Geometry - Previous Year IPM/BBA Questions
The best way to prepare for Geometry is by going through the previous year Geometry questions for IPMAT - Indore. Here we bring you all previous year Geometry IPMAT - Indore questions along with detailed solutions.
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In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA arc in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be
- (a)
12 : 11
- (b)
12 : 11
- (c)
11 : 4√10
- (d)
11 : 12
Solution
Discuss
ReportThe lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is
- (a)
18
- (b)
20
- (c)
19
- (d)
16
In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is
- (a)
12 cm
- (b)
5 cm
- (c)
2√3 cm
- (d)
8 cm
If the angles A, B, C of a triangle are in arithmetic progression such that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
- (a)
-1/2
- (b)
1/2
- (c)
-1/√2
- (d)
3/√2
ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
- (a)
26
- (b)
25
- (c)
21
- (d)
16
The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is
- (a)
28
- (b)
29
- (c)
31
- (d)
33
The sum of the interior angles of a convex n-sided polygon is less than 2019°. The maximum possible value of n is
The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right-angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the tiles and plate are of uniform thickness, and there is no loss of material in the melting and recasting process) is
A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals
- (a)
2 + √3
- (b)
1 + √2
- (c)
7 + 4√3
- (d)
97 + 56√3
Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n . Then the ratio of the area of PQRS to the area of ABCD is
- (a)
1 : (1 + n)
- (b)
1 : n
- (c)
1 + n2 : (1 + n)2
- (d)
(1 + n) : (1 + n2)
On a circular path of radius 6 m a boy starts from a point A on the circumference and walks along a chord AB of length 3 m. He then walks along another chord BC of length 2 m to reach point C. The point B lies on the minor arc AC. The distance between point C from point A is
- (a)
(√15 + √35)/2 m
- (b)
8 m
- (c)
√13 m
- (d)
6 m
Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 cm2 Then the possible values of the sum of their volumes are
- (a)
764 cm3 and 586 cm3
- (b)
586 cm3 and 564 cm3
- (c)
764 cm3 and 564 cm3
- (d)
586 cm3 and 786 cm3