A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance

• 2H/A-B

• H/A+B

• H/2(A+B)

• H/2(A+B)

The plane x + 2y – z = 4 cuts the sphere x² + y² + z² – x + z – 2 = 0 in a circle of radius

• 3

• 1

• 2

• 2

Let A (2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

• 2x + 3y = 9

• 2x – 3y = 7

• 3x + 2y = 5

• 3x + 2y = 5

A line makes the same angle θ, with each of the x and z-axis. If the angle β, which it makes with y-axis, is such that sin²β = 3sin²θ , then cos2θ equals 

• 2/3

• 1/5

• 3/5

• 3/5

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

• 3/2

• 5/2

• 7/2

• 7/2

A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

• (3a, 3a, 3a), (a, a, a)

• (3a, 2a, 3a), (a, a, a)

• (3a, 2a, 3a), (a, a, 2a)

• (3a, 2a, 3a), (a, a, 2a)

47.

If the straight lines x = 1 + s, y = –3 – λs, z = 1 + λs and x = t/ 2 , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then λ equals

• –2

• –1

• -1/2

• -1/2

The intersection of the spheres x² +y² +z² + 7x -2y-z =13 and x² +y² +z² -3x +3y +4z = 8 is the same as the intersection of one of the sphere and the plane

• x-y-z =1

• x-2y-z =1

• x-y-2z=1

• x-y-2z=1

If the straight line y = mx + c (m > 0) touches the parabola y² = 8(x + 2), then the minimum value taken by c is

• 12

• 8

• 4

• 4

The equation of the plane which contains the line of intersection of the planes x + y + z – 6 = 0 and 2x + 3y + z + 5 = 0 and perpendicular to the xy plane is:

• x – 2y + 11 = 0

• x + 2y + 11 = 0

• x + 2y – 11 = 0

• x + 2y – 11 = 0