51. Find the coordinates of the point which divides the line joining (5, -2) and (9, 6) internally in the ratio 1 : 3.
(a) (6, 0)
(b) (6, 3)
(c) (0, 6)
(d) (3, 6)
Ans : (a)
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52. Find the number of triangles in an octagon.
(a) 326
(b) 120
(c) 56
(d) Cannot be determined
Ans : (c)
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53. Find the equation of a line whose intercepts are twice of the line 3x - 2y - 12 = 0
(a) 3x - 2y = 24
(b) 2x - 3y = 12
(c) 2x - 3y = 24
(d) None of these
Ans : (a)
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54. Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm.
(a) 77 sq.cm
(b) 38.5 sq.cm
(c) 35 sq.cm
(d) 70 sq.cm
Ans : (b)
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55. Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).
(a) 36
(b) 18
(c) 15
(d) 30
Ans : (c)
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56. A stairway 10ft high is such that each step accounts for half a foot upward and one-foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?
(a) 30 ft
(b) 33 ft
(c) 10 ft
(d) 29 ft
Ans : (d)
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57. Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?
(a) 6
(b) 8
(c) 12
(d) 3
Ans : (c)
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58. What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?
(a) lw/3
(b) (2lw)/3
(c) (3lw)/4
(d) (lw)/2
Ans : (d)
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59. Which of the following is inCorrect?
(a) An incentre is a point where the angle bisectors meet.
(b) The median of any side of a triangle bisects the side at right angle
(c) The point at which the three altitudes of a triangle meet is the orthocentre
(d) The point at which the three perpendicular bisectors meet is the centre of the circumcircle.
Ans : (b)
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60. A and B are two points with the co-ordinates (-2, 0) and (0, 5). What is the length of the diagonal AC if AB form one of the sides of the square ABCD?
(a) units
(b) units
(c) units
(d) units
Ans : (b)
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