfrac{7}{3}\right)$
3. C
   $\left(\dfrac{1}{3}, \dfrac{7}{3}\right)$
4. D
   $\left(1, \dfrac{7}{3}\right)$

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1. A
   $\left(1, \dfrac{\sqrt{3}}{2}\right)$
2. B
   $\left(\dfrac{2}{3}, \dfrac{1}{\sqrt{3}}\right)$
3. C
   $\left(\dfrac{2}{3}, \dfrac{\sqrt{3}}{2}\right)$
4. D
   $\left(1, \dfrac{1}{\sqrt{3}}\right)$

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1. A
   $(1, 2)$
2. B
   $(1, 0)$
3. C
   $(0, 0)$
4. D
   $(1, -1)$

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1. A
   $2<r<8$
2. B
   $r=2$ or $r=8$
3. C
   $r<2$
4. D
   $r>2$

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1. A
   $x^2+y^2+3x+2=0$
2. B
   $x^2+y^2+3x+12y+2=0$
3. C
   $x^2+y^2+2x=0$
4. D
   $x^2+y^2=5$

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1. A
   $1:3$
2. B
   $3:4$
3. C
   $1:2$
4. D
   $2:3$

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1. A
   $\dfrac{x^2}{64}+\dfrac{y^2}{60}=1$
2. B
   $\dfrac{x^2}{60}+\dfrac{y^2}{64}=1$
3. C
   $\dfrac{x^2}{20}+\dfrac{y^2}{24}=1$
4. D
   $\dfrac{x^2}{24}+\dfrac{y^2}{20}=1$

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1. A
   $2x+3y-4=0$
2. B
   $2x+3y-5=0$
3. C
   $x+y-1=0$
4. D
   $3x-2y+7=0$

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1. A
   $\tan^{-1}\!\left(\dfrac{1}{2\sqrt{6}}\right)$
2. B
   $\tan^{-1}\!\left(\dfrac{1}{\sqrt{2}}\right)$
3. C
   $\tan^{-1}(3)$
4. D
   $\tan^{-1}\!\left(\dfrac{1}{\sqrt{3}}\right)$

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1. A
   5, 2
2. B
   2, 5
3. C
   1, 0
4. D
   0, 0

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