A piece of wire is used to make circles of the following pattern.
The radius of the first circle is ^@r \space cm^@ and it is increased by ^@1 \space cm^@ successively. Find the length of the wire that is required to make ^@5^@ such circles.
Point ^@P^@ divides the line segment joining the points ^@A(10, 25)^@ and ^@B(15, 20)^@ such that ^@AP = \dfrac{ 2 }{ 5 } AB^@. If ^@ P ^@ lies on the line ^@2x - y + k = 0^@, find the value of ^@k^@.
A man in a boat rowing away from a lighthouse ^@ 147 \space m^@ high takes ^@ 6 \space minutes ^@ to change the angle of elevation of the top of the lighthouse from ^@ 60^\circ ^@ to ^@ 30^\circ ^@. Find the speed of the boat.
The radii of two circles are ^@12 \space cm^@ and ^@16 \space cm^@ respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.
A solid metallic right circular cone ^@24 \space cm^@ high and whose vertical angle is ^@120^\circ^@ is cut into two parts at the middle point of its height by a plane parallel to the base. If the frustum, so obtained, be drawn into a wire of diameter ^@\dfrac { 1 } { 6 } \space cm^@, find the length of the wire.
According to a meteorological report for ^@ 350 ^@ consecutive days in a year, its weather forecasts were correct ^@ 112 ^@ times.
Out of these days, one day is chosen at random.
What is the probability that the weather forecast was not correct on that day?
From a point ^@ P ^@ outside a circle with center ^@ O ^@, tangents ^@ PA ^@ and ^@ PB ^@ are drawn to the circle. The line segment formed by joining the points ^@ A ^@ and ^@ B ^@ intersect the line segment ^@ OP ^@ at ^@ M ^@. What is the measure of ^@ \angle BMP ^@ ?
Faces of a cube are marked with A,B,C,D,E and F. Two views of the cube are as shown below, if face B is opposite to face D, what will be there on the face opposite to face F?
Following chart shows number of students in a school who got distinction in one of three subjects. Find the number of students who got distinction in exactly two subjects.
USA
