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

385.

The curve y = (λ + 1)x² + 2 intersects the curve y = λx + 3 in exactly one point, if λ equals -

• {–2, 2}

• {1}

• {-2}

• {-2}

If the curves y² = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is

• 9/2

• 6

• 7/2

• 4

If L₁ is the line of intersection of the plane 2x – 2y + 3z – 2 = 0, x – y + z + 1 = 0 and L₂ is the line of intersection of the plane x + 2y – z – 3 = 0, 3x – y + 2z – 1 = 0, then the distance of the origin from the plane containing the lines L₁
and L₂ is :

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{4\sqrt{2}}$

• $\frac{1}{3\sqrt{2}}$

• $\frac{1}{2\sqrt{2}}$

The equation of the plane through (1, 2,- 3) and (2,- 2, 1) and parallel to X-axis is

• y - z + 1 = 0

• y - z - 1 = 0

• y + z - 1 = 0

• y + z + 1 = 0

Three lines are drawn from the origin O with direction cosines proportional to (L,-1, 1), (2,-3, 0) and (1, 0, 3). The three lines are

• not coplanar

• coplanar

• perpendicular to each other

• coincident

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at

• (1, 2, 5)

• (2, 2, 2)

• (2, 1, 5)

• (1, 1, 6)