21.

GM and HM of two numbers are 10 and 8 respectively. The numbers are

• 5, 20

• 4, 25

• 2, 50

• 1,100

The value of n for which is the $\frac{{\mathrm{x}}^{\mathrm{n} +\hspace{0.17em}1} + {\mathrm{y}}^{\mathrm{n} + 1}}{{\mathrm{x}}^{\mathrm{n}} + {\mathrm{y}}^{\mathrm{n}}}$ geometric mean of x and y is

• n = - $\frac{1}{2}$

• n = $\frac{1}{2}$

• n = 1

• n = - 1

If angles A, B and C are in AP, then $\frac{\mathrm{a} + \mathrm{c}}{\mathrm{b}}$ equal to

• 2$\sin \left(\frac{\mathrm{A} - \mathrm{C}}{2}\right)$

• $2\cos \left(\frac{\mathrm{A} - \mathrm{C}}{2}\right)$

• $\cos \left(\frac{\mathrm{A} - \mathrm{C}}{2}\right)$

• $\sin \left(\frac{\mathrm{A} - \mathrm{C}}{2}\right)$

If $\frac{\cos \left(\mathrm{A}\right)}{3} = \frac{\cos \left(\mathrm{B}\right)}{4} = \frac{1}{5}, - \frac{\mathrm{\pi }}{2} < \mathrm{A} < 0, - \frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 2}} < \mathrm{B} < 0$ then value of $2\sin \left(\mathrm{A}\right) + 4\sin \left(\mathrm{B}\right)$ is

• 4

• - 2

• - 4

• 0

The value of $\frac{\cot \left(54°\right)}{\tan \left(36°\right)} + \frac{\tan \left(20°\right)}{\cot \left(70°\right)}$ is

• 0

• 2

• 3

• 1

If $\sin \left(6\mathrm{\theta }\right) + \sin \left(4\mathrm{\theta }\right) + \sin \left(2\mathrm{\theta }\right) = 0$, then the general value of $\mathrm{\theta }$

• $\frac{\mathrm{n\pi }}{4}, \mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{n\pi }}{4}, \mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{n\pi }}{4}, 2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{n\pi }}{4}, 2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

In a $∆\mathrm{ABC}$, 2ac$\sin \left(\frac{\mathrm{A} - \mathrm{B} +\hspace{0.17em}\mathrm{C}}{2}\right)$ is equal to

• a² + b² - c²

• c² + a² - b²

• b² - a² - c²

• c² - a² - b²

Value of ${\tan }^{-1}\left(\frac{\sin \left(2\right) - 1}{\cos \left(2\right)}\right)$

• $\frac{\mathrm{\pi }}{2} - 1$

• $1 - \frac{\mathrm{\pi }}{4}$

• $2 - \frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4} - 1$

The straight line 3x + y divides the line segment joining the points (1, 3) and (2, 7) in the ratio

• 3 : 4 externally

• 3 : 4 internally

• 4 : 5 internally

• 5 : 6 externally

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is

• a parabola

• a circle

• an ellipse

• a straight line