A flagpole stands on a building of height 450 ft and an observer

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 Multiple Choice QuestionsMultiple Choice Questions

91.

If from a point P (a, b, c) perpendiculars PA, PB are drawn to yz and zx planes, then the equation of the plane OAB is

  • bcx + cay + abz = 0

  • bcx + cay - abz = 0

  • bcx - cay + abz = 0

  • - bcx + cay + abz = 0


92.

If P (x, y, z) is a point on the line segment joning Q (2, 2, 4) and R (3, 5, 6) such thatprojections of OP on the axes are 135, 195, 265 respectively, then P divides QR in the ratio

  • 1 : 2

  • 3 : 2

  • 2 : 3

  • 1 : 3


93.

The equation to the plane through the points (2, 3, 1) and ( 4, - 5 3) paralled to x - axis is

  • x + y + 4z = 7

  • x + 4z = 7

  • y - 4z = 7

  • y + 4z = 7


94.

The angle between r = (1 + 2µ)i +(2 + µ)j + (2µ - 1)k and the plane 3x - 2y + 6z = 0 (whereµ is a scalar) is

  • sin-11521

  • cos-11621

  • sin-11621

  • π2


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95.

The length of the shortest distance between the two lines r = (- 3i + 6j) + s (- 4i + 3j + 2k) and r = (- 2i + 7k) + t(- 4i + j + k) is

  • 7 unit

  • 13 unit

  • 8 unit

  • 9 unit


96.

The perpendicular distance of the point (6, 5, 8) from y-axis is

  • 5 unit

  • 6 unit

  • 8 unit

  • 10 unit


97.

The equation of the plane passing through the origin and containing the line

x - 15 = y - 24 = z - 35 is

  • x + 5y - 3z = 0

  • x - 5y + 3z = 0

  • x - 5y - 3z = 0

  • 3x - 10y + 5z = 0


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98.

A flagpole stands on a building of height 450 ft and an observer on a level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is 30° and the height of the flagpole is SO ft. If 8 is the angle of elevation of the top of the flagpole, then tanθ is equal to

  • 433

  • 32

  • 92

  • 35


A.

433

In DCE,

tan30° = 150CD  CD = 15013   CD = 3 × 150Now, in  DCF,   tanθ = DFCD = 2003 . 150 = 433


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99.

If A (0, 0), B (12, 0), C (12, 2), D (6, 7) and E (0, 5) are the vertices of the pentagon ABCDE, then its area in square units, is

  • 58

  • 60

  • 61

  • 63


100.

The equation of the plane perpendicular to the line x - 11 = y - 2- 1 = z + 12  afd passing through the point (2, 3, 1) is

  • r . i^ + j^ + 2k^ = 1

  • r . i^ - j^ + 2k^ = 1

  • r . i^ - j^ + 2k^ = 7

  • r . i^ + j^ - 2k^ = 10


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