A cylinder with radius r and height h has volume 1 and total surface area 12. Find the value of 1/r +1/h

a)2
b)3
c)4
d)5
e)6

Two circles of equal radius are tightly fit as in a triangle ABC as shown. AB=13,BC=12 and CA=5


Find the radius of the circle

a)3/2
b)20/9
c)26/17
d)5/2
e)None of these

A large park contains a building in the shape of pentagon whose sides is 6m. A goat is tied to a 10m long rope which is tied to the one corner of the building. Find the approx area in m² which goat can graze.

a)240
b)100
c)215
d)220
e)230

A triangle ABC whose sides are AB=8, BC=13 and CA=15. Find the number of points P on CA such that AP and BP both are integers.


a)2
b)3
c)4
d)5
e)None of these

A boy has a square of side length 5 which is divides into unit squares by lines parallel to its sides. Let A be the set of vertexes of the unit squares which are not on the sides of the given squares. How many points from A can be chosen at most in a way that no three of them are vertexes of isosceles rectangle triangle.

a)6
b)8
c)10
d)12
e)None of these

Semi circles are drawn on each side of the right angle triangle. Find the area of the shaded region. AB=8 BC=15 and CA=17



a) 40
b) 30√2
c) 60
d) 30√3
e) None of these

The diagram shows a semicircle and two quarter circles inscribed in a square of side length 2. The difference between the area of the shaded region A and the area of the shaded region B equals a)3π/2 - 4
b)π/3 - 1/3
c)3/2 - π/4
d)4 - π
e)π/4

An equilateral triangle of side length 'a' in which three circles of radii 2,3 and 4 without common innner points can be placed.Find smallest possible value of 'a'.

a)11√3
b)9√3
c)8√3
d)4√3
e)None of these

A square ABCD of side length 1 unit. M and N are two points on BC and CD respectively, such that the perimeter of the triangle MCN is 2 units. Find the value of angle MAN in degrees.

a)30
b)45
c)60
d)75
e)None of these

ABCDE is a convex pentagon and let M,P,N,Q be the midpoints of the segments AB,BC,CD,DE respectively.If K,L are the mid points of the segment MN and PQ respectively and segment AE is of length a,Find the length KL.

a)a/3
b)a/4
c)a/5
d)a/2
e)None of these