From a rope ^@11^@ m long, two pieces of lengths ^@ \dfrac{ 10 } { 6 } ^@ m and ^@ \dfrac{ 15 } { 7 } ^@ m are cut off. What is the length of the remaining rope?
Two sides ^@AB^@ and ^@BC,^@ and the median ^@AD^@ of ^@ \triangle ABC^@ are correspondingly equal to the two sides ^@PQ^@ and ^@QR,^@ and the median ^@PM^@ of ^@\triangle PQR.^@ If ^@AB = 13 \space cm, AD = 7 \space cm,^@ and ^@AC = 8 \space cm,^@ then the length of ^@ PR^@ is:
In a triangle, ABC, P, Q and R are the midpoints of sides BC, CA, and AB respectively. If AC = 20 cm, BC = 28 cm and AB = 25 cm, find the perimeter of the quadrilateral ARPQ.
The area of a trapezium is 456 cm2 and the distance between its parallel sides is 24 cm. If one of the parallel sides is of length 20 cm, find the length of the other side.
The numbers 1 to 7 are written on 7 pieces of paper and dropped into a box. Three of them are drawn at random. What is the probability that the three pieces of paper picked have numbers that are in arithmetic progression?
Two candles have different lengths and thickness. The shorter lasts 7 hours and the longer 4 hours when both are lit simultaneously. If after 2 hours of their being lit together at the same time, both have the same length, then find the ratio of their original lengths.
At what point does the line represented by the equation 3x + 2y = 32 intersects a line which is parallel to the y-axis, and at a distance 4 units from the origin and in the positive direction of the x-axis.
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