CAT4MBA

1) The ratio of sides of a triangle ABC is 1:2:4. What is the ratio of the altitude drawn onto these sides?

a) 4:2:1   b) 1:2:4   c) 1:4:16   d) None of these

2)  A quadrilateral is inscribed in a circle . If an angle is inscribed in each of the segment outside the quadrilateral ,then what is the sum of the four angles?

3) A squre is inscribed in a circle which is inscribed in an equilateral triangle . If one side of the triangle is a, find the area of the square.

4) A cyclic quadrilateral is such that two of its adjacent angles are divisible by 6 and 10 respectively. One of the remaining angles will be divisible by

5) If in the above question if one of the remaining angle be necessarily didvisible by 16 ,then its measure can be

6)The volume of the square is proportional to the cube of their radii.Two sphere of the same material weighs 3.6 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two were melted down and formed into single sphere,what would be its radius.

7) ABCD is a parellogram in which angle B = 70 dgree. Find the number of the points X in the plane of the parallelogram such that it is equidistant from the vertices.

8)Two circle of equal radii are drawn without any overlap,in a semicircle of radius 2 cm. If these are the large possible circle that the semicircle can accomodate .What is the radius (in cm) of each the circles?

9) Two circles with centre C1 and C2 and radii 6 cm and 8 cm respectively cut each other at right angles. find the lenght of common chord.

10) Let ABCDEF be a regular hexagon . What is the ratio of the area of the triangle ACe to that of the hexagon ABCDEF?

11) Let A be the area of a square inscribed in a circle of radius "r" and let B be the area of a hexagon inscribed in the same circle. Then B/A equals.

12) The ratio of the area of a square inscribed in a semicircle to that of the area of the square inscribed in the circles of the same radius is 

13) What is the area of the triangle in which two of its median 9 cm and 12 cm long intersect at the right angles.

14) If one leg of the isosceles right angled triangle is increased be by 6 cm and that of the other leg decreased by 6 cm and that of the other leg dcreased by 4 cm. Then the area of the triangle is decreased by 24 cm square . then the area of the traingle decreased by 24 cm square . find the length of the original triangle.

15) ABCDE is a parellogram in which angle D is 120 degree. The bisector of angle D bisect the side AB. If the length of bisector is 5 cm ,what is the perimeter of the parallelogram?

16) Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 metre square at the centre . Find the ungrazed area.

17) Euclid has a triangle inscribed . Its longest side has length 20 and another of its sides has lentgth 10 . Its area is 80. What is the exact length of 3rd side?

18) AB is the hypotenuous in the right angle triangle ABC. N is the point inside te triangle which divides the triangle in three equal parts between the circumcentre from this point N?

Ans:
1) d) None of these
2) 540
4) 3
5) 112
6) 206
7) 0
8) 0.414
9) 9.6
10) 1/2
11) 3 x 1.732/4
12) 2:3
13) 72
15) 30 cm
16) 42
17)  root 20
18) AB/r