If one of the lines of my²+ (1 − m²)xy − mx² = 0 is a bisector of the angle between the lines xy = 0, then m is

• −1/2

• -2

• 1

• 1

Angle between the tangents to the curve y = x² − 5x + 6 at the points (2, 0) and (3, 0) is

• π/2

• π/4

• π/6

• π/6

33.

The image of the point (−1, 3, 4) in the plane x − 2y = 0 is

• 
• 

• (15, 11, 4)

• (15, 11, 4)

The normal to the curve x = a(cosθ + θ sinθ), y = a( sinθ - θ cosθ) at any point ‘θ’ is such that

• it passes through the origin

• it makes angle π/2 + θ with the x-axis

• it passes through (aπ/2 ,-a)

• it passes through (aπ/2 ,-a)

The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

• below the x−axis at a distance of 3/2 from it

• below the x−axis at a distance of 2 /3 from it

• above the x−axis at a distance of 3/ 2 from it

• above the x−axis at a distance of 3/ 2 from it

If the angle θ between the line and the plane  is such of sin θ = 1/3 the value of λ is

• 5/3

• -3/5

• 3/4

• 3/4

The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

• 0^o

• 90^o

• 45^o

• 45^o

If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x² + y² + z² + 6x − 8y − 2z = 13 and x² + y² + z² − 10x + 4y − 2z = 8, then a equals

• -1

• 1

• -2

• -2

The distance between the line  and the plane 

• 10/9

• 

• 3/10

• 3/10

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

• (-1, 7/3)

• (-1/3, 7/3)

• (1, 7/3)

• (1, 7/3)