11.

If the three points A(1, 6), B(3,- 4) and C(x, y) are collinear, then the equation satisfying by x and y is

• 5x + y - 11 = 0

• 5x + 13y + 5 = 0

• 5x - 13y + 5 = 0

• 13x - 5y + 5 = 0

If $\sin \left(\mathrm{\theta }\right) = \frac{2\mathrm{t}}{1 + {\mathrm{t}}^2}$ and $\mathrm{\theta }$ lies in the second quadrant, then $\cos \left(\mathrm{\theta }\right)$ is equal to 

• $\frac{1 - {\mathrm{t}}^2}{1 + {\mathrm{t}}^2}$

• $\frac{{\mathrm{t}}^2 - 1}{1 + {\mathrm{t}}^2}$

• $\frac{- \left|1 - {\mathrm{t}}^2\right|}{1 + {\mathrm{t}}^2}$

• $\frac{1 + {\mathrm{t}}^2}{\left|1 - {\mathrm{t}}^2\right|}$

The solutions set of in equation ${\cos }^{-1}\left(\mathrm{x}\right) < {\sin }^{-1}\left(\mathrm{x}\right)$

• [- 1, 1]

• $\left[\frac{1}{\sqrt{2}}, 1\right]$

• [0, 1]

• $(\frac{1}{\sqrt{2}}, 1]$

The number of solutions of $2\sin \left(\mathrm{x}\right) + \cos \left(\mathrm{x}\right) = 3$

• 1

• 2

• infinite

• no solution

Let $\tan \left(\mathrm{\alpha }\right) = \frac{\mathrm{a}}{\mathrm{a} + 1} \mathrm{and} \tan \left(\mathrm{\beta }\right) = \frac{1}{2\mathrm{a} + 1}$, then $\mathrm{\alpha } + \mathrm{\beta }$ is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{3\mathrm{\pi }}{4}$

The approximate value of $\sqrt[5]{33}$ correct to 4 decimal places is

• 2.0000

• 2.1001

• 2.0125

• 2.0500

If $\mathrm{\theta } + \mathrm{\varphi } = \frac{\mathrm{\pi }}{4}, \mathrm{then} \left(1 + \tan \left(\mathrm{\theta }\right)\right) \left(1 + \tan \left(\mathrm{\varphi }\right)\right)$ is equal to

• 1

• 2

• 5/2

• 1/3

If $\sin \left(\mathrm{\theta }\right) \mathrm{and} \cos \left(\mathrm{\theta }\right)$ are the roots of the equation ax² - bx + c = 0, then a, b and c satisfy the relation

• a² + b² + 2ac = 0

• a² - b² + 2ac = 0

• a² + c² + 2ab = 0

• a² - b² - 2ac = 0

The equation of the locus of the point of intersection of the straight lines
$$\begin{gathered} \mathrm{xsin}\left(\mathrm{\theta }\right) + (1 - \cos \left(\mathrm{\theta }\right))\mathrm{y} = \mathrm{a} \sin \left(\mathrm{\theta }\right) \mathrm{and} \\ \mathrm{xsin}\left(\mathrm{\theta }\right) - (1 + \cos \left(\mathrm{\theta }\right)) \mathrm{y} + \mathrm{a} \sin \left(\mathrm{\theta }\right)= 0 \mathrm{is} \end{gathered}$$

• $\mathrm{y} = \pm \mathrm{ax}$

• $\mathrm{x} = \pm \mathrm{ay}$

• y² = 4x

• x² + y² = a²

If $\sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right) = 0 \mathrm{and} 0 < \mathrm{\theta } < \mathrm{\pi }, \mathrm{then} \mathrm{\theta }$

• 0

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{3\mathrm{\pi }}{4}$