Geometry - Basics - Previous Year CAT/MBA Questions
You can practice all previous year OMET questions from the topic Geometry - Basics. This will help you understand the type of questions asked in OMET. It would be best if you clear your concepts before you practice previous year OMET questions.
A rod is cut into 3 equal parts. The resulting portions are then cut into 12, 18 and 32 equal parts, respectively. If each of the resulting portions have integer length, the minimum length of the rod is
Answer: Option B
As the three portions of the rod correspond to 12, 18 and 32 equal parts, their length will be equal to LCM of 12, 18 and 32.
LCM of 12, 18 and 32 = 288
Since there are three equal parts of the rod, total length = 288 × 3 = 864
Hence, option 2.
In a square of side 2 meters, isosceles triangles of equal area are cut from the corners to form a regular octagon. Find the perimeter and area of the regular octagon.
None of these
Answer: Option D
Let the side of isosceles triangle be x.
∴ The side of octagon x.
∴ x + x + x = 2
∴ 2x + x = 2
∴ x =
∴ Side of octagon = x = =
∴ Perimeter of octagon = 8 × = units
Area of octagon = Area of square – 4 × Area of isosceles triangle
= 22 - 4 × x2
= 4 - 4 × ×
= 4 - = sq. units
Hence, option 4.
Let A1 be a square whose side is ‘a’ metres. Circle C1 circumscribes the square A1 such that all its vertices are on C1. Another square A2 circumscribes C1. Circle C2 circumscribes A2, and A3 circumscribes C2, and so on. If DN is the area between the square AN and the circle CN, where N is a natural number, then the ratio of the sum of all DN to D1 is:
None of the above
Answer: Option C
Area of square 1 = a2
Area of circle 1 = π
∴ D1 = (π - 2)
Area of square 2 = (a)2
Area of circle 2 = πa2
∴ D2 = a2(π - 2)
D3 = 2a2 (π - 2), and so on.
∴ D1 + D2 + D3 + ... = a2(π - 2) [0.5 + 1 + 2 + 4 + ...]
Hence, option 3.
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