A train covered a certain distance at a uniform speed. If the train would have been ^@3 \space km/hr^@ faster, it would have taken ^@5 \space hours^@ less than the scheduled time. And if the train was slower by ^@3 \space km/hr^@, it would have taken ^@6 \space hours^@ more than the scheduled time. Find the distance covered by the train.
If the sum of the first ^@ p ^@ terms of an AP is the same as the sum of its first ^@ q ^@ terms (where ^@ p \ne q ^@) then what is the sum of its first ^@(p + q)^@ terms?
^@ D^@, ^@E^@ and ^@F^@ are respectively the midpoints of sides ^@AB^@, ^@BC^@ and ^@CA^@ of ^@\Delta ABC^@. Find the ratio of the areas of ^@\Delta DEF^@ and ^@\Delta ABC^@.
In the given figure, a circle is inscribed in a ^@ \triangle PQR.^@ ^@ PQ = 7 \space cm, QR = 5 \space cm, ^@ and ^@ PR = 9 \space cm.^@ What is the length of ^@RM^@ ?
Find the difference between the area of a regular hexagonal plot each of whose side is ^@ 48 \space m ^@ and the area of the circular swimming tank inscribed in it. ^@ \bigg[π = \dfrac { 22 } { 7 } \text { and } \sqrt { 3 } = 1.732 \bigg]^@
Afzal filled a glass with milk. The lower base radius and the upper base radius of the glass is ^@6 \space cm^@ and ^@10 \space cm^@ respectively. The height of the glass is ^@ 15 \space cm^@. At first, the glass is filled full with milk and the milk is poured into another container which is cylindrical in shape with the diameter and the height as ^@ 28 \space cm ^@ and ^@ 17 \space cm ^@ respectively. Again the glass is filled one-fourth with milk and then this milk is poured into the same cylindrical container. How much more milk is to be put into the cylindrical container so as to fill the container up to the brim? (Where ^@\pi = 3.14^@)
In the adjoining figure, ^@ S ^@ and ^@ T ^@ are points on the sides ^@PQ ^@ and ^@ PR ^@ respectively of ^@ \Delta PQR ^@ such that ^@ PT = 5 \space cm^@, ^@TR = 10 \space cm^@ and ^@ ST ^@ is parallel to ^@ QR ^@. Find the ratio of the areas of ^@ \Delta PST ^@ and ^@ \Delta PQR ^@.
Pakistan
