Show the points \((0,-\frac{3}{2}),(1,-1)\) and \((2,-\frac{1}{2})\) are collinear.

Find the equations of the straight lines, making the y-intercept of 7 and angle between the line and the y-axis is 30°.

The length of the perpendicular drawn from the origin to a line is 12 and makes an angle 150° with positive direction of the x-axis. Find the equation of the line.

Area of the triangle formed by a line with the coordinate axes, is 36 square units. Find the equation of the line if the perpendicular drawn from the origin to the line makes an angle of 45° with positive the x-axis.

Separate the equations 5x² + 6xy + y² = 0.

If exists, find the straight lines by separating the equations 2x² + 2xy + y² = 0.

Find the equations of a parallel line and a perpendicular line passing through the point (1, 2) to the line 3x + 4y = 7.

Find the separate equation of the following pair of straight lines.
\(2x^2 -xy - 3y^2 - 6x + 19y - 20 = 0\)

Evaluate: \(\underset { x\rightarrow \infty }{ lim } \sqrt { x } \left( \sqrt { x+c } -\sqrt { x } \right) \) 

Evaluate: \(\underset { x\rightarrow \infty }{ lim } \left( \sqrt { { x }^{ 2 }+x+1 } -\sqrt { { x }^{ 2 }+1 } \right) \)