In order to eliminate the first degree terms from the equation 2x² + 4xy + 5y² - 4x - 22y + 7 = 0, the point to which origin is to be shifted, is

• (1, - 3)

• (2, 3)

• (- 2, 3)

• (1, 3)

The angle between the line joining the points (1, - 2), (3, 2) and the line x + 2y - 7 = 0 is

• $\mathrm{\pi }$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$

If A(2, - 1) and B(6, 5) are two points the ratio in which the foot of the perpendicular from(4, 1) to AB divides it, is

• 8 : 15

• 5 : 8

• - 5 : 8

• - 8 : 5

The angle between the pair of straight lines formed by joining the points of intersection of x² + y² = 4 and y = 3x + c to the ongin is a right angle. Then c² is equal to

• 20

• 13

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$

• 5

$$\begin{gathered} \mathrm{If} \mathrm{the} \mathrm{lines} {\mathrm{x}}^2 +\hspace{0.17em}2\mathrm{xy} - 35{\mathrm{y}}^2 - 4\mathrm{x} + 44\mathrm{y} - 12 = 0 \mathrm{and} \\ 5\mathrm{x} + \mathrm{\lambda y} - 8 = 0 \mathrm{are} \mathrm{concurrent}, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{\lambda } \mathrm{is} \end{gathered}$$

• 0

• 1

• - 1

• 2

If the sum of the distances of a point P from two perpendicular lines in a plane is 1, then the locus of P is a

• rhombus

• circle

• sr==traight line

• pair o straight lines

The transformed equation of 3x² + 3y² + 2xy = 2, when the coordinate axes are rotated through an angle of 45°, is

• ${\mathrm{x}}^2 + 2{\mathrm{y}}^2 = 1$

• $2{\mathrm{x}}^2 + {\mathrm{y}}^2 = 1$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 = 1$

• x² + 3y² = 1

The value of k such that the lines 2x - 3y + k = 0,

3x - 4y - 13 = 0 and 8x - 11y - 33 = 0 are concurrent, is

• 20

• - 7

• 7

• - 20

The value of A such that ${\mathrm{\lambda x}}^2 - 10\mathrm{xy} +12{\mathrm{y}}^2 +\hspace{0.17em}5\mathrm{x} - 16\mathrm{y} - 3 = 0$ represents a pair of straight lines, is

• 1

• - 1

• 2

• - 2

150.

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x² + y² = 4 with x + y = a. The set containing the value of 'a' is

• {- 2, 2}

• {- 3, 3}

• {- 4, 4}

• {- 5, 5}