There are 10 points in a plane. No three of these pointsare in a straight line. What is the total number of straight lines which can be formed by joining the points ?

• 90

• 45

• 40

• 30

If the angles of a triangle ABC are in the ratio 1 : 2 : 3, then the corresponding sides are in the ratio : 

• 1 : 2 : 3

• 3 : 2 : 1

• 1 : $\sqrt{3}$ : 2

• $1 :\hspace{0.17em}\sqrt{3} :\hspace{0.17em}\sqrt{2}$

3.

Consider the following statements :

1.For an equation of a line, xcos$\left(\mathrm{\theta }\right)$ + y sin($\left(\mathrm{\theta ) }\right)$= p, in normal form, the length of the perpendicular from the point $\left(\mathrm{\alpha }, \mathrm{\beta }\right) \mathrm{to} \mathrm{the} \mathrm{line} \mathrm{is} \left|\mathrm{\alpha cos}\left(\mathrm{\theta }\right) + \mathrm{\beta sin}\left(\mathrm{\theta }\right) + \mathrm{p}\right|$

2. The length of the perpendicular from the point$\left(\mathrm{\alpha }, \mathrm{\beta }\right) \mathrm{to} \mathrm{the} \mathrm{line} \frac{\mathrm{x}}{\mathrm{a}} + \frac{\mathrm{y}}{\mathrm{b}} = 1 \mathrm{is} \left|\frac{\mathrm{a\alpha } + \mathrm{b\beta } - \mathrm{ab}}{\sqrt{{\mathrm{a}}^2 + {\mathrm{b}}^2}}\right|$

Which of the above statements is/are correct ?

• 1 Only

• 2 Only

• Both 1 and 2

• Neither 1 nor 2

The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c ?

• 2

•  - 2

• 4

•  - 4

If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b ?

• 1

• 3

• 6

• $\frac{1}{2}$

What is the equation of the straight line which is perpendicular to y = x and passes through (3, 2) ?

• x - y = 5

• x + y = 5

• x + y = 1

• x - y = 1

The straight lines x + y - 4 = 0, 3x + y - 4 = 0 and x + 3y - 4 = 0, form a triangle, which is :

• isosceles

• right - angled

• equilateral

• scalene

The angle of elevation of a tower of height h from apoint A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct ?

• ${\mathrm{h}}^2\left({\cot }^2\left(\mathrm{y}\right) - {\cot }^2\left(\mathrm{x}\right)\right) = {\mathrm{z}}^2$

• ${\mathrm{z}}^2\left({\cot }^2\left(\mathrm{y}\right) - {\cot }^2\left(\mathrm{x}\right)\right) = {\mathrm{h}}^2$

• ${\mathrm{h}}^2\left({\tan }^2\left(\mathrm{y}\right) - {\tan }^2\left(\mathrm{x}\right)\right) = {\mathrm{z}}^2$

• ${\mathrm{z}}^2\left({\tan }^2\left(\mathrm{y}\right) - {\tan }^2\left(\mathrm{x}\right)\right) = {\mathrm{h}}^2$

What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3 ?

• $\frac{12\sqrt{17}}{5}$

• $\frac{13\sqrt{17}}{5}$

• $\frac{\sqrt{17}}{5}$

• $\frac{6\sqrt{17}}{5}$

What is the angle between the straight lines (m² - mn)y = (mn + n²) x + n³ and (mn + m)y = (mn - n)r + m³, where m > n ?

• ${\tan }^{-1}\left(\frac{2\mathrm{mn}}{{\mathrm{m}}^2 +\hspace{0.17em}{\mathrm{n}}^2}\right)$

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

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

• 45⁰