Trigonometry · NDA previous year questions

2019 4 questions

1. Q512019 · 21 Apr 2019

   The angle of elevation of a tower of height $h$ from a point A due South of it is $x$ and from a point B due East of A is $y$. If AB = $z$, then which one of the following is correct?

   1. A.$h^2({\cot }^{2}y-{\cot }^{2}x)=z^2$
   2. B.$z^2({\cot }^{2}y-{\cot }^{2}x)=h^2$
   3. C.$h^2({\tan }^{2}y-{\tan }^{2}x)=z^2$
   4. D.$z^2({\tan }^{2}y-{\tan }^{2}x)=h^2$
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   Answer: A

2. Q522019 · 21 Apr 2019

   If the angles of a triangle ABC are in the ratio 1 : 2 : 3, then the corresponding sides are in the ratio

   1. A.1 : 2 : 3
   2. B.3 : 2 : 1
   3. C.$1:\sqrt{3}:2$
   4. D.$1:\sqrt{3}:\sqrt{2}$
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   Answer: C

3. Q532019 · 21 Apr 2019

   Consider the following statements: 1. For an equation of a line, $x\cos \theta +y\sin \theta =p$, in normal form, the length of the perpendicular from the point $(\alpha ,\beta )$ to the line is $|\alpha \cos \theta +\beta \sin \theta +p|$. 2. The length of the perpendicular from the point $(\alpha ,\beta )$ to the line $\frac{x}{a}+\frac{y}{b}=1$ is $\left|\frac{a\alpha +b\beta -ab}{\sqrt{a^2+b^2}}\right|$. Which of the above statements is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: D

4. Q952019 · 21 Apr 2019

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

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