31.

The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

• (2, - 1)

• (- 2, 1)

• (1, 1)

• (1, 2)

The equation of chord of the circle x² + y² - 4x = 0, whose mid-point is (1, 0) is

• y = 2

• y = 1

• x = 2

• x = 1

The value of $\cos \left(45°\right)\cos \left(7\frac{1}{2}°\right)\sin \left(7\frac{1}{2}°\right)$ is 

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{4}$

• $\frac{1}{16}$

The line y = 2t² intersects the ellipse $\frac{{\mathrm{x}}^2}{9} + \frac{{\mathrm{y}}^2}{4} = 1$ in real points, if

• $\left|\mathrm{t}\right| \le 1$

• $\left|\mathrm{t}\right| < 1$

• $\left|\mathrm{t}\right| > 1$

• $\left|\mathrm{t}\right| \ge 1$

General solution of $\sin \left(\mathrm{x}\right) + \cos \left(\mathrm{x}\right) = \underset{\mathrm{a}\in \mathrm{R}}{\min }\left\{1, {\mathrm{a}}^2 - 4\mathrm{a} + 6\right\}$ is

• $\frac{\mathrm{n\pi }}{2} + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4}$

• $2\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4}$

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n} +\hspace{0.17em}1}\frac{\mathrm{\pi }}{4}$

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4} - \frac{\mathrm{\pi }}{4}$

The coordinates of the focus of the parabola described parametrically by x = 5t² + 2, y = 10t + 4 are

• (7, 4)

• (3, 4)

• (3, - 4)

• (- 7, 4)

For any two sets A and B, A - (A - B) equals

• B

• A - B

• $\mathrm{A} \cap \mathrm{B}$

• ${\mathrm{A}}^{\mathrm{C}} \cap {\mathrm{B}}^{\mathrm{C}}$

If a= 2$\sqrt{2}$, b = 6, A= 45°, then

• no triangle is possible

• one triangle is possible

• two triangles are possible

• either no triangle or two triangles are possible

In a triangle ABC, if $\sin \left(\mathrm{A}\right) \sin \left(\mathrm{B}\right) = \frac{\mathrm{ab}}{{\mathrm{c}}^2}$, then the triangle is

• equilateral

• isosceles

• right angled

• obtuse angled

The value of $\left(1 + \cos \left(\frac{\mathrm{\pi }}{6}\right)\right)\left(1 + \cos \left(\frac{\mathrm{\pi }}{3}\right)\right)\left(1 + \cos \left(\frac{2\mathrm{\pi }}{3}\right)\right)\left(1 + \cos \left(\frac{7\mathrm{\pi }}{6}\right)\right)$ is

• $\frac{3}{16}$

• $\frac{3}{8}$

• $\frac{3}{4}$

• $\frac{1}{2}$