31.

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

If l, m, n are in arithmetic progression, then the straight line b + my + n = 0 will pass through the point

• (- 1, 2)

• (1, - 2)

• (1, 2)

• (2, 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

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}

In $∆$ABC the mid points of the sides AB, BC and CA are respectively (l, 0, 0), (0, m, 0) and (0, 0, n). Then, $\frac{{\mathrm{AB}}^2 + {\mathrm{BC}}^2 + {\mathrm{CA}}^2}{{\mathrm{l}}^2 + {\mathrm{m}}^2 + {\mathrm{n}}^2} = ?$

• 2

• 4

• 8

• 16

If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is

• x² + y² + 2x - 4y - 47 = 0

• x² + y² = 49

• x² + y² - 2x + 2y - 47 = 0

• x² + y² = 17

The inverse of the point (1, 2) with respect to the circle   

x² + y² - 4x - 6y + 9 = 0, is

• $\left(1, \frac{1}{2}\right)$

• $\left(2, 1\right)$

• $\left(0, 1\right)$

• $\left(1, 0\right)$

If $\mathrm{\theta }$ is the angle between the tangents from(- 1, 0) to the circle x² + y² - 5x + 4y - 2 = 0, then $\mathrm{\theta }$ is equal to

• $2{\tan }^{-1}\left(\frac{7}{4}\right)$

• ${\tan }^{-1}\left(\frac{7}{4}\right)$

• $2{\cos }^{-1}\left(\frac{7}{4}\right)$

• ${\cot }^{-1}\left(\frac{7}{4}\right)$