Build a question paper in 60 seconds.

1. A
   $5$
2. B
   $\sqrt{5}$
3. C
   $25$
4. D
   $\frac{9}{5}$

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

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1. A
   $\frac{23}{25}$
2. B
   $\frac{25}{23}$
3. C
   $\frac{23}{24}$
4. D
   $\frac{24}{23}$

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1. A
   10
2. B
   15
3. C
   20
4. D
   21

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1. A
   3.0008686
2. B
   1.99991314
3. C
   2.0008686
4. D
   2.9991314

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1. A
   $4x-2y+5z=45$
2. B
   $-4x+2y+5z=45$
3. C
   $4x-2y+5z+45=0$
4. D
   $4x+2y+5z+45=0$

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1. A
   2 units/sec
2. B
   $3\sqrt{3}$ units/sec
3. C
   $\sqrt{3}$ units/sec
4. D
   $2\sqrt{3}$ units/sec

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

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1. A
   $\sin^2\alpha$
2. B
   $3\sin^2\alpha$
3. C
   $9\sin^2\alpha$
4. D
   $49\sin^2\alpha$

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1. A
   $2\sqrt{3}$ sq. units
2. B
   $8\sqrt{3}$ sq. units
3. C
   $4\sqrt{3}$ sq. units
4. D
   $6\sqrt{3}$ sq. units

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1. A
   $-\frac{3}{4}$
2. B
   $\frac{1}{3}$
3. C
   $\frac{1}{4}$
4. D
   $0$

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1. A
   $1$
2. B
   $-\frac{13}{29}$
3. C
   $\frac{13}{29}$
4. D
   $-1$

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1. A
   $\frac{1}{9}\begin{pmatrix}5&7\\3&3&4\end{pmatrix}$
2. B
   $\frac{1}{9}\begin{pmatrix}5&-7\\3&3&-4\end{pmatrix}$
3. C
   $\frac{1}{9}\begin{pmatrix}5&-7\\-3&3&4\end{pmatrix}$
4. D
   $\frac{1}{9}\begin{pmatrix}5&4\\3&3&7\end{pmatrix}$

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1. A
   $\frac{36}{169}$
2. B
   $\frac{144}{169}$
3. C
   $\frac{9}{169}$
4. D
   $\frac{16}{169}$

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1. A
   $12$
2. B
   $19$
3. C
   $23$
4. D
   $33$

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1. A
   $\sqrt{15}$
2. B
   $5$
3. C
   $\sqrt{10}$
4. D
   $1$

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1. A
   $-\frac{80}{41}$
2. B
   $\frac{80}{41}$
3. C
   $\frac{12}{5}$
4. D
   $-\frac{12}{5}$

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1. A
   $20$
2. B
   $16$
3. C
   $24$
4. D
   $8$

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1. A
   $\frac{1}{3}$
2. B
   $\frac{1}{2}$
3. C
   $\frac{1}{4}$
4. D
   $\frac{1}{5}$

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1. A
   $2$
2. B
   $4$
3. C
   $6$
4. D
   $8$

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1. A
   $\vec{r}=\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}+\hat{k}+\lambda(\hat{i}+2\hat{j}+3\hat{k})$
2. B
   $\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(\hat{i}+2\hat{j}+3\hat{k})$
3. C
   $\vec{r}=-\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}+\hat{k}+\lambda(\hat{i}+2\hat{j}+3\hat{k})$
4. D
   $\vec{r}=\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}-\hat{k}+\lambda(\hat{i}-\hat{j}+3\hat{k})$

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1. A
   $7:3$
2. B
   $4:6$
3. C
   $6:4$
4. D
   $3:7$

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1. A
   $0.7$
2. B
   $0.75$
3. C
   $0.65$
4. D
   $0.62$

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

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1. A
   $\log\frac{xe^x}{1+xe^x}+c$
2. B
   $\log\frac{xe^x}{1+xe^x}-\frac{1}{1+xe^x}+c$
3. C
   $\log\frac{1+xe^x}+\frac{1}{1+xe^x}+c$
4. D
   $\log\frac{xe^x}{1+xe^x}+\frac{1}{1+xe^x}+c$

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