A boat running upstream takes ^@ 8{\space} hours^@ ^@41{\space} minutes^@ to cover a certain distance, while it takes ^@4{\space} hours^@ to cover the same distance in running downstream. What is the ratio between the speed of the boat and the speed of stream?
Let ^@\alpha^@ and ^@\beta^@ be the roots of the quadratic equation ^@x^2 + 2 bx + b = 5^@. What is the smallest possible value of ^@(\alpha - \beta)^2^@ ?
Given a right-angled ^@\Delta ABC^@. The lengths of the sides containing the right angle are ^@35 \space cm^@ and ^@12 \space cm^@. A circle is inscribed in ^@\Delta ABC^@. Find the radius of the circle.
Let ^@D(10,9), E(7,11),^@ and ^@F(11,15)^@ be the mid points of the sides ^@BC, CA,^@ and ^@AB^@ respectively of a ^@\Delta{ABC}^@. Then, find the coordinates of the vertex ^@A^@.
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 building 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 building. (Assume π =
Laura and Deborah each have a bag that contains one ball each of the colors yellow, blue, pink, black and green. Laura randomly selects a ball from her bag and puts it in Deborah's bag. Then Deborah randomly selects a ball from her bag and puts it in Laura's bag. What is the probability that after this the contents of the bag are the same as before?
In the following diagram rectangle represents men, triangle represents teachers, circle represents rural and square represents sports persons. Find number of men who are rural.
Australia
