Two poles are 10 m and 20 m high. The line joining their tops makes an angle of \( 15^{\circ} \) with the horizontal. The distance between the poles is approximately equal to
If A is an orthogonal matrix of order 3 and \( B = \begin{bmatrix} 1 & 2 & 3 \\ -3 & 0 & 2 \\ 2 & 5 & 0 \end{bmatrix} \), then which of the following is/are correct?
1. \( |AB| = \pm 47 \)
2. \( AB = BA \)
Select the correct answer using the code given below.
If a, b, c are real numbers, then the value of the determinant \( \begin{vmatrix} 1-a & a-b-c & b+c \\ 1-b & b-c-a & c+a \\ 1-c & c-a-b & a+b \end{vmatrix} \) is
If the point \( z_{1} = 1 + i \), where \( i = \sqrt{-1} \), is the reflection of a point \( z_{2} = x + iy \) in the line \( i\bar{z} - iz = 5 \), then the point \( z_{2} \) is
If \( \sin x + \sin y = a \) and \( \cos x + \cos y = b \), then \( \tan^{2}\left(\frac{x+y}{2}\right) + \tan^{2}\left(\frac{x-y}{2}\right) \) is equal to
B. \( \frac{a^{4} - b^{4} + 4b^{2}}{a^{2}b^{2} + b^{4}} \)
30.
A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are \( 30^{\circ} \) and \( 45^{\circ} \) respectively. Which one of the following gives the best approximation to the height of the tower?
