Trigonometry · NDA previous year questions

2016 3 questions

1. Q472016 · 18 Sept 2016

   A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from $60^{\circ }$ to $45^{\circ }$ in 2 minutes. What is the speed of the boat in metres per hour?

   1. A.$\frac{4500}{\sqrt{3}}$
   2. B.$\frac{4500(\sqrt{3}-1)}{\sqrt{3}}$
   3. C.$4500\sqrt{3}$
   4. D.$\frac{4500(\sqrt{3}+1)}{\sqrt{3}}$
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   Answer: B

2. Q952016 · 18 Sept 2016

   In a right-angled triangle ABC, if the hypotenuse AB = p, then what is $\overrightarrow{AB}\cdot \overrightarrow{AC}+\overrightarrow{BC}\cdot \overrightarrow{BA}+\overrightarrow{CA}\cdot \overrightarrow{CB}$ equal to?

   1. A.$p$
   2. B.$p^2$
   3. C.$2p^2$
   4. D.$\frac{p^2}{2}$
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   Answer: B

3. Q962016 · 18 Sept 2016

   A force $\vec{F}=3\hat{i}+2\hat{j}-4\hat{k}$ is applied at the point $(1,-1,2)$. What is the moment of the force about the point $(2,-1,3)$?

   1. A.$\hat{i}+4\hat{j}+4\hat{k}$
   2. B.$2\hat{i}+\hat{j}+2\hat{k}$
   3. C.$2\hat{i}-7\hat{j}-2\hat{k}$
   4. D.$2\hat{i}+4\hat{j}-\hat{k}$
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   Answer: C