In the given figure, ^@\Delta AHK^@ is similar to ^@\Delta ABC^@. ^@AK = 8.5 \space cm^@, ^@BC = 3.5 \space cm^@ and ^@HK = 14 \space cm^@. What is the length of ^@AC^@ ?
In the given figure, ^@ PQ ^@ is a chord of a circle with centre ^@ O ^@ and ^@ PT ^@ is a tangent at point ^@ P ^@. If ^@\angle QPT ^@ = ^@ 41^\circ ^@, find ^@ \angle PRQ ^@.
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 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 } { 4 } \space cm^@, find the length of the wire.
Solve the following system of linear equations by using the method of elimination by equating the coefficients.
@^\begin{aligned}
& \dfrac { x } { 5 } - \dfrac { y } { 3 } = -4 \\
& \dfrac { x } { 2 } - \dfrac { y } { 6 } = 26
\end{aligned}@^
In this diagram, the triangle represents women, the square represents engineers and the circle represents sports persons. Find the number of men who are engineers and sports persons.