791.

$$\begin{gathered} \mathrm{The} \mathrm{shadow} \mathrm{of} \mathrm{a} \mathrm{tower} \mathrm{standing} \mathrm{on} \mathrm{a} \mathrm{level} \mathrm{ground} \mathrm{is} \mathrm{found} \mathrm{to} \mathrm{be} 60\mathrm{m} \mathrm{longer} \mathrm{when} \mathrm{the} \mathrm{sun}\text{'}\mathrm{s} \\ \mathrm{altitude} \mathrm{is} 30° \mathrm{than} \mathrm{when} \mathrm{it} \mathrm{is} 45°.\mathrm{The} \mathrm{height} \mathrm{of} \mathrm{the} \mathrm{tower} \mathrm{is} \end{gathered}$$

• $30\mathrm{m}$

• $90\mathrm{m}$

• $60\sqrt{3}\mathrm{m}$

• $30\left(\sqrt{3} + 1\right)\mathrm{m}$

$\mathrm{If} \mathrm{cosec\theta } = \frac{\mathrm{p} + \mathrm{q}}{\mathrm{p} - \mathrm{q}},\mathrm{then} \cot \left(\frac{\mathrm{\pi }}{4} + \frac{\mathrm{\theta }}{4}\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\frac{\sqrt{\mathrm{p}}}{\mathrm{q}}$

• $\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$

• $\sqrt{\mathrm{pq}}$

• $\mathrm{pq}$

From a point on the level ground, the angle of elevation of top of a pole is $30°$ on moving 20metres nearer,the angle of elevation is $45°$. Then,the height of the pole $\left(\mathrm{in} \mathrm{metres}\right)$, is

• $10\left(\sqrt{3} - 1\right)$

• $10\left(\sqrt{3} - 1\right)$

• 15

• 20

If the axes are rotated through an angle 45° in the positive direction without changing the origin,then the co-ordinates of the point ($\sqrt{2}$, 4) in the old system are

• $\left(1 - 2\sqrt{2}, 1 + 2\sqrt{2}\right)$

• $\left(1 + 2\sqrt{2}, 1 - 2\sqrt{2}\right)$

• $\left(2\sqrt{2}, \sqrt{2}\right)$

• $\left(\sqrt{2}, 2\right)$

• ${\left({\mathrm{x}}^2\mathrm{y}\right)}^{2/3} + ({\mathrm{xy}}^2{)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} = 1$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right) = 4\mathrm{xy}$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right) = 12\mathrm{xy}$

• ${\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right)}^2 = 16\mathrm{xy}$

$\mathrm{f}\left(\mathrm{x}\right) = \frac{{\cos }^2\left(\mathrm{x}\right) + {\sin }^4\left(\mathrm{x}\right)}{{\sin }^2\left(\mathrm{x}\right) + {\cos }^4\left(\mathrm{x}\right)}, \mathrm{for} \mathrm{x} \in \mathrm{R}$, then f(2002) is equal to

• 1

• 2

• 3

• 4

The function f : R $\to$ R is defined by f(x) = ${\cos }^2\left(\mathrm{x}\right) + {\sin }^4\left(\mathrm{x}\right) \mathrm{for} \mathrm{x} \in \mathrm{R}$, then f(R) is equal to

• $(\frac{3}{4}, 1]$

• $[\frac{3}{4}, 1)$

• $\left[\frac{3}{4}, 1\right]$

• $\left(\frac{3}{4}, 1\right)$

$\mathrm{If} {\mathrm{x}}_{\mathrm{n}} = \cos \left(\frac{\mathrm{\pi }}{4^{\mathrm{n}}}\right) + \mathrm{isin}\left(\frac{\mathrm{\pi }}{4^{\mathrm{n}}}\right), \mathrm{then} {\mathrm{x}}_1, {\mathrm{x}}_2, {\mathrm{x}}_3...\infty \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\frac{1 + \mathrm{i}\sqrt{3}}{2}$

• $\frac{- 1 + \mathrm{i}\sqrt{3}}{2}$

• $\frac{1 - \mathrm{i}\sqrt{3}}{2}$

• $\frac{- 1 - \mathrm{i}\sqrt{3}}{2}$

$\mathrm{If} \mathrm{z} = 3 + 5\mathrm{i}, \mathrm{then} {\mathrm{z}}^3 + \overline{\mathrm{z}} + 198 \mathrm{is} \mathrm{equal} \mathrm{to}$

• - 3 - 5i

• - 3 + 5i

• 3 - 5i

• 3 + 5i

$\mathrm{If} \mathrm{f}\left(\mathrm{x}\right) = {\sin }^2\left(\frac{\mathrm{\pi }}{8} + \frac{\mathrm{x}}{2}\right) - {\sin }^2\left(\frac{\mathrm{\pi }}{8} - \frac{\mathrm{x}}{2}\right), \mathrm{then} \mathrm{the} \mathrm{period} \mathrm{of} \mathrm{f} \mathrm{is}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• $\mathrm{\pi }$

• $2\mathrm{\pi }$