Question Bank  Geometry  Shashank Prabhu, CAT 100 Percentiler

Number of Questions  100
Topic  Geometry
Answer Key Available ? : Yes
Source : Learningroots forum

Q 7) A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is _____.
(a) 10
(b) 12
(c) 14
(d) 16
(e) None of these[OA: Option b]

Q24) A colorless cube is painted blue and then cut parallel to sides to form two rectangular solids of equal volume. What percentage of surface area of each of new solids is not painted blue?
a. 25
b. 16
c. 20
d. 18

Q35) The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is 3/2 times that of the side of the square, then the side of the square is :
(a) 15 cm
(b) 20 cm
(c) 30 cm
(d) 60 cm

Q45) The exterior angles of a quadrilateral are in the ratio 1:3:4:7. What is the sum of the largest and the smallest interior angles of the quadrilateral?

Q46) The sides of a rhombus ABCD measure 2 cm each and the difference between two angles is 90°. The area of the rhombus is

Q47) ABCD is a rectangle with AB = 6 cm and AD = 8 cm. QR is an arc which cuts the extension of AD at Q and AB at R. What is the length of the arc QR if C is a point on it ?
(a) 10 pi
(b) 5 pi
(c) 20 pi
(d) 24 pi

Q55) An isosceles trapezium is circumscribed about a circle. One of the parallel sides is thrice the other. Find the area (in sq cm) of the trapezium, if its perimeter is 8 cm.
a. sqrt(3)
b. 2sqrt(3)
c. 3sqrt(3)
d. 4sqrt(3)

Q60) The longest side of a triangle is 10 cm and one of the other sides is 5 cm long. If the area of the triangle is 20 sq cm, what is the length of the third side of the triangle?

Q69) Chord PQ of a circle is the perpendicular bisector of chord XY of the same circle such that they intersect at point M inside the circle. XY = PM = 14. What is the area of the circle?

Q77) Identical black tiles, in the shape of a square of side 4 cm, are placed along the two diagonals of a square shaped floor of side 52 cm. The rest of the floor is covered with identical white tiles of same shape and size. How many white tiles need to be replaced by the black tiles so that the black and the white tiles are in alternate positions in all the rows and columns?

Q81) A circle of radius 6.5 cm is circumscribed around a rightangled triangle with the sides a, b and c cm where a, b and c are natural numbers. What is the perimeter of the triangle?

Q83) 216 small cubes are aggregated to form a larger cube whose 3 faces are painted blue and 3 faces are painted red. None of the small cubes has all the three faces of the same colour. How many of the small cubes have exactly 2 faces coloured both of which are either blue or red?

Q23) D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC. What is the ratio of the circumradii of triangles DEF and ABC respectively?
[OA: 1/2]

Q28) In Δ PQR, S and T are the midpoints of PR and PQ respectively; QS is perpendicular to RT; QS = 8; RT = 12. What is the area of triangle PQR?
a. 24
b. 32
c. 48
d. 64
[OA: 64]

Q37) In a trapezium, when the midpoints of the diagonals are joined, the line so formed is 5 cm long. Further, if the length of one of the parallel sides of the trapezium is 25 cm, then find the length of the other parallel side.
[OA: 15]

Q40) The midpoints, P, Q and R, of triangle ABC are joined to form a new triangle PQR at the centre and three other triangles on the sides PQ, QR and PR. Then the midpoints of triangle PQR are joined to form another new central triangle along with three other triangles on its sides. This process of joining the midpoints of the central triangle is repeated infinite times. If the area of triangle ABC is 6 sq. cm then what is the sum of the areas of all the new triangles formed in the figure?
[OA: 2 sq cm]

Q77) The number of values of b for which there is an isosceles triangle with sides of lengths (b + 5), (3b – 2) and (6 – b) is
[OA: 2]

Q78) Let ABCD be a square and P be a point on segment CD such that DP:PC = 1:2. Let W be a point on AP such that < BQP = 90 degrees.Then the ratio of the area of the quadrilateral PQBC to the area of the square ABCD is
[OA: 41/60]

Q86)
[OA: C]