Day 341: MHT-CET Maths

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

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

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1. A.
   $\left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\}$
2. B.
   $\left\{\frac{\pi}{3}, \frac{5\pi}{3}\right\}$
3. C.
   $\left\{\frac{\pi}{3}, \frac{2\pi}{3}\right\}$
4. D.
   $\left\{\frac{2\pi}{3}, \frac{4\pi}{3}\right\}$

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

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1. A.
   $0$
2. B.
   $\frac{1}{2\sqrt{2}}$
3. C.
   $\frac{1}{4\sqrt{2}}$
4. D.
   $\frac{1}{2\sqrt{2}(\sqrt{2}+1)}$

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