The value of $\frac{2}{3!} + \frac{4}{5!} + \frac{6}{7!} + ...$

• e

• 2e

• e²

• $\frac{1}{\mathrm{e}}$

$\left(1 + \cos \left(\frac{\mathrm{\pi }}{8}\right)\right)\left(1 + \cos \left(\frac{3\mathrm{\pi }}{8}\right)\right)\left(1 + \cos \left(\frac{5\mathrm{\pi }}{8}\right)\right)\left(1 + \cos \left(\frac{7\mathrm{\pi }}{8}\right)\right)$ is equal to

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\cos \left(\frac{\mathrm{\pi }}{8}\right)$

• $\frac{1}{4}$

3.

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°

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

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

Y-axis cuts the line joining the points (- 3, - 4) and (1, - 2) in the ratio

• 1 : 3

• 2 : 3

• 3 : 1

• 3 : 2

The value of k for which the lines 7x - 8y + 5 = 0, 3x - 4y + 5 = 0 and 4x + 5y + k = 0 are concurrent, is given by

• - 45

• 44

• 54

• - 54

The angle between the straight lines x - y$\sqrt{3}$ = 5 and $\sqrt{3}$x + y = 7, is

• $0°$

• $90°$

• $120°$

• $30°$

Orthocentre of the triangle formed by the points (0, 0), (3, 4), (4,0) is

• $\left(3, \frac{5}{4}\right)$

• (3, 12)

• $\left(3, \frac{3}{4}\right)$

• (3, 9)

Equation of straight line passing through intersection of x + 5y + 7 = 0, 3x + 2y - 5 = 0 and perpendicularto 7x + 2y - 5 = 0, is

• 2x - 7y - 20 = 0

• 2x + 7y - 20 = 0

• - 2x + 7y - 20 = 0

• 2x + 7y + 20 = 0