Build a question paper in 60 seconds.

1. A
   1
2. B
   $\cos\theta$
3. C
   $\sin\theta$
4. D
   $\cos 2\theta$

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1. A
   202
2. B
   101
3. C
   51
4. D
   50

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1. A
   $2^{26}$
2. B
   $2^{49}$
3. C
   $2^{50}$
4. D
   $2^{51}$

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1. A
   $\begin{pmatrix}a^{-1} & 0 & 0 \\ 0 & b^{-1} & 0 \\ 0 & 0 & c^{-1}\end{pmatrix}$
2. B
   $\dfrac{1}{abc}\begin{pmatrix}a^{-1} & 0 & 0 \\ 0 & b^{-1} & 0 \\ 0 & 0 & c^{-1}\end{pmatrix}$
3. C
   $\dfrac{1}{abc}\begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{pmatrix}$
4. D
   $\dfrac{1}{abc}\begin{pmatrix}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{pmatrix}$

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1. A
   24 minutes
2. B
   34 minutes
3. C
   125 minutes
4. D
   135 minutes

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1. A
   1
2. B
   4
3. C
   8
4. D
   16

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1. A
   symmetric only
2. B
   symmetric and transitive only
3. C
   equivalence relation
4. D
   reflexive only

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1. A
   $x = \dfrac{y}{1+y}$
2. B
   $x = \dfrac{y}{1-y}$
3. C
   $x = \dfrac{1+y}{y}$
4. D
   $x = \dfrac{1-y}{y}$

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1. A
   $3x^2 + 8x + 16 = 0$
2. B
   $3x^2 - 8x - 16 = 0$
3. C
   $3x^2 + 8x - 16 = 0$
4. D
   $x^2 + 8x + 16 = 0$

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1. A
   $\log_e 9$
2. B
   0
3. C
   1
4. D
   $\log_e 3$

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1. A
   $24 \times 8! \times 8!$
2. B
   $(8!)^3$
3. C
   $210 \times 8! \times 8!$
4. D
   $16!$

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

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1. A
   $n,\ 2$
2. B
   $n,\ 3$
3. C
   $n+1,\ 2$
4. D
   $n+1,\ 3$

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1. A
   $a = b + c$
2. B
   $b = c + a$
3. C
   $c = a + b$
4. D
   $b = c$

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

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1. A
   25 m
2. B
   $25\sqrt{3}$ m
3. C
   50 m
4. D
   $50\sqrt{3}$ m

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

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

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1. A
   $\dfrac{(p+q)\sin\alpha}{p-q}$
2. B
   $\dfrac{p\sin\alpha}{p+q}$
3. C
   $\dfrac{p\sin\alpha}{p-q}$
4. D
   $\dfrac{(p-q)\sin\alpha}{p+q}$

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1. A
   0
2. B
   $\dfrac{\pi}{4}$
3. C
   $\dfrac{\pi}{3}$
4. D
   $\dfrac{\pi}{2}$

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

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1. A
   $\dfrac{9}{2}$
2. B
   3
3. C
   $\dfrac{3}{2}$
4. D
   1

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1. A
   $\dfrac{3\pi}{2} < A < \dfrac{5\pi}{2}$ only
2. B
   $\dfrac{\pi}{2} < A < \dfrac{3\pi}{2}$ only
3. C
   $\dfrac{3\pi}{2} < A < \dfrac{7\pi}{2}$
4. D
   $0 < A < \dfrac{3\pi}{2}$

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1. A
   right-angled
2. B
   equilateral
3. C
   isosceles
4. D
   obtuse-angled

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1. A
   $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$
2. B
   $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$
3. C
   $\left[0,\dfrac{\pi}{2}\right]$
4. D
   $[0,\pi]$

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