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

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 Multiple Choice QuestionsMultiple Choice Questions

41.

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)

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42.

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

158 Views

43.

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

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44.

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

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45.

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

  • 3/2

  • 5/2

  • 7/2

  • 7/2


C.

7/2

The distance between 4x + 2y + 4z - 16 = 0 and 4x + 2y + 4z + 5 = 0 is

open vertical bar fraction numerator 5 plus 16 over denominator square root of 16 plus 4 plus 16 end root end fraction close vertical bar space equals space open vertical bar fraction numerator 21 over denominator square root of 36 end fraction close vertical bar space equals space 21 over 6 space equals space 7 over 2

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46.

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)

200 Views

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

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48.

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

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49.

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

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50.

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

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