The equation of the plane through the line of intersection of the

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The angle between the planes 3x + 4y + 5z = 3 and 4x - 3y + 5z = 9 is equal to

  • π2

  • π4

  • π6

  • π3


42.

The vector equation of the plane through the point (2, 1, - 1) and parallel to the plane r - (i + 3j - k) = 0 is

  • r . (i + 9j + 11k) = 6

  • r . (i - 9j + 11k) = 4

  • r . (i + 3j - k) = 6

  • r . (i + 3j - k) = 4


43.

If the foot of the perpendicular drawn from the point (5, 1, - 3) to a plane is (1, - 1, 3), then the equation of the plane is

  • 2x + y - 3z + 8 = 0

  • 2x + y + 3z + 8 = 0

  • 2x - y - 3z + 8 = 0

  • 2x - y + 3z + 8 = 0


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44.

The equation of the plane through the line of intersection of the planes x - y + z + 3 = 0 and x + y + 22 + 1 = 0 and parallel to x-axis is

  • 2y - z = 2

  • 2y + z = 2

  • 4y + z = 4

  • y - 2z = 3


B.

2y + z = 2

The intersection equation of planes x - y + z + 3 = 0 and x + y + 2z + 1 = 0 is (x - y + z + 3) + λ(x + y + 2z + 1) = 0

 1 + λx + - 1 + λy + 1 + 2λz + 3 + λ = 0DR's of x - axis is (1, 0, 0)Since, above plane is parallel to x-axis  Coefficient of x = 01 - λ = 0   λ = - 1 1 - 1x + - 1 - 1y + 1 - 2z + 3 - 1 = 0 0 - 2y - z + 2 = 0                2y + z = 2


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45.

5x dx1 - x3 is equal to

  • 52x - 12 - 5x - 1 + C

  • 52x - 12 + 5x - 1 + C

  • 53x - 12 + 52x - 1 + C

  • 53x - 12 - 52x - 1 + C


46.

dxx - x is equal to

  • 2logx - 1 + C

  • 2logx + 1 + C

  • logx - 1 + C

  • 12logx + 1 + C


47.

dx4sin2x + 3cos2x

  • 34tan-12tanx3 + C

  • 123tan-1tanx3 + C

  • 23tan-12tanx3 + C

  • 123tan-12tanx3 + C


48.

secxdxcos2x is equal to

  • 2sin-1tanx

  • tan-1tanx2 + C

  • sin-1tanx

  • 32tan-1tanx3 + C


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49.

exxxlogx + 1dx is equal to

  • exx + C

  • xexlogx + C

  • exlogx + C

  • x(exlogx) + C


50.

1 + logx1 + x logx2dx is equal to

  • 11 + xlogx + C

  • 11 + logx + C

  • - 11 + xlogx + C

  • log11 + logx + C


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