If $\sqrt{3}\cos \left(\mathrm{\theta }\right) + \sin \left(\mathrm{\theta }\right) = \sqrt{2}$, then the value of $\mathrm{\theta }$ is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4}$

• ${\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4} - \frac{\mathrm{\pi }}{3}$

• $\mathrm{n\pi } + \frac{\mathrm{\pi }}{4} - \frac{\mathrm{\pi }}{3}$

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4} - \frac{\mathrm{\pi }}{3}$

If in a AABC, (s - a)(s - b) = s(s - c) then angle C is equal to

• 90°

• 45°

• 30°

• 60°

743.

The length of the shadows of a vertical pole of height h, thrown by the sun's rays at three different moments are h, 2h and 3h. The sum of the angles of elevation of the rays at these three moments is equal to

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

${\cos }^4\left(\frac{\mathrm{\pi }}{8}\right) + {\cos }^4\left(\frac{3\mathrm{\pi }}{8}\right) +\hspace{0.17em}{\cos }^4\left(\frac{5\mathrm{\pi }}{8}\right) + {\cos }^4\left(\frac{7\mathrm{\pi }}{8}\right)$ is equal to

• $\frac{3}{2}$

• $- \frac{2}{3}$

• - 1

• 1

Number of solutions of the equationan $\tan \left(\mathrm{x}\right) + \sec \left(\mathrm{x}\right) = 2\cos \left(\mathrm{x}\right)$ lying in the interval $\left[0, 2\mathrm{\pi }\right]$ is

• 0

• 1

• 2

• 3

In a triangle ABC, if $\tan \left(\frac{\mathrm{A}}{2}\right) = \frac{5}{6} \mathrm{and} \tan \left(\frac{\mathrm{B}}{2}\right) = \frac{20}{37}$ , then a + c is equal to

• b

• 2b

• 3b

• 4b

The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 10s, the angle of elevation changes to 30°. If thejet is flying at a speed of 432 km/h. Find the constant height at which thejet is flying.

• $200\sqrt{3} \mathrm{m}$

• $400\sqrt{3} \mathrm{m}$

• $600\sqrt{3} \mathrm{m}$

• $800\sqrt{3} \mathrm{m}$

In a $∆\mathrm{ABC}, \mathrm{if} \tan \left(\frac{\mathrm{A}}{2}\right) = \frac{5}{6} \mathrm{and} \tan \left(\frac{\mathrm{C}}{2}\right) = \frac{2}{5}$, then the sides a, b, c are in

• AP

• GP

• HP

• None of these

The value of $\cos \left(\frac{\mathrm{\pi }}{5}\right)\cos \left(\frac{2\mathrm{\pi }}{5}\right)\cos \left(\frac{4\mathrm{\pi }}{5}\right)\cos \left(\frac{8\mathrm{\pi }}{5}\right)$ will be

• $\frac{1}{16}$

• $- \frac{1}{16}$

• 0

• $\frac{1}{2}$

The function f(x) = sin(x) + cos(x) will be

• an even function

• an odd function

• a constant function

• None of these