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Maths Inverse Trigonometric Functions Class 12 Case Based MCQ Questions | CBSE Case Based MCQ Quiz

Question 1 of 10

Two men on

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:

$$ \angle \mathrm{CAB}=\alpha= $$

A $\sin ^{-1}\left(\frac{2}{\sqrt{3}}\right)$ B $\sin ^{-1}\left(\frac{1}{2}\right)$ C $\sin ^{-1}(2)$ D $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

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Question 2 of 10

Two men on

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:

$$ \angle \mathrm{CAB}=\alpha= $$

A $\cos ^{-1}\left(\frac{1}{5}\right)$ B $\cos ^{-1}\left(\frac{2}{5}\right)$ C $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ D $\cos ^{-1}\left(\frac{4}{5}\right)$

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Question 3 of 10

Two men on

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:

$$ \angle \mathrm{BCA}=\beta= $$

A $\tan ^{-1}\left(\frac{1}{2}\right)$ B $\tan ^{-1}(2)$ C $\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ D $\tan ^{-1}(\sqrt{3})$

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Question 4 of 10

Two men on

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:

$$ \angle A B C= $$

A $\frac{\pi}{4}$ B $\frac{\pi}{6}$ C $\frac{\pi}{2}$ D $\frac{\pi}{3}$

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Question 5 of 10

Two men on

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:

Domain and Range of $\cos ^{-1} x=$

A $(-1,1),(0, \pi)$ B $[-1,1],(0, \pi)$ C $[-1,1],[0, \pi]$ D $(-1,1),\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

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Question 6 of 10

The Government of

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 $\mathrm{C}, \mathrm{D}$ 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 and the following:

Measure of $\angle C A B=$

A $\tan ^{-1}(2)$ B $\tan ^{-1}\left(\frac{1}{2}\right)$ C $\tan ^{-1}(1)$ D $\tan ^{-1}(3)$

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Question 7 of 10

The Government of

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 $\mathrm{C}, \mathrm{D}$ 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 and the following:

Measure of $\angle \mathrm{DAB}$

A $\tan ^{-1}\left(\frac{3}{4}\right)$ B $\tan ^{-1}(3)$ C $\tan ^{-1}\left(\frac{4}{3}\right)$ D $\tan ^{-1}(4)$

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Question 8 of 10

The Government of

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 $\mathrm{C}, \mathrm{D}$ 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 and the following:

Measure of $\angle \mathrm{EAB}$

A $\tan ^{-1}(11)$ B $\tan ^{-1} 3$ C $\tan ^{-1}\left(\frac{2}{11}\right)$ D $\tan ^{-1}\left(\frac{11}{2}\right)$

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Question 9 of 10

The Government of

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 $\mathrm{C}, \mathrm{D}$ 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 and the following:

$A^{\prime}$ 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 $\angle C A B$ and $\angle C A^{\prime} B$ Is

A $\tan ^{-1}\left(\frac{1}{2}\right)$ B $\tan ^{-1}\left(\frac{1}{8}\right)$ C $\tan ^{-1}\left(\frac{2}{5}\right)$ D $\tan ^{-1}\left(\frac{1}{12}\right)$

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Question 10 of 10

The Government of

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 $\mathrm{C}, \mathrm{D}$ 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 and the following:

Domain and Range of $\tan ^{-1} x=$

A $\mathrm{R}^{+},\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ B $\mathrm{R}^{-},\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ C $\mathrm{R},\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ D $R,\left(0, \frac{\pi}{2}\right)$

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