The angles of a triangle are in the ratio 1 : 3 : 5. Then the gre

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191.

The angles of a triangle are in the ratio 1 : 3 : 5. Then the greatest angle is :

  • 5π9

  • 2π9

  • 7π9

  • 11π9


A.

5π9

 Let x, 3x and 5x are angles of triangle x + 3x + 5x = π x = π9, so  greatest angle = 5π9.


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192.

A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. Then angle subtended by the arc at the centre is:

  • 50°

  • 210°

  • 100°

  • 60°


193.

The radius of the circle x2 + y2 + z2 - 2y - 4z - 11 = 0 and x + 2y + 2z - 15 = 0 is :

  • 3

  • 5

  • 7

  • 3


194.

If a + b + c = 0, a = 3, b = 5 and c = 7, then angle between a and b is :

  • 0

  • 30°

  • 45°

  • 60°


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195.

The points A (4, 5, 1), B (0, - 1, - 1), C(3, 9, 4) and D(- 4, 4, 4) are

  • collinear

  • coplanar

  • non-coplanar

  • non-collinear


196.

If a + b + c = 0, a = 3, b = 5 and c = 7, then the angle between a and b is :

  • π3

  • π2

  • cos-12225

  • π4


197.

The shortest distance from the point (1, 2, - 1) to the surface of the sphere x2 + y2 + z2 = 24 is :

  • 36 unit

  • 6 unit

  • 26

  • 2 sq unit


198.

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is :

  • x - y - z - 15 = 0

  • x - y - z - 15 = 0

  • x + y + z - 15 = 0

  • x + y + z + 15 = 0


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199.

A line makes acute angles of α, β and γ with the co-ordinate axes such that cosαcosβ = cosβcosγ = 29 and cosγcosα = 49, then cosα + cosβ + cosγ is equal to :

  • 259

  • 59

  • 53

  • 23


200.

The equation of the plane through the point (1, 2, 3), (- 1,  4, 2) and (3, 1, 1) is :

  • 5x + y + 12z - 23 = 0

  • 5x + 6y + 2z - 23 = 0

  • x + 6y + 2z - 13 = 0

  • x + y + z - 13 = 0


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