A two digit number is such that the product of its digits is 54. If 27 is subtracted from the number, the digits interchange their places. Find the number.

If ^@ D ^@ is a point on the side ^@AB^@ of ^@\Delta ABC^@ such that ^@AD:DB = 8:6^@ and ^@E^@ is a point on ^@BC^@ such that ^@DE || AC^@, find the ratio of the areas of ^@\Delta ABC^@ and ^@\Delta DBE^@.

The three vertices of a parallelogram ^@ABCD^@ taken in order are ^@A(4,-2)^@, ^@B(8, -2)^@ and ^@C(6, -6)^@. Find the coordinates of the fourth vertex ^@D^@.

A rope is tightly stretched and attached from top of a vertical tower to the ground. The angle made by rope with ground is 45°. If height of the tower is m, find length of the rope.

A chord of a circle of radius ^@ 56 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding major segment.^@ \bigg[\pi = \dfrac { 22 } { 7 }\bigg] ^@

A hall is in form of a right circular cylinder and cone as shown in the picture. The radius of cone and cylinder is 4 meters. The height of cylinder and cone are 8 meters and 3 meters respectively. Find the outer surface area of the hall. (Assume π =

There are 4 pens belonging to 4 students. The pens were put into a box, and each student pulls out an pen one after the other. What is the probability that each student gets his or her own pen?

In this diagram, the triangle represents women, the square represents accountants and the circle represents sports persons. Find the number of women who are sports persons but not accountants.