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Solved Examples
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D   Which of the following is not a possible sum of angles of a spherical triangle?   D View Solution
D   The amount by which the sum of the angles of a triangle exceeds 180° is called :   D View Solution
D   Which of the following is a possible sum of the angles of a spherical triangle?
   D
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D   If the sum of the angles of a spherical triangle is 240°, then what is the spherical excess?
   D
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D   If the arc lengths of a spherical triangle are π2, π3 and π6 respectively, then what is the spherical defect?
   D
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D   The surface area of the spherical triangle with angles A = 5π6, B = t and C = π2, which sits on a sphere of radius 2 cm is 2π, find the angle B.   D View Solution
D   The shortest path from one point to another on a spherical surface is along the arc of a great circle. This shortest path is called as:
   D
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D   If the radius of a sphere is 1 cm, then what is the area of any great circle on the sphere?   D View Solution
D   The surface area of the spherical triangle with angles A = t, B = π4 and C = π4, which sits on a sphere of radius 1 cm is π6, find the angle A.   D View Solution
D   If the radius of a sphere is 3cm, then what is the circumference of any great circle on the sphere?
   D
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D   If the radius of a sphere is 2 cm, then what is the diameter of any great circle on the sphere?   D View Solution
D   If the radius of any great circle on a sphere is 5 cm, then what is the surface area of that sphere?   D View Solution
D   If the radius of any great circle on a sphere is 10 cm, then what is the volume of that sphere?   D View Solution
D   Let (3, 4) be a point on a sphere. If the center of that sphere is (0, 0), then what is the radius of any great circle?   D View Solution
D   Which of the following is false about spherical triangle?
I. The three sides are all arcs of great circles.
II. The sum of all angles is between 90° and 180°.
III. The sum of the three angles is greater than 180°.
IV. Each spherical angle is less than 180°.   D
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D   The parallel postulate for Spherical Geometry is:
   D
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D   Which of the following statements is correct?
I. Two distinct lines in Euclidean Geometry intersect in at most one point.
II. Two distinct lines in Euclidean Geometry intersect in finite number of points.
III. Two distinct lines (great circles) in Spherical Geometry intersect in at most one point.
IV. Two distinct lines (great circles) in Spherical Geometry intersect in finite number of points.   D
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D   Find the surface area of the spherical triangle with angles A = 90°, B = 60° and C = 45°, which sits on a sphere of radius R = 6 cm.
   D
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D   The sum of the angles of a spherical triangle is between:   D View Solution
D   Which of the following statements is correct?
I. There is a unique straight line passing through any two points on a plane, in plane Euclidean Geometry.
II. There are finite number of straight lines passing through any two points on a plane, in plane Euclidean Geometry.
III. There is a unique circle passing through any two non-polar points on sphere, in Spherical Geometry.
IV. There are finite number of great circles passing through any two non-polar points on a sphere, in Spherical Geometry.   D
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D   Which of the following statements is correct?
I. There are finite number of staright lines passing through any two points on a plane, in plane Euclidean Geometry.
II.There are finite number of great circles passing through any two non-polar points on a sphere, in spherical seometry.
III. There are infinite number of straight lines passing through any two points on a sphere, in spherical geometry.
IV. There are infinite number of great circles passing through any non-polar point on a sphere, in spherical geometry.
   D
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D   Which of the following statements is correct?
I. Every great circle of a sphere intersects all the other great circles of a sphere in exactly one point.
II. Every great circle of a sphere intersects all the other great circles of a sphere in exactly two points.
III. Every great circle of a sphere intersects all the other great circles of a sphere in finite number of points.
IV. Every great circle of a sphere intersects all the other great circles of a sphere in infinite number of points.
   D
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D   The difference between 2π and the sum of the side arc lengths a, b and c of a spherical triangle is called :   D View Solution
D   The surface area of the spherical triangle with angles A = 120°, B = 90° C = 60°, which sits on a sphere of radius R is 2π3 cm2, find R?   D View Solution
D   The surface area of the spherical triangle with angles A = 2π3, B = π3 and C = t, which sits on a sphere of radius 3 cm is π, find the angle C.   D View Solution