51.

Consider a parallelogram whose vertices are A(1, 2), B(4, y), C(x, 6) and D(3, 5) taken in order

What is the point of the intersection of the diagonals ?

• $\left(\frac{7}{2}, 4\right)$

• (3, 4)

• $\left(\frac{7}{2}, 5\right)$

• (3, 5)

Consider a parallelogram whose vertices are A(1, 2), B(4, y), C(x, 6) and D(3, 5) taken in order

What is the area of parallelogram ?

• $\frac{7}{2}$ square units

• 4 square units

• $\frac{11}{2}$ square units

• 7 square units

(a, 2b) is the mid-point of the line segment joining the points (10, - 6) and (k, 4). If a - 2b = 7, then what is the value of R ?

• 2

• 3

• 4

• 5

What is the area of the paralleloram having diaonals $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}} \mathrm{and} \hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}} ?$

• $5\sqrt{5}$ square units

• $4\sqrt{5}$ square units

• $5\sqrt{3}$ square units

• $15\sqrt{2}$ square units

What is the acute angle between the lines represented by the equations

$\mathrm{y} - \sqrt{3}\mathrm{x} - 5 = 0 \mathrm{and} \sqrt{3}\mathrm{y} - \mathrm{x} + 6 = 0$

• $30°$

• $45°$

• $60°$

• $75°$

The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill ?

• $\frac{\mathrm{hcot}\left(\mathrm{q}\right)}{\cot \left(\mathrm{q}\right) - \cot \left(\mathrm{p}\right)}$

• $\frac{\mathrm{hcot}\left(\mathrm{p}\right)}{\cot \left(\mathrm{p}\right) - \cot \left(\mathrm{q}\right)}$

• $\frac{2\mathrm{htan}\left(\mathrm{p}\right)}{\tan \left(\mathrm{p}\right) - \tan \left(\mathrm{q}\right)}$

• $\frac{2\mathrm{h}\tan \left(\mathrm{q}\right)}{\tan \left(\mathrm{q}\right) - \tan \left(\mathrm{p}\right)}$

A moving boat is observed from the top of a cliff of 150m height. The angle of depression of the boatchanges from 60° to 45° in 2 minutes. What is the speed of the boat in metres per hour ?

• $\frac{4500}{\sqrt{3}}$

• $\frac{4500\left(\sqrt{3} - 1\right)}{\sqrt{3}}$

• $4500\sqrt{3}$

• $\frac{4500\left(\sqrt{3} + 1 \right)}{\sqrt{3}}$

What is the equation of the right bisector of the line segment joining (1, 1) and (2, 3) ?

• 2x + 4y - 11 = 0

• 2x - 4y - 5 = 0

• 2x - 4y - 11 = 0

• 2x - 4y - 5 = 0

An equilateral triangle has one vertex at (0, 0) and another at (3, $\sqrt{3}$). What are the coordinates of the third vertex ?

• $\left(0, 2\sqrt{3}\right)$ only

• $\left(3, - \sqrt{3}\right) \mathrm{only}$

• $\left(0, 2\sqrt{3}\right) \mathrm{or} \left(3, - \sqrt{3}\right)$

• Neither $\left(0, 2\sqrt{3}\right) \mathrm{nor} \left(3, - \sqrt{3}\right)$

If the point (a, a) lies between the lines $\left|\mathrm{x} + \mathrm{y}\right|$ = 2, then which one of the following is correct ?

• $\mathrm{a} < 2$

• $\mathrm{a} < \sqrt{2}$

• $\left|a\right| < 1$

• $\left|\mathrm{a}\right| < \frac{1}{\sqrt{2}}$