In triangle ABC, a = 2, b = 3 and sin(A) = $\frac{2}{3}$, then B is equal to

• 30$°$

• 60$°$

• 90$°$

• 120$°$

The coefficient of xⁿ, where n is any positive integer, in the expansion of ${\left(1 + 2\mathrm{x} + 3{\mathrm{x}}^2 + ... \infty \right)}^{\frac{1}{2}}$

• 1

• $\frac{\mathrm{n} + 1}{2}$

• 2n + 1

• n + 1

3.

The circles x² + y² - 10x + 16 = 0 and x² + y² = a² intersect at two distinct points, if

• a < 2

• 2 < a < 8

• a > 8

• a = 2

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

• 0

• 1

• 2

• $\infty$

Simplest form of $\frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos \left(4\mathrm{x}\right)}}}}$ is

• $\sec \left(\frac{\mathrm{x}}{2}\right)$

• $\sec \left(\mathrm{x}\right)$

• $\csc \left(\mathrm{x}\right)$

• 1

If y = ${\tan }^{-1}\sqrt{\frac{1 - \sin \left(\mathrm{x}\right)}{1 + \sin \left(\mathrm{x}\right)}}$, then the value of $\frac{\mathrm{dy}}{\mathrm{dx}}$ at x = $\frac{\mathrm{\pi }}{6}$ is

• - $\frac{1}{2}$

• $\frac{1}{2}$

• 1

• - 1

The sum of the infinite series

$1 + \frac{1}{2!} + \frac{1 . 3}{4!} + \frac{1 . 3. 5}{6!} + ...$

• e

• e²

• $\sqrt{\mathrm{e}}$

• $\frac{1}{\mathrm{e}}$

If three positive real numbers a, b, c are in AP and abc = 4, then the minimum possible value of b is 2

• $2^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

• $2^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

• $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

• $2^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

If $5\cos \left(2\mathrm{\theta }\right) + 2{\cos }^2\left(\frac{\mathrm{\theta }}{2}\right) + 1 = 0$, when $\left(0 < \mathrm{\theta } < \mathrm{\pi }\right)$, then the values of $\mathrm{\theta }$ are

• $\frac{\mathrm{\pi }}{3} \pm \mathrm{\pi }$

• $\frac{\mathrm{\pi }}{3}, {\cos }^{-1}\left(\frac{3}{5}\right)$

• ${\cos }^{-1}\left(\frac{3}{5}\right) \pm \mathrm{\pi }$

• $\frac{\mathrm{\pi }}{3}, \mathrm{\pi } - {\cos }^{-1}\left(\frac{3}{5}\right)$

For any complex number z, the minimum value of $\left|\mathrm{z}\right| + \left|\mathrm{z} - 1\right|$ is

• 0

• 1

• 2

• - 1