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question_answer1)
Directions: (1 - 5) |
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Two men on either side of a temple of 30 meters high observe its top at the angles of elevation \[\alpha \] and \[\beta \] respectively, (as shown in the figure above). The distance between the two men is \[40\sqrt{3}\] meters and the distance between the first person A and the temple is \[30\sqrt{3}\] meters. Based on the above information answer the following : |
\[\angle CAB=\alpha =\]
A)
\[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] done
clear
B)
\[{{\sin }^{-1}}\left( \frac{1}{2} \right)\] done
clear
C)
\[{{\sin }^{-1}}\left( 2 \right)\] done
clear
D)
\[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done
clear
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question_answer2)
\[\angle CAB=\alpha =\]
A)
\[{{\cos }^{-1}}\left( \frac{1}{5} \right)\] done
clear
B)
\[{{\cos }^{-1}}\left( \frac{2}{5} \right)\] done
clear
C)
\[{{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done
clear
D)
\[{{\cos }^{-1}}\left( \frac{4}{5} \right)\] done
clear
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question_answer3)
\[\angle BCA=\beta =\]
A)
\[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( 2 \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \sqrt{3} \right)\] done
clear
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question_answer4)
\[\angle ABC=\]
A)
\[\frac{\pi }{4}\] done
clear
B)
\[\frac{\pi }{6}\] done
clear
C)
\[\frac{\pi }{2}\] done
clear
D)
\[\frac{\pi }{3}\] done
clear
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question_answer5)
Domain and Range of \[{{\cos }^{-1}}x=\]
A)
\[\left( -1,\,\,1 \right),\,\left( 0,\,\,\pi \right)\] done
clear
B)
\[\left[ -1,\,\,1 \right],\,\left( 0,\,\pi \right)\] done
clear
C)
\[\left[ -1,\,1 \right],\,\left[ 0,\,\,\pi \right]\] done
clear
D)
\[\left( -1,\,\,1 \right),\,\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\] done
clear
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question_answer6)
Directions : (6 - 10) |
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. "A" is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. "C" is at the height of 10 metres from the ground level. |
For the viewer A, the angle of elevation of "D" is double the angle of elevation of "C". The angle of elevation of "E" is triple the angle of elevation of "C" for the same viewer. Look at the figure given and based on the above information answer the following : |
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Measure of \[\angle CAB=\]
A)
\[{{\tan }^{-1}}\left( 2 \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( \frac{1}{2} \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( 1 \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( 3 \right)\] done
clear
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question_answer7)
Measure of \[\angle DAB=\]
A)
\[{{\tan }^{-1}}\left( \frac{3}{4} \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( 3 \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{4}{3} \right)\] done
clear
D)
\[{{\tan }^{-1}}(4)\] done
clear
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question_answer8)
Measure of \[\angle EAB=\]
A)
\[{{\tan }^{-1}}\left( 11 \right)\] done
clear
B)
\[{{\tan }^{-1}}3\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{2}{11} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \frac{11}{2} \right)\] done
clear
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question_answer9)
A' is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between \[\angle CAB\]and \[\angle CA'B\]is
A)
\[{{\tan }^{-1}}\left( 1/2 \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( \frac{1}{12} \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{2}{5} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \frac{11}{21} \right)\] done
clear
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question_answer10)
Domain and Range of \[{{\tan }^{-1}}x=\]
A)
\[{{R}^{+}},\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done
clear
B)
\[{{R}^{-}},\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done
clear
C)
\[R,\,\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] done
clear
D)
\[R,\,\left( 0,\,\frac{\pi }{2} \right)\] done
clear
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